diff --git a/.cirrus.yml b/.cirrus.yml
index 0b904a4e38..12e9870340 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -176,7 +176,7 @@ task:
     CTIMETESTS: no
   matrix:
     - env: {}
-    - env: {EXPERIMENTAL: yes, ASM: arm}
+    - env: {EXPERIMENTAL: yes, ASM: arm32}
   << : *MERGE_BASE
   test_script:
     - ./ci/cirrus.sh
@@ -397,13 +397,13 @@ task:
     - PowerShell -NoLogo -Command if ($env:CIRRUS_PR -ne $null) { git fetch $env:CIRRUS_REPO_CLONE_URL pull/$env:CIRRUS_PR/merge; git reset --hard FETCH_HEAD; }
   configure_script:
     - '%x64_NATIVE_TOOLS%'
-    - cmake -G "Visual Studio 17 2022" -A x64 -S . -B build -DSECP256K1_ENABLE_MODULE_RECOVERY=ON -DSECP256K1_BUILD_EXAMPLES=ON
+    - cmake -E env CFLAGS="/WX" cmake -G "Visual Studio 17 2022" -A x64 -S . -B build -DSECP256K1_ENABLE_MODULE_RECOVERY=ON -DSECP256K1_BUILD_EXAMPLES=ON
   build_script:
     - '%x64_NATIVE_TOOLS%'
     - cmake --build build --config RelWithDebInfo -- -property:UseMultiToolTask=true;CL_MPcount=5
   check_script:
     - '%x64_NATIVE_TOOLS%'
-    - ctest --test-dir build -j 5
+    - ctest -C RelWithDebInfo --test-dir build -j 5
     - build\src\RelWithDebInfo\bench_ecmult.exe
     - build\src\RelWithDebInfo\bench_internal.exe
     - build\src\RelWithDebInfo\bench.exe
diff --git a/.gitignore b/.gitignore
index 53818a6ffd..c1968c0195 100644
--- a/.gitignore
+++ b/.gitignore
@@ -60,5 +60,7 @@ build-aux/compile
 build-aux/test-driver
 libsecp256k1.pc
 
+### CMake
+/CMakeUserPresets.json
 # Default CMake build directory.
 /build
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6d23662a93..6c5dbb843a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,7 +5,24 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
-## [Unreleased]
+## [0.3.2] - 2023-05-13
+We strongly recommend updating to 0.3.2 if you use or plan to use GCC >=13 to compile libsecp256k1. When in doubt, check the GCC version using `gcc -v`.
+
+#### Security
+ - Module `ecdh`: Fix "constant-timeness" issue with GCC 13.1 (and potentially future versions of GCC) that could leave applications using libsecp256k1's ECDH module vulnerable to a timing side-channel attack. The fix avoids secret-dependent control flow during ECDH computations when libsecp256k1 is compiled with GCC 13.1.
+
+#### Fixed
+ - Fixed an old bug that permitted compilers to potentially output bad assembly code on x86_64. In theory, it could lead to a crash or a read of unrelated memory, but this has never been observed on any compilers so far.
+
+#### Changed
+ - Various improvements and changes to CMake builds. CMake builds remain experimental.
+   - Made API versioning consistent with GNU Autotools builds.
+   - Switched to `BUILD_SHARED_LIBS` variable for controlling whether to build a static or a shared library.
+   - Added `SECP256K1_INSTALL` variable for the controlling whether to install the build artefacts.
+ - Renamed asm build option `arm` to `arm32`. Use `--with-asm=arm32` instead of `--with-asm=arm` (GNU Autotools), and `-DSECP256K1_ASM=arm32` instead of `-DSECP256K1_ASM=arm` (CMake).
+
+#### ABI Compatibility
+The ABI is compatible with versions 0.3.0 and 0.3.1.
 
 ## [0.3.1] - 2023-04-10
 We strongly recommend updating to 0.3.1 if you use or plan to use Clang >=14 to compile libsecp256k1, e.g., Xcode >=14 on macOS has Clang >=14. When in doubt, check the Clang version using `clang -v`.
@@ -68,7 +85,8 @@ This version was in fact never released.
 The number was given by the build system since the introduction of autotools in Jan 2014 (ea0fe5a5bf0c04f9cc955b2966b614f5f378c6f6).
 Therefore, this version number does not uniquely identify a set of source files.
 
-[unreleased]: https://github.com/bitcoin-core/secp256k1/compare/v0.3.1...HEAD
+[unreleased]: https://github.com/bitcoin-core/secp256k1/compare/v0.3.2...HEAD
+[0.3.2]: https://github.com/bitcoin-core/secp256k1/compare/v0.3.1...v0.3.2
 [0.3.1]: https://github.com/bitcoin-core/secp256k1/compare/v0.3.0...v0.3.1
 [0.3.0]: https://github.com/bitcoin-core/secp256k1/compare/v0.2.0...v0.3.0
 [0.2.0]: https://github.com/bitcoin-core/secp256k1/compare/423b6d19d373f1224fd671a982584d7e7900bc93..v0.2.0
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 21201f9851..01df73b290 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,16 +1,33 @@
 cmake_minimum_required(VERSION 3.13)
 
-if(CMAKE_VERSION VERSION_GREATER 3.14)
+if(CMAKE_VERSION VERSION_GREATER_EQUAL 3.15)
   # MSVC runtime library flags are selected by the CMAKE_MSVC_RUNTIME_LIBRARY abstraction.
   cmake_policy(SET CMP0091 NEW)
   # MSVC warning flags are not in CMAKE_<LANG>_FLAGS by default.
   cmake_policy(SET CMP0092 NEW)
 endif()
 
-# The package (a.k.a. release) version is based on semantic versioning 2.0.0 of
-# the API. All changes in experimental modules are treated as
-# backwards-compatible and therefore at most increase the minor version.
-project(libsecp256k1 VERSION 0.3.2.1 LANGUAGES C) # FROST_SPECIFIC: the fourth number must be equal to the value of _PKG_VERSION_FROST_BUILD in configure.ac
+project(libsecp256k1
+  # The package (a.k.a. release) version is based on semantic versioning 2.0.0 of
+  # the API. All changes in experimental modules are treated as
+  # backwards-compatible and therefore at most increase the minor version.
+  VERSION 0.3.2.1 # FROST_SPECIFIC: the fourth number must be equal to the value of _PKG_VERSION_FROST_BUILD in configure.ac
+  DESCRIPTION "Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1."
+  HOMEPAGE_URL "https://github.com/bancaditalia/secp256k1-frost" # FROST_SPECIFIC: replaced URIs with those of Bank of Italy's fork.
+  LANGUAGES C
+)
+
+if(CMAKE_VERSION VERSION_LESS 3.21)
+  get_directory_property(parent_directory PARENT_DIRECTORY)
+  if(parent_directory)
+    set(PROJECT_IS_TOP_LEVEL OFF CACHE INTERNAL "Emulates CMake 3.21+ behavior.")
+    set(${PROJECT_NAME}_IS_TOP_LEVEL OFF CACHE INTERNAL "Emulates CMake 3.21+ behavior.")
+  else()
+    set(PROJECT_IS_TOP_LEVEL ON CACHE INTERNAL "Emulates CMake 3.21+ behavior.")
+    set(${PROJECT_NAME}_IS_TOP_LEVEL ON CACHE INTERNAL "Emulates CMake 3.21+ behavior.")
+  endif()
+  unset(parent_directory)
+endif()
 
 # The library version is based on libtool versioning of the ABI. The set of
 # rules for updating the version can be found here:
@@ -26,36 +43,37 @@ set(CMAKE_C_EXTENSIONS OFF)
 
 list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
 
-# We do not use CMake's BUILD_SHARED_LIBS option.
-option(SECP256K1_BUILD_SHARED "Build shared library." ON)
-option(SECP256K1_BUILD_STATIC "Build static library." ON)
-if(NOT SECP256K1_BUILD_SHARED AND NOT SECP256K1_BUILD_STATIC)
-  message(FATAL_ERROR "At least one of SECP256K1_BUILD_SHARED and SECP256K1_BUILD_STATIC must be enabled.")
+option(BUILD_SHARED_LIBS "Build shared libraries." ON)
+option(SECP256K1_DISABLE_SHARED "Disable shared library. Overrides BUILD_SHARED_LIBS." OFF)
+if(SECP256K1_DISABLE_SHARED)
+  set(BUILD_SHARED_LIBS OFF)
 endif()
 
+option(SECP256K1_INSTALL "Enable installation." ${PROJECT_IS_TOP_LEVEL})
+
 option(SECP256K1_ENABLE_MODULE_ECDH "Enable ECDH module." ON)
 if(SECP256K1_ENABLE_MODULE_ECDH)
-  add_definitions(-DENABLE_MODULE_ECDH=1)
+  add_compile_definitions(ENABLE_MODULE_ECDH=1)
 endif()
 
 option(SECP256K1_ENABLE_MODULE_RECOVERY "Enable ECDSA pubkey recovery module." OFF)
 if(SECP256K1_ENABLE_MODULE_RECOVERY)
-  add_definitions(-DENABLE_MODULE_RECOVERY=1)
+  add_compile_definitions(ENABLE_MODULE_RECOVERY=1)
 endif()
 
 option(SECP256K1_ENABLE_MODULE_EXTRAKEYS "Enable extrakeys module." ON)
 option(SECP256K1_ENABLE_MODULE_SCHNORRSIG "Enable schnorrsig module." ON)
 if(SECP256K1_ENABLE_MODULE_SCHNORRSIG)
   set(SECP256K1_ENABLE_MODULE_EXTRAKEYS ON)
-  add_definitions(-DENABLE_MODULE_SCHNORRSIG=1)
+  add_compile_definitions(ENABLE_MODULE_SCHNORRSIG=1)
 endif()
 if(SECP256K1_ENABLE_MODULE_EXTRAKEYS)
-  add_definitions(-DENABLE_MODULE_EXTRAKEYS=1)
+  add_compile_definitions(ENABLE_MODULE_EXTRAKEYS=1)
 endif()
 
 option(SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS "Enable external default callback functions." OFF)
 if(SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS)
-  add_definitions(-DUSE_EXTERNAL_DEFAULT_CALLBACKS=1)
+  add_compile_definitions(USE_EXTERNAL_DEFAULT_CALLBACKS=1)
 endif()
 
 set(SECP256K1_ECMULT_WINDOW_SIZE "AUTO" CACHE STRING "Window size for ecmult precomputation for verification, specified as integer in range [2..24]. \"AUTO\" is a reasonable setting for desktop machines (currently 15). [default=AUTO]")
@@ -65,7 +83,7 @@ check_string_option_value(SECP256K1_ECMULT_WINDOW_SIZE)
 if(SECP256K1_ECMULT_WINDOW_SIZE STREQUAL "AUTO")
   set(SECP256K1_ECMULT_WINDOW_SIZE 15)
 endif()
-add_definitions(-DECMULT_WINDOW_SIZE=${SECP256K1_ECMULT_WINDOW_SIZE})
+add_compile_definitions(ECMULT_WINDOW_SIZE=${SECP256K1_ECMULT_WINDOW_SIZE})
 
 set(SECP256K1_ECMULT_GEN_PREC_BITS "AUTO" CACHE STRING "Precision bits to tune the precomputed table size for signing, specified as integer 2, 4 or 8. \"AUTO\" is a reasonable setting for desktop machines (currently 4). [default=AUTO]")
 set_property(CACHE SECP256K1_ECMULT_GEN_PREC_BITS PROPERTY STRINGS "AUTO" 2 4 8)
@@ -73,29 +91,35 @@ check_string_option_value(SECP256K1_ECMULT_GEN_PREC_BITS)
 if(SECP256K1_ECMULT_GEN_PREC_BITS STREQUAL "AUTO")
   set(SECP256K1_ECMULT_GEN_PREC_BITS 4)
 endif()
-add_definitions(-DECMULT_GEN_PREC_BITS=${SECP256K1_ECMULT_GEN_PREC_BITS})
+add_compile_definitions(ECMULT_GEN_PREC_BITS=${SECP256K1_ECMULT_GEN_PREC_BITS})
 
 set(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY "OFF" CACHE STRING "Test-only override of the (autodetected by the C code) \"widemul\" setting. Legal values are: \"OFF\", \"int128_struct\", \"int128\" or \"int64\". [default=OFF]")
 set_property(CACHE SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY PROPERTY STRINGS "OFF" "int128_struct" "int128" "int64")
 check_string_option_value(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY)
 if(SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY)
   string(TOUPPER "${SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY}" widemul_upper_value)
-  add_definitions(-DUSE_FORCE_WIDEMUL_${widemul_upper_value}=1)
+  add_compile_definitions(USE_FORCE_WIDEMUL_${widemul_upper_value}=1)
 endif()
 mark_as_advanced(FORCE SECP256K1_TEST_OVERRIDE_WIDE_MULTIPLY)
 
-set(SECP256K1_ASM "AUTO" CACHE STRING "Assembly optimizations to use: \"AUTO\", \"OFF\", \"x86_64\" or \"arm\" (experimental). [default=AUTO]")
-set_property(CACHE SECP256K1_ASM PROPERTY STRINGS "AUTO" "OFF" "x86_64" "arm")
+set(SECP256K1_ASM "AUTO" CACHE STRING "Assembly optimizations to use: \"AUTO\", \"OFF\", \"x86_64\" or \"arm32\" (experimental). [default=AUTO]")
+set_property(CACHE SECP256K1_ASM PROPERTY STRINGS "AUTO" "OFF" "x86_64" "arm32")
 check_string_option_value(SECP256K1_ASM)
-if(SECP256K1_ASM STREQUAL "arm")
+if(SECP256K1_ASM STREQUAL "arm32")
   enable_language(ASM)
-  add_definitions(-DUSE_EXTERNAL_ASM=1)
+  include(CheckArm32Assembly)
+  check_arm32_assembly()
+  if(HAVE_ARM32_ASM)
+    add_compile_definitions(USE_EXTERNAL_ASM=1)
+  else()
+    message(FATAL_ERROR "ARM32 assembly optimization requested but not available.")
+  endif()
 elseif(SECP256K1_ASM)
-  include(Check64bitAssembly)
-  check_64bit_assembly()
-  if(HAS_64BIT_ASM)
+  include(CheckX86_64Assembly)
+  check_x86_64_assembly()
+  if(HAVE_X86_64_ASM)
     set(SECP256K1_ASM "x86_64")
-    add_definitions(-DUSE_ASM_X86_64=1)
+    add_compile_definitions(USE_ASM_X86_64=1)
   elseif(SECP256K1_ASM STREQUAL "AUTO")
     set(SECP256K1_ASM "OFF")
   else()
@@ -105,8 +129,8 @@ endif()
 
 option(SECP256K1_EXPERIMENTAL "Allow experimental configuration options." OFF)
 if(NOT SECP256K1_EXPERIMENTAL)
-  if(SECP256K1_ASM STREQUAL "arm")
-    message(FATAL_ERROR "ARM assembly optimization is experimental. Use -DSECP256K1_EXPERIMENTAL=ON to allow.")
+  if(SECP256K1_ASM STREQUAL "arm32")
+    message(FATAL_ERROR "ARM32 assembly optimization is experimental. Use -DSECP256K1_EXPERIMENTAL=ON to allow.")
   endif()
 endif()
 
@@ -129,7 +153,7 @@ if(SECP256K1_VALGRIND)
   if(Valgrind_FOUND)
     set(SECP256K1_VALGRIND ON)
     include_directories(${Valgrind_INCLUDE_DIR})
-    add_definitions(-DVALGRIND)
+    add_compile_definitions(VALGRIND)
   elseif(SECP256K1_VALGRIND STREQUAL "AUTO")
     set(SECP256K1_VALGRIND OFF)
   else()
@@ -176,42 +200,47 @@ mark_as_advanced(
   CMAKE_SHARED_LINKER_FLAGS_COVERAGE
 )
 
-if(CMAKE_CONFIGURATION_TYPES)
-  set(CMAKE_CONFIGURATION_TYPES "RelWithDebInfo" "Release" "Debug" "MinSizeRel" "Coverage")
-endif()
-
-get_property(cached_cmake_build_type CACHE CMAKE_BUILD_TYPE PROPERTY TYPE)
-if(cached_cmake_build_type)
+get_property(is_multi_config GLOBAL PROPERTY GENERATOR_IS_MULTI_CONFIG)
+set(default_build_type "RelWithDebInfo")
+if(is_multi_config)
+  set(CMAKE_CONFIGURATION_TYPES "${default_build_type}" "Release" "Debug" "MinSizeRel" "Coverage" CACHE STRING
+    "Supported configuration types."
+    FORCE
+  )
+else()
   set_property(CACHE CMAKE_BUILD_TYPE PROPERTY
-    STRINGS "RelWithDebInfo" "Release" "Debug" "MinSizeRel" "Coverage"
+    STRINGS "${default_build_type}" "Release" "Debug" "MinSizeRel" "Coverage"
   )
+  if(NOT CMAKE_BUILD_TYPE)
+    message(STATUS "Setting build type to \"${default_build_type}\" as none was specified")
+    set(CMAKE_BUILD_TYPE "${default_build_type}" CACHE STRING
+      "Choose the type of build."
+      FORCE
+    )
+  endif()
 endif()
 
-set(default_build_type "RelWithDebInfo")
-if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
-  message(STATUS "Setting build type to \"${default_build_type}\" as none was specified")
-  set(CMAKE_BUILD_TYPE "${default_build_type}" CACHE STRING "Choose the type of build." FORCE)
-endif()
-
-include(TryAddCompileOption)
+include(TryAppendCFlags)
 if(MSVC)
-  try_add_compile_option(/W2)
-  try_add_compile_option(/wd4146)
+  # Keep the following commands ordered lexicographically.
+  try_append_c_flags(/W2) # Moderate warning level.
+  try_append_c_flags(/wd4146) # Disable warning C4146 "unary minus operator applied to unsigned type, result still unsigned".
 else()
-  try_add_compile_option(-pedantic)
-  try_add_compile_option(-Wall)
-  try_add_compile_option(-Wcast-align)
-  try_add_compile_option(-Wcast-align=strict)
-  try_add_compile_option(-Wconditional-uninitialized)
-  try_add_compile_option(-Wextra)
-  try_add_compile_option(-Wnested-externs)
-  try_add_compile_option(-Wno-long-long)
-  try_add_compile_option(-Wno-overlength-strings)
-  try_add_compile_option(-Wno-unused-function)
-  try_add_compile_option(-Wreserved-identifier)
-  try_add_compile_option(-Wshadow)
-  try_add_compile_option(-Wstrict-prototypes)
-  try_add_compile_option(-Wundef)
+  # Keep the following commands ordered lexicographically.
+  try_append_c_flags(-pedantic)
+  try_append_c_flags(-Wall) # GCC >= 2.95 and probably many other compilers.
+  try_append_c_flags(-Wcast-align) # GCC >= 2.95.
+  try_append_c_flags(-Wcast-align=strict) # GCC >= 8.0.
+  try_append_c_flags(-Wconditional-uninitialized) # Clang >= 3.0 only.
+  try_append_c_flags(-Wextra) # GCC >= 3.4, this is the newer name of -W, which we don't use because older GCCs will warn about unused functions.
+  try_append_c_flags(-Wnested-externs)
+  try_append_c_flags(-Wno-long-long) # GCC >= 3.0, -Wlong-long is implied by -pedantic.
+  try_append_c_flags(-Wno-overlength-strings) # GCC >= 4.2, -Woverlength-strings is implied by -pedantic.
+  try_append_c_flags(-Wno-unused-function) # GCC >= 3.0, -Wunused-function is implied by -Wall.
+  try_append_c_flags(-Wreserved-identifier) # Clang >= 13.0 only.
+  try_append_c_flags(-Wshadow)
+  try_append_c_flags(-Wstrict-prototypes)
+  try_append_c_flags(-Wundef)
 endif()
 
 set(CMAKE_C_VISIBILITY_PRESET hidden)
@@ -236,8 +265,13 @@ message("\n")
 message("secp256k1 configure summary")
 message("===========================")
 message("Build artifacts:")
-message("  shared library ...................... ${SECP256K1_BUILD_SHARED}")
-message("  static library ...................... ${SECP256K1_BUILD_STATIC}")
+if(BUILD_SHARED_LIBS)
+  set(library_type "Shared")
+else()
+  set(library_type "Static")
+endif()
+
+message("  library type ........................ ${library_type}")
 message("Optional modules:")
 message("  ECDH ................................ ${SECP256K1_ENABLE_MODULE_ECDH}")
 message("  ECDSA pubkey recovery ............... ${SECP256K1_ENABLE_MODULE_RECOVERY}")
@@ -282,7 +316,7 @@ message("CFLAGS ................................ ${CMAKE_C_FLAGS}")
 get_directory_property(compile_options COMPILE_OPTIONS)
 string(REPLACE ";" " " compile_options "${compile_options}")
 message("Compile options ....................... " ${compile_options})
-if(DEFINED CMAKE_BUILD_TYPE)
+if(NOT is_multi_config)
   message("Build type:")
   message(" - CMAKE_BUILD_TYPE ................... ${CMAKE_BUILD_TYPE}")
   string(TOUPPER "${CMAKE_BUILD_TYPE}" build_type)
@@ -290,7 +324,7 @@ if(DEFINED CMAKE_BUILD_TYPE)
   message(" - LDFLAGS for executables ............ ${CMAKE_EXE_LINKER_FLAGS_${build_type}}")
   message(" - LDFLAGS for shared libraries ....... ${CMAKE_SHARED_LINKER_FLAGS_${build_type}}")
 else()
-  message("Available configurations .............. ${CMAKE_CONFIGURATION_TYPES}")
+  message("Supported configurations .............. ${CMAKE_CONFIGURATION_TYPES}")
   message("RelWithDebInfo configuration:")
   message(" - CFLAGS ............................. ${CMAKE_C_FLAGS_RELWITHDEBINFO}")
   message(" - LDFLAGS for executables ............ ${CMAKE_EXE_LINKER_FLAGS_RELWITHDEBINFO}")
diff --git a/CMakePresets.json b/CMakePresets.json
new file mode 100644
index 0000000000..b35cd80579
--- /dev/null
+++ b/CMakePresets.json
@@ -0,0 +1,19 @@
+{
+  "cmakeMinimumRequired": {"major": 3, "minor": 21, "patch": 0}, 
+  "version": 3,
+  "configurePresets": [
+    {
+      "name": "dev-mode",
+      "displayName": "Development mode (intended only for developers of the library)",
+      "cacheVariables": {
+        "SECP256K1_EXPERIMENTAL": "ON",
+        "SECP256K1_ENABLE_MODULE_RECOVERY": "ON",
+        "SECP256K1_BUILD_EXAMPLES": "ON"
+      },
+      "warnings": {
+        "dev": true,
+        "uninitialized": true
+      }
+    }
+  ]
+}
diff --git a/Makefile.am b/Makefile.am
index 9a039de71e..2388a19469 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -1,5 +1,3 @@
-.PHONY: clean-precomp precomp
-
 ACLOCAL_AMFLAGS = -I build-aux/m4
 
 # AM_CFLAGS will be automatically prepended to CFLAGS by Automake when compiling some foo
@@ -65,6 +63,7 @@ noinst_HEADERS += src/hash_impl.h
 noinst_HEADERS += src/field.h
 noinst_HEADERS += src/field_impl.h
 noinst_HEADERS += src/bench.h
+noinst_HEADERS += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h
 noinst_HEADERS += contrib/lax_der_parsing.h
 noinst_HEADERS += contrib/lax_der_parsing.c
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
@@ -217,7 +216,7 @@ precompute_ecmult_gen_LDADD = $(COMMON_LIB)
 # otherwise make's decision whether to rebuild them (even in the first
 # build by a normal user) depends on mtimes, and thus is very fragile.
 # This means that rebuilds of the prebuilt files always need to be
-# forced by deleting them, e.g., by invoking `make clean-precomp`.
+# forced by deleting them.
 src/precomputed_ecmult.c:
 	$(MAKE) $(AM_MAKEFLAGS) precompute_ecmult$(EXEEXT)
 	./precompute_ecmult$(EXEEXT)
@@ -232,11 +231,29 @@ precomp: $(PRECOMP)
 # e.g., after `make maintainer-clean`).
 BUILT_SOURCES = $(PRECOMP)
 
-maintainer-clean-local: clean-precomp
-
+.PHONY: clean-precomp
 clean-precomp:
 	rm -f $(PRECOMP)
+maintainer-clean-local: clean-precomp
+
+### Pregenerated test vectors
+### (see the comments in the previous section for detailed rationale)
+TESTVECTORS = src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h
+
+src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h:
+	mkdir -p $(@D)
+	python3 $(top_srcdir)/tools/tests_wycheproof_generate.py $(top_srcdir)/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json > $@
 
+testvectors: $(TESTVECTORS)
+
+BUILT_SOURCES += $(TESTVECTORS)
+
+.PHONY: clean-testvectors
+clean-testvectors:
+	rm -f $(TESTVECTORS)
+maintainer-clean-local: clean-testvectors
+
+### Additional files to distribute
 EXTRA_DIST = autogen.sh CHANGELOG.md SECURITY.md
 EXTRA_DIST += doc/release-process.md doc/safegcd_implementation.md
 EXTRA_DIST += examples/EXAMPLES_COPYING
@@ -246,6 +263,9 @@ EXTRA_DIST += sage/group_prover.sage
 EXTRA_DIST += sage/prove_group_implementations.sage
 EXTRA_DIST += sage/secp256k1_params.sage
 EXTRA_DIST += sage/weierstrass_prover.sage
+EXTRA_DIST += src/wycheproof/WYCHEPROOF_COPYING
+EXTRA_DIST += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json
+EXTRA_DIST += tools/tests_wycheproof_generate.py
 
 if ENABLE_MODULE_ECDH
 include src/modules/ecdh/Makefile.am.include
@@ -268,20 +288,3 @@ if ENABLE_MODULE_FROST
 include src/modules/frost/Makefile.am.include
 endif
 # FROST_SPECIFIC - END
-
-EXTRA_DIST += src/wycheproof/WYCHEPROOF_COPYING
-EXTRA_DIST += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h
-EXTRA_DIST += src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json
-EXTRA_DIST += tools/tests_wycheproof_generate.py
-
-TESTVECTORS = src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h
-
-src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h:
-	python3 tools/tests_wycheproof_generate.py src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.json > $@
-
-testvectors: $(TESTVECTORS)
-
-maintainer-clean-testvectors: clean-testvectors
-
-clean-testvectors:
-	rm -f $(TESTVECTORS)
diff --git a/build-aux/m4/bitcoin_secp.m4 b/build-aux/m4/bitcoin_secp.m4
index 624f5e956e..11adef4f22 100644
--- a/build-aux/m4/bitcoin_secp.m4
+++ b/build-aux/m4/bitcoin_secp.m4
@@ -1,12 +1,31 @@
 dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell.
-AC_DEFUN([SECP_64BIT_ASM_CHECK],[
+AC_DEFUN([SECP_X86_64_ASM_CHECK],[
 AC_MSG_CHECKING(for x86_64 assembly availability)
 AC_LINK_IFELSE([AC_LANG_PROGRAM([[
   #include <stdint.h>]],[[
   uint64_t a = 11, tmp;
   __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
-  ]])],[has_64bit_asm=yes],[has_64bit_asm=no])
-AC_MSG_RESULT([$has_64bit_asm])
+  ]])], [has_x86_64_asm=yes], [has_x86_64_asm=no])
+AC_MSG_RESULT([$has_x86_64_asm])
+])
+
+AC_DEFUN([SECP_ARM32_ASM_CHECK], [
+  AC_MSG_CHECKING(for ARM32 assembly availability)
+  SECP_ARM32_ASM_CHECK_CFLAGS_saved_CFLAGS="$CFLAGS"
+  CFLAGS="-x assembler"
+  AC_LINK_IFELSE([AC_LANG_SOURCE([[
+    .syntax unified
+    .eabi_attribute 24, 1
+    .eabi_attribute 25, 1
+    .text
+    .global main
+    main:
+      ldr r0, =0x002A
+      mov r7, #1
+      swi 0   
+    ]])], [has_arm32_asm=yes], [has_arm32_asm=no])
+  AC_MSG_RESULT([$has_arm32_asm])
+  CFLAGS="$SECP_ARM32_ASM_CHECK_CFLAGS_saved_CFLAGS"
 ])
 
 AC_DEFUN([SECP_VALGRIND_CHECK],[
@@ -21,6 +40,7 @@ if test x"$has_valgrind" != x"yes"; then
     #  error "Valgrind does not support this platform."
     #endif
   ]])], [has_valgrind=yes])
+  CPPFLAGS="$CPPFLAGS_TEMP"
 fi
 AC_MSG_RESULT($has_valgrind)
 ])
diff --git a/cmake/CheckArm32Assembly.cmake b/cmake/CheckArm32Assembly.cmake
new file mode 100644
index 0000000000..15c44b24b0
--- /dev/null
+++ b/cmake/CheckArm32Assembly.cmake
@@ -0,0 +1,6 @@
+function(check_arm32_assembly)
+  try_compile(HAVE_ARM32_ASM
+    ${CMAKE_BINARY_DIR}/check_arm32_assembly
+    SOURCES ${CMAKE_SOURCE_DIR}/cmake/source_arm32.s
+  )
+endfunction()
diff --git a/cmake/CheckStringOptionValue.cmake b/cmake/CheckStringOptionValue.cmake
index bc4d7b5749..5a4d939b9e 100644
--- a/cmake/CheckStringOptionValue.cmake
+++ b/cmake/CheckStringOptionValue.cmake
@@ -1,11 +1,9 @@
 function(check_string_option_value option)
   get_property(expected_values CACHE ${option} PROPERTY STRINGS)
   if(expected_values)
-    foreach(value IN LISTS expected_values)
-      if(value STREQUAL "${${option}}")
-        return()
-      endif()
-    endforeach()
+    if(${option} IN_LIST expected_values)
+      return()
+    endif()
     message(FATAL_ERROR "${option} value is \"${${option}}\", but must be one of ${expected_values}.")
   endif()
   message(AUTHOR_WARNING "The STRINGS property must be set before invoking `check_string_option_value' function.")
diff --git a/cmake/Check64bitAssembly.cmake b/cmake/CheckX86_64Assembly.cmake
similarity index 70%
rename from cmake/Check64bitAssembly.cmake
rename to cmake/CheckX86_64Assembly.cmake
index 3f65887765..ae82cd476e 100644
--- a/cmake/Check64bitAssembly.cmake
+++ b/cmake/CheckX86_64Assembly.cmake
@@ -1,6 +1,6 @@
 include(CheckCSourceCompiles)
 
-function(check_64bit_assembly)
+function(check_x86_64_assembly)
   check_c_source_compiles("
     #include <stdint.h>
 
@@ -9,6 +9,6 @@ function(check_64bit_assembly)
       uint64_t a = 11, tmp;
       __asm__ __volatile__(\"movq $0x100000000,%1; mulq %%rsi\" : \"+a\"(a) : \"S\"(tmp) : \"cc\", \"%rdx\");
     }
-  " HAS_64BIT_ASM)
-  set(HAS_64BIT_ASM ${HAS_64BIT_ASM} PARENT_SCOPE)
+  " HAVE_X86_64_ASM)
+  set(HAVE_X86_64_ASM ${HAVE_X86_64_ASM} PARENT_SCOPE)
 endfunction()
diff --git a/cmake/FindValgrind.cmake b/cmake/FindValgrind.cmake
index f6c1f58649..3af5e691e4 100644
--- a/cmake/FindValgrind.cmake
+++ b/cmake/FindValgrind.cmake
@@ -1,4 +1,4 @@
-if(CMAKE_HOST_SYSTEM_NAME STREQUAL "Darwin")
+if(CMAKE_HOST_APPLE)
   find_program(BREW_COMMAND brew)
   execute_process(
     COMMAND ${BREW_COMMAND} --prefix valgrind
diff --git a/cmake/TryAddCompileOption.cmake b/cmake/TryAddCompileOption.cmake
deleted file mode 100644
index f53c252c2d..0000000000
--- a/cmake/TryAddCompileOption.cmake
+++ /dev/null
@@ -1,23 +0,0 @@
-include(CheckCCompilerFlag)
-
-function(try_add_compile_option option)
-  string(MAKE_C_IDENTIFIER ${option} result)
-  string(TOUPPER ${result} result)
-  set(result "C_SUPPORTS${result}")
-  set(CMAKE_TRY_COMPILE_TARGET_TYPE STATIC_LIBRARY)
-  if(NOT MSVC)
-    set(CMAKE_REQUIRED_FLAGS "-Werror")
-  endif()
-  check_c_compiler_flag(${option} ${result})
-  if(${result})
-    get_property(compile_options
-      DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
-      PROPERTY COMPILE_OPTIONS
-    )
-    list(APPEND compile_options "${option}")
-    set_property(
-      DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
-      PROPERTY COMPILE_OPTIONS "${compile_options}"
-    )
-  endif()
-endfunction()
diff --git a/cmake/TryAppendCFlags.cmake b/cmake/TryAppendCFlags.cmake
new file mode 100644
index 0000000000..1d81a9317a
--- /dev/null
+++ b/cmake/TryAppendCFlags.cmake
@@ -0,0 +1,24 @@
+include(CheckCCompilerFlag)
+
+function(secp256k1_check_c_flags_internal flags output)
+  string(MAKE_C_IDENTIFIER "${flags}" result)
+  string(TOUPPER "${result}" result)
+  set(result "C_SUPPORTS_${result}")
+  if(NOT MSVC)
+    set(CMAKE_REQUIRED_FLAGS "-Werror")
+  endif()
+
+  # This avoids running a linker.
+  set(CMAKE_TRY_COMPILE_TARGET_TYPE STATIC_LIBRARY)
+  check_c_compiler_flag("${flags}" ${result})
+
+  set(${output} ${${result}} PARENT_SCOPE)
+endfunction()
+
+# Append flags to the COMPILE_OPTIONS directory property if CC accepts them.
+macro(try_append_c_flags)
+  secp256k1_check_c_flags_internal("${ARGV}" result)
+  if(result)
+    add_compile_options(${ARGV})
+  endif()
+endmacro()
diff --git a/cmake/source_arm32.s b/cmake/source_arm32.s
new file mode 100644
index 0000000000..d3d9347057
--- /dev/null
+++ b/cmake/source_arm32.s
@@ -0,0 +1,9 @@
+.syntax unified
+.eabi_attribute 24, 1
+.eabi_attribute 25, 1
+.text
+.global main
+main:
+	ldr	r0, =0x002A
+	mov	r7, #1
+	swi	0   
diff --git a/configure.ac b/configure.ac
index 38624d6891..ea5c541f2e 100644
--- a/configure.ac
+++ b/configure.ac
@@ -7,7 +7,7 @@ define(_PKG_VERSION_MAJOR, 0)
 define(_PKG_VERSION_MINOR, 3)
 define(_PKG_VERSION_PATCH, 2)
 define(_PKG_VERSION_FROST_BUILD, 1) # FROST_SPECIFIC: this field controls the final digit in the version identifier "MAJOR.MINOR.BUILD-frost-FROST_BUILD". WARNING: this number should be equal to the fourth digit of project(... VERSION ...) in CMakeLists.txt
-define(_PKG_VERSION_IS_RELEASE, false)
+define(_PKG_VERSION_IS_RELEASE, true)
 
 # The library version is based on libtool versioning of the ABI. The set of
 # rules for updating the version can be found here:
@@ -123,7 +123,6 @@ AC_DEFUN([SECP_TRY_APPEND_DEFAULT_CFLAGS], [
     # Note that "/opt" and "-opt" are equivalent for MSVC; we use "-opt" because "/opt" looks like a path.
     if test x"$GCC" != x"yes" && test x"$build_windows" = x"yes"; then
       SECP_TRY_APPEND_CFLAGS([-W2 -wd4146], $1) # Moderate warning level, disable warning C4146 "unary minus operator applied to unsigned type, result still unsigned"
-      SECP_TRY_APPEND_CFLAGS([-external:anglebrackets -external:W0], $1) # Suppress warnings from #include <...> files
       # We pass -ignore:4217 to the MSVC linker to suppress warning 4217 when
       # importing variables from a statically linked secp256k1.
       # (See the libtool manual, section "Windows DLLs" for background.)
@@ -205,8 +204,8 @@ AC_ARG_ENABLE(external_default_callbacks,
 #  *  and auto (the default).
 AC_ARG_WITH([test-override-wide-multiply], [] ,[set_widemul=$withval], [set_widemul=auto])
 
-AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto],
-[assembly optimizations to use (experimental: arm) [default=auto]])],[req_asm=$withval], [req_asm=auto])
+AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm32|no|auto],
+[assembly optimizations to use (experimental: arm32) [default=auto]])],[req_asm=$withval], [req_asm=auto])
 
 AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto],
 [window size for ecmult precomputation for verification, specified as integer in range [2..24].]
@@ -271,8 +270,8 @@ else
 fi
 
 if test x"$req_asm" = x"auto"; then
-  SECP_64BIT_ASM_CHECK
-  if test x"$has_64bit_asm" = x"yes"; then
+  SECP_X86_64_ASM_CHECK
+  if test x"$has_x86_64_asm" = x"yes"; then
     set_asm=x86_64
   fi
   if test x"$set_asm" = x; then
@@ -282,12 +281,16 @@ else
   set_asm=$req_asm
   case $set_asm in
   x86_64)
-    SECP_64BIT_ASM_CHECK
-    if test x"$has_64bit_asm" != x"yes"; then
+    SECP_X86_64_ASM_CHECK
+    if test x"$has_x86_64_asm" != x"yes"; then
       AC_MSG_ERROR([x86_64 assembly optimization requested but not available])
     fi
     ;;
-  arm)
+  arm32)
+    SECP_ARM32_ASM_CHECK
+    if test x"$has_arm32_asm" != x"yes"; then
+      AC_MSG_ERROR([ARM32 assembly optimization requested but not available])
+    fi
     ;;
   no)
     ;;
@@ -304,7 +307,7 @@ case $set_asm in
 x86_64)
   SECP_CONFIG_DEFINES="$SECP_CONFIG_DEFINES -DUSE_ASM_X86_64=1"
   ;;
-arm)
+arm32)
   enable_external_asm=yes
   ;;
 no)
@@ -434,8 +437,8 @@ else
     AC_MSG_ERROR([frost module is experimental. Use --enable-experimental to allow.])
   fi
   # FROST_SPECIFIC - END
-  if test x"$set_asm" = x"arm"; then
-    AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.])
+  if test x"$set_asm" = x"arm32"; then
+    AC_MSG_ERROR([ARM32 assembly optimization is experimental. Use --enable-experimental to allow.])
   fi
 fi
 
@@ -458,7 +461,7 @@ AM_CONDITIONAL([ENABLE_MODULE_EXTRAKEYS], [test x"$enable_module_extrakeys" = x"
 AM_CONDITIONAL([ENABLE_MODULE_SCHNORRSIG], [test x"$enable_module_schnorrsig" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_FROST], [test x"$enable_module_frost" != x"no"]) # FROST_SPECIFIC
 AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$enable_external_asm" = x"yes"])
-AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"])
+AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm32"])
 AM_CONDITIONAL([BUILD_WINDOWS], [test "$build_windows" = "yes"])
 AC_SUBST(LIB_VERSION_CURRENT, _LIB_VERSION_CURRENT)
 AC_SUBST(LIB_VERSION_REVISION, _LIB_VERSION_REVISION)
diff --git a/doc/release-process.md b/doc/release-process.md
index 70a35f0910..79dc36ecc3 100644
--- a/doc/release-process.md
+++ b/doc/release-process.md
@@ -16,8 +16,10 @@ This process also assumes that there will be no minor releases for old major rel
 
 1. Open a PR to the master branch with a commit (using message `"release: prepare for $MAJOR.$MINOR.$PATCH"`, for example) that
    * finalizes the release notes in [CHANGELOG.md](../CHANGELOG.md) (make sure to include an entry for `### ABI Compatibility`),
-   * updates `_PKG_VERSION_*` and `_LIB_VERSION_*` and sets `_PKG_VERSION_IS_RELEASE` to `true` in `configure.ac`, and
-   * updates `project(libsecp256k1 VERSION ...)` and `${PROJECT_NAME}_LIB_VERSION_*` in `CMakeLists.txt`.
+   * sets `_PKG_VERSION_IS_RELEASE` to `true` in `configure.ac`, and
+   * if this is not a patch release
+       * updates `_PKG_VERSION_*` and `_LIB_VERSION_*`  in `configure.ac` and
+       * updates `project(libsecp256k1 VERSION ...)` and `${PROJECT_NAME}_LIB_VERSION_*` in `CMakeLists.txt`.
 2. After the PR is merged, tag the commit and push it:
    ```
    RELEASE_COMMIT=<merge commit of step 1>
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index f069ad3806..5e5a708ba2 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -2,41 +2,34 @@ add_library(example INTERFACE)
 target_include_directories(example INTERFACE
   ${PROJECT_SOURCE_DIR}/include
 )
-target_compile_options(example INTERFACE
-  $<$<C_COMPILER_ID:MSVC>:/wd4005>
-)
 target_link_libraries(example INTERFACE
+  secp256k1
   $<$<PLATFORM_ID:Windows>:bcrypt>
 )
-if(SECP256K1_BUILD_SHARED)
-  target_link_libraries(example INTERFACE secp256k1)
-elseif(SECP256K1_BUILD_STATIC)
-  target_link_libraries(example INTERFACE secp256k1_static)
-  if(MSVC)
-    target_link_options(example INTERFACE /IGNORE:4217)
-  endif()
+if(NOT BUILD_SHARED_LIBS AND MSVC)
+  target_link_options(example INTERFACE /IGNORE:4217)
 endif()
 
 add_executable(ecdsa_example ecdsa.c)
 target_link_libraries(ecdsa_example example)
-add_test(ecdsa_example ecdsa_example)
+add_test(NAME ecdsa_example COMMAND ecdsa_example)
 
 if(SECP256K1_ENABLE_MODULE_ECDH)
   add_executable(ecdh_example ecdh.c)
   target_link_libraries(ecdh_example example)
-  add_test(ecdh_example ecdh_example)
+  add_test(NAME ecdh_example COMMAND ecdh_example)
 endif()
 
 if(SECP256K1_ENABLE_MODULE_SCHNORRSIG)
   add_executable(schnorr_example schnorr.c)
   target_link_libraries(schnorr_example example)
-  add_test(schnorr_example schnorr_example)
+  add_test(NAME schnorr_example COMMAND schnorr_example)
 endif()
 
 # FROST_SPECIFIC - START
 if(SECP256K1_ENABLE_MODULE_FROST)
   add_executable(frost_example frost.c)
   target_link_libraries(frost_example example)
-  add_test(frost_example frost_example)
+  add_test(NAME frost_example COMMAND frost_example)
 endif()
 # FROST_SPECIFIC - END
\ No newline at end of file
diff --git a/examples/examples_util.h b/examples/examples_util.h
index a52b1fa115..8e3a8f00cf 100644
--- a/examples/examples_util.h
+++ b/examples/examples_util.h
@@ -17,7 +17,13 @@
  */
 
 #if defined(_WIN32)
+/*
+ * The defined WIN32_NO_STATUS macro disables return code definitions in
+ * windows.h, which avoids "macro redefinition" MSVC warnings in ntstatus.h.
+ */
+#define WIN32_NO_STATUS
 #include <windows.h>
+#undef WIN32_NO_STATUS
 #include <ntstatus.h>
 #include <bcrypt.h>
 #elif defined(__linux__) || defined(__APPLE__) || defined(__FreeBSD__)
@@ -77,7 +83,7 @@ static void print_hex(unsigned char* data, size_t size) {
 #include <Windows.h>
 #endif
 /* Cleanses memory to prevent leaking sensitive info. Won't be optimized out. */
-static SECP256K1_INLINE void secure_erase(void *ptr, size_t len) {
+static void secure_erase(void *ptr, size_t len) {
 #if defined(_MSC_VER)
     /* SecureZeroMemory is guaranteed not to be optimized out by MSVC. */
     SecureZeroMemory(ptr, len);
diff --git a/include/secp256k1.h b/include/secp256k1.h
index 4ce3e500ba..a7a2be7a3a 100644
--- a/include/secp256k1.h
+++ b/include/secp256k1.h
@@ -122,18 +122,6 @@ typedef int (*secp256k1_nonce_function)(
 #  endif
 # endif
 
-# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
-#  if SECP256K1_GNUC_PREREQ(2,7)
-#   define SECP256K1_INLINE __inline__
-#  elif (defined(_MSC_VER))
-#   define SECP256K1_INLINE __inline
-#  else
-#   define SECP256K1_INLINE
-#  endif
-# else
-#  define SECP256K1_INLINE inline
-# endif
-
 /*  When this header is used at build-time the SECP256K1_BUILD define needs to be set
  *  to correctly setup export attributes and nullness checks.  This is normally done
  *  by secp256k1.c but to guard against this header being included before secp256k1.c
diff --git a/include/secp256k1_schnorrsig.h b/include/secp256k1_schnorrsig.h
index 733fee5282..1ee665fd19 100644
--- a/include/secp256k1_schnorrsig.h
+++ b/include/secp256k1_schnorrsig.h
@@ -141,12 +141,20 @@ SECP256K1_API int secp256k1_schnorrsig_sign(
  *  variable length messages and accepts a pointer to an extraparams object that
  *  allows customizing signing by passing additional arguments.
  *
- *  Creates the same signatures as schnorrsig_sign if msglen is 32 and the
- *  extraparams.ndata is the same as aux_rand32.
+ *  Equivalent to secp256k1_schnorrsig_sign32(..., aux_rand32) if msglen is 32
+ *  and extraparams is initialized as follows:
+ *  ```
+ *  secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT;
+ *  extraparams.ndata = (unsigned char*)aux_rand32;
+ *  ```
  *
+ *  Returns 1 on success, 0 on failure.
+ *  Args:   ctx: pointer to a context object (not secp256k1_context_static).
+ *  Out:  sig64: pointer to a 64-byte array to store the serialized signature.
  *  In:     msg: the message being signed. Can only be NULL if msglen is 0.
- *       msglen: length of the message
- *  extraparams: pointer to a extraparams object (can be NULL)
+ *       msglen: length of the message.
+ *      keypair: pointer to an initialized keypair.
+ *  extraparams: pointer to an extraparams object (can be NULL).
  */
 SECP256K1_API int secp256k1_schnorrsig_sign_custom(
     const secp256k1_context *ctx,
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 59a1d51425..6020a93229 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -1,156 +1,167 @@
 # Must be included before CMAKE_INSTALL_INCLUDEDIR is used.
 include(GNUInstallDirs)
-set(${PROJECT_NAME}_installables "")
 
-if(SECP256K1_ASM STREQUAL "arm")
-  add_library(common OBJECT
-    asm/field_10x26_arm.s
-  )
-  set(common_obj "$<TARGET_OBJECTS:common>")
-else()
-  set(common_obj "")
-endif()
-
-add_library(precomputed OBJECT
+add_library(secp256k1_precomputed OBJECT EXCLUDE_FROM_ALL
   precomputed_ecmult.c
   precomputed_ecmult_gen.c
 )
-set(internal_obj "$<TARGET_OBJECTS:precomputed>" "${common_obj}")
 
-add_library(secp256k1 SHARED EXCLUDE_FROM_ALL
-  secp256k1.c
-  ${internal_obj}
-)
-target_include_directories(secp256k1 INTERFACE
-  $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}>
-)
-target_compile_definitions(secp256k1 PRIVATE
-  $<$<PLATFORM_ID:Windows>:DLL_EXPORT>
-)
-set_target_properties(secp256k1 PROPERTIES
-  VERSION "${${PROJECT_NAME}_LIB_VERSION_CURRENT}.${${PROJECT_NAME}_LIB_VERSION_AGE}.${${PROJECT_NAME}_LIB_VERSION_REVISION}"
-  SOVERSION "${${PROJECT_NAME}_LIB_VERSION_CURRENT}"
-)
-if(SECP256K1_BUILD_SHARED)
-  get_target_property(use_pic secp256k1 POSITION_INDEPENDENT_CODE)
-  set_target_properties(precomputed PROPERTIES POSITION_INDEPENDENT_CODE ${use_pic})
-  set_target_properties(secp256k1 PROPERTIES EXCLUDE_FROM_ALL FALSE)
-  list(APPEND ${PROJECT_NAME}_installables secp256k1)
-endif()
+# Add objects explicitly rather than linking to the object libs to keep them
+# from being exported.
+add_library(secp256k1 secp256k1.c $<TARGET_OBJECTS:secp256k1_precomputed>)
 
-add_library(secp256k1_static STATIC EXCLUDE_FROM_ALL
-  secp256k1.c
-  ${internal_obj}
-)
-target_include_directories(secp256k1_static INTERFACE
-  $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}>
-)
-if(NOT MSVC)
-  set_target_properties(secp256k1_static PROPERTIES
-    OUTPUT_NAME secp256k1
+add_library(secp256k1_asm INTERFACE)
+if(SECP256K1_ASM STREQUAL "arm32")
+  add_library(secp256k1_asm_arm OBJECT EXCLUDE_FROM_ALL)
+  target_sources(secp256k1_asm_arm PUBLIC
+    asm/field_10x26_arm.s
   )
+  target_sources(secp256k1 PRIVATE $<TARGET_OBJECTS:secp256k1_asm_arm>)
+  target_link_libraries(secp256k1_asm INTERFACE secp256k1_asm_arm)
 endif()
-if(SECP256K1_BUILD_STATIC)
-  set_target_properties(secp256k1_static PROPERTIES EXCLUDE_FROM_ALL FALSE)
-  list(APPEND ${PROJECT_NAME}_installables secp256k1_static)
+
+# Define our export symbol only for Win32 and only for shared libs.
+# This matches libtool's usage of DLL_EXPORT
+if(WIN32)
+  set_target_properties(secp256k1 PROPERTIES DEFINE_SYMBOL "DLL_EXPORT")
 endif()
 
-add_library(binary_interface INTERFACE)
-target_compile_definitions(binary_interface INTERFACE
-  $<$<C_COMPILER_ID:MSVC>:_CRT_SECURE_NO_WARNINGS>
+# Object libs don't know if they're being built for a shared or static lib.
+# Grab the PIC property from secp256k1 which knows.
+get_target_property(use_pic secp256k1 POSITION_INDEPENDENT_CODE)
+set_target_properties(secp256k1_precomputed PROPERTIES POSITION_INDEPENDENT_CODE ${use_pic})
+
+target_include_directories(secp256k1 INTERFACE
+  # Add the include path for parent projects so that they don't have to manually add it.
+  $<BUILD_INTERFACE:$<$<NOT:$<BOOL:${PROJECT_IS_TOP_LEVEL}>>:${PROJECT_SOURCE_DIR}/include>>
+  $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}>
 )
 
-add_library(link_library INTERFACE)
-if(SECP256K1_BUILD_SHARED)
-  target_link_libraries(link_library INTERFACE secp256k1)
-elseif(SECP256K1_BUILD_STATIC)
-  target_link_libraries(link_library INTERFACE secp256k1_static)
+# This emulates Libtool to make sure Libtool and CMake agree on the ABI version,
+# see below "Calculate the version variables" in build-aux/ltmain.sh.
+math(EXPR ${PROJECT_NAME}_soversion "${${PROJECT_NAME}_LIB_VERSION_CURRENT} - ${${PROJECT_NAME}_LIB_VERSION_AGE}")
+set_target_properties(secp256k1 PROPERTIES
+  SOVERSION ${${PROJECT_NAME}_soversion}
+)
+if(CMAKE_SYSTEM_NAME STREQUAL "Linux")
+  set_target_properties(secp256k1 PROPERTIES
+    VERSION ${${PROJECT_NAME}_soversion}.${${PROJECT_NAME}_LIB_VERSION_AGE}.${${PROJECT_NAME}_LIB_VERSION_REVISION}
+  )
+elseif(APPLE)
+  if(CMAKE_VERSION VERSION_GREATER_EQUAL 3.17)
+    math(EXPR ${PROJECT_NAME}_compatibility_version "${${PROJECT_NAME}_LIB_VERSION_CURRENT} + 1")
+    set_target_properties(secp256k1 PROPERTIES
+      MACHO_COMPATIBILITY_VERSION ${${PROJECT_NAME}_compatibility_version}
+      MACHO_CURRENT_VERSION ${${PROJECT_NAME}_compatibility_version}.${${PROJECT_NAME}_LIB_VERSION_REVISION}
+    )
+    unset(${PROJECT_NAME}_compatibility_version)
+  elseif(BUILD_SHARED_LIBS)
+    message(WARNING
+      "The 'compatibility version' and 'current version' values of the DYLIB "
+      "will diverge from the values set by the GNU Libtool. To ensure "
+      "compatibility, it is recommended to upgrade CMake to at least version 3.17."
+    )
+  endif()
+elseif(CMAKE_SYSTEM_NAME STREQUAL "Windows")
+  set(${PROJECT_NAME}_windows "secp256k1")
+  if(MSVC)
+    set(${PROJECT_NAME}_windows "${PROJECT_NAME}")
+  endif()
+  set_target_properties(secp256k1 PROPERTIES
+    ARCHIVE_OUTPUT_NAME "${${PROJECT_NAME}_windows}"
+    RUNTIME_OUTPUT_NAME "${${PROJECT_NAME}_windows}-${${PROJECT_NAME}_soversion}"
+  )
+  unset(${PROJECT_NAME}_windows)
 endif()
+unset(${PROJECT_NAME}_soversion)
 
 if(SECP256K1_BUILD_BENCHMARK)
   add_executable(bench bench.c)
-  target_link_libraries(bench binary_interface link_library)
-  add_executable(bench_internal bench_internal.c ${internal_obj})
-  target_link_libraries(bench_internal binary_interface)
-  add_executable(bench_ecmult bench_ecmult.c ${internal_obj})
-  target_link_libraries(bench_ecmult binary_interface)
+  target_link_libraries(bench secp256k1)
+  add_executable(bench_internal bench_internal.c)
+  target_link_libraries(bench_internal secp256k1_precomputed secp256k1_asm)
+  add_executable(bench_ecmult bench_ecmult.c)
+  target_link_libraries(bench_ecmult secp256k1_precomputed secp256k1_asm)
 endif()
 
 if(SECP256K1_BUILD_TESTS)
-  add_executable(noverify_tests tests.c ${internal_obj})
-  target_link_libraries(noverify_tests binary_interface)
-  add_test(noverify_tests noverify_tests)
+  add_executable(noverify_tests tests.c)
+  target_link_libraries(noverify_tests secp256k1_precomputed secp256k1_asm)
+  add_test(NAME noverify_tests COMMAND noverify_tests)
   if(NOT CMAKE_BUILD_TYPE STREQUAL "Coverage")
-    add_executable(tests tests.c ${internal_obj})
+    add_executable(tests tests.c)
     target_compile_definitions(tests PRIVATE VERIFY)
-    target_link_libraries(tests binary_interface)
-    add_test(tests tests)
+    target_link_libraries(tests secp256k1_precomputed secp256k1_asm)
+    add_test(NAME tests COMMAND tests)
   endif()
 endif()
 
 if(SECP256K1_BUILD_EXHAUSTIVE_TESTS)
-  # Note: do not include $<TARGET_OBJECTS:precomputed> in exhaustive_tests (it uses runtime-generated tables).
-  add_executable(exhaustive_tests tests_exhaustive.c ${common_obj})
+  # Note: do not include secp256k1_precomputed in exhaustive_tests (it uses runtime-generated tables).
+  add_executable(exhaustive_tests tests_exhaustive.c)
+  target_link_libraries(exhaustive_tests secp256k1_asm)
   target_compile_definitions(exhaustive_tests PRIVATE $<$<NOT:$<CONFIG:Coverage>>:VERIFY>)
-  target_link_libraries(exhaustive_tests binary_interface)
-  add_test(exhaustive_tests exhaustive_tests)
+  add_test(NAME exhaustive_tests COMMAND exhaustive_tests)
 endif()
 
 if(SECP256K1_BUILD_CTIME_TESTS)
   add_executable(ctime_tests ctime_tests.c)
-  target_link_libraries(ctime_tests binary_interface link_library)
+  target_link_libraries(ctime_tests secp256k1)
 endif()
 
-install(TARGETS ${${PROJECT_NAME}_installables}
-  EXPORT ${PROJECT_NAME}-targets
-  RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR}
-  LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
-  ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR}
-)
-set(${PROJECT_NAME}_headers
-  "${PROJECT_SOURCE_DIR}/include/secp256k1.h"
-  "${PROJECT_SOURCE_DIR}/include/secp256k1_preallocated.h"
-)
-if(SECP256K1_ENABLE_MODULE_ECDH)
-  list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_ecdh.h")
-endif()
-if(SECP256K1_ENABLE_MODULE_RECOVERY)
-  list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_recovery.h")
-endif()
-if(SECP256K1_ENABLE_MODULE_EXTRAKEYS)
-  list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_extrakeys.h")
-endif()
-if(SECP256K1_ENABLE_MODULE_SCHNORRSIG)
-  list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_schnorrsig.h")
-endif()
-# FROST_SPECIFIC - START
-if(SECP256K1_ENABLE_MODULE_FROST)
+if(SECP256K1_INSTALL)
+  install(TARGETS secp256k1
+    EXPORT ${PROJECT_NAME}-targets
+    RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR}
+    LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
+    ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR}
+  )
+  set(${PROJECT_NAME}_headers
+    "${PROJECT_SOURCE_DIR}/include/secp256k1.h"
+    "${PROJECT_SOURCE_DIR}/include/secp256k1_preallocated.h"
+  )
+  if(SECP256K1_ENABLE_MODULE_ECDH)
+    list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_ecdh.h")
+  endif()
+  if(SECP256K1_ENABLE_MODULE_RECOVERY)
+    list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_recovery.h")
+  endif()
+  if(SECP256K1_ENABLE_MODULE_EXTRAKEYS)
+    list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_extrakeys.h")
+  endif()
+  if(SECP256K1_ENABLE_MODULE_SCHNORRSIG)
+    list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_schnorrsig.h")
+  endif()
+  # FROST_SPECIFIC - START
+  if(SECP256K1_ENABLE_MODULE_FROST)
   list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_frost.h")
-endif()
-# FROST_SPECIFIC - END
-install(FILES ${${PROJECT_NAME}_headers}
-  DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}
-)
+  endif()
+  # FROST_SPECIFIC - END
+  install(FILES ${${PROJECT_NAME}_headers}
+    DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}
+  )
 
-install(EXPORT ${PROJECT_NAME}-targets
-  FILE ${PROJECT_NAME}-targets.cmake
-  NAMESPACE ${PROJECT_NAME}::
-  DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
-)
+  install(EXPORT ${PROJECT_NAME}-targets
+    FILE ${PROJECT_NAME}-targets.cmake
+    NAMESPACE ${PROJECT_NAME}::
+    DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
+  )
 
-include(CMakePackageConfigHelpers)
-configure_package_config_file(
-  ${PROJECT_SOURCE_DIR}/cmake/config.cmake.in
-  ${PROJECT_NAME}-config.cmake
-  INSTALL_DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
-  NO_SET_AND_CHECK_MACRO
-)
-write_basic_package_version_file(${PROJECT_NAME}-config-version.cmake
-  COMPATIBILITY SameMajorVersion
-)
-install(
-  FILES
-    ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config.cmake
-    ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config-version.cmake
-  DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
+  include(CMakePackageConfigHelpers)
+  configure_package_config_file(
+    ${PROJECT_SOURCE_DIR}/cmake/config.cmake.in
+    ${PROJECT_NAME}-config.cmake
+    INSTALL_DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
+    NO_SET_AND_CHECK_MACRO
+  )
+  write_basic_package_version_file(${PROJECT_NAME}-config-version.cmake
+    COMPATIBILITY SameMinorVersion
+  )
+
+  install(
+    FILES
+      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config.cmake
+      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config-version.cmake
+    DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
 )
+endif()
diff --git a/src/bench.c b/src/bench.c
index 833f70718b..9992056871 100644
--- a/src/bench.c
+++ b/src/bench.c
@@ -64,11 +64,11 @@ typedef struct {
     size_t siglen;
     unsigned char pubkey[33];
     size_t pubkeylen;
-} bench_verify_data;
+} bench_data;
 
 static void bench_verify(void* arg, int iters) {
     int i;
-    bench_verify_data* data = (bench_verify_data*)arg;
+    bench_data* data = (bench_data*)arg;
 
     for (i = 0; i < iters; i++) {
         secp256k1_pubkey pubkey;
@@ -85,15 +85,9 @@ static void bench_verify(void* arg, int iters) {
     }
 }
 
-typedef struct {
-    secp256k1_context* ctx;
-    unsigned char msg[32];
-    unsigned char key[32];
-} bench_sign_data;
-
 static void bench_sign_setup(void* arg) {
     int i;
-    bench_sign_data *data = (bench_sign_data*)arg;
+    bench_data *data = (bench_data*)arg;
 
     for (i = 0; i < 32; i++) {
         data->msg[i] = i + 1;
@@ -105,7 +99,7 @@ static void bench_sign_setup(void* arg) {
 
 static void bench_sign_run(void* arg, int iters) {
     int i;
-    bench_sign_data *data = (bench_sign_data*)arg;
+    bench_data *data = (bench_data*)arg;
 
     unsigned char sig[74];
     for (i = 0; i < iters; i++) {
@@ -137,7 +131,7 @@ int main(int argc, char** argv) {
     int i;
     secp256k1_pubkey pubkey;
     secp256k1_ecdsa_signature sig;
-    bench_verify_data data;
+    bench_data data;
 
     int d = argc == 1;
     int default_iters = 20000;
diff --git a/src/bench.h b/src/bench.h
index bf9a932ff4..1564b1a176 100644
--- a/src/bench.h
+++ b/src/bench.h
@@ -15,7 +15,7 @@
 #if (defined(_MSC_VER) && _MSC_VER >= 1900)
 #  include <time.h>
 #else
-#  include "sys/time.h"
+#  include <sys/time.h>
 #endif
 
 static int64_t gettime_i64(void) {
diff --git a/src/bench_ecmult.c b/src/bench_ecmult.c
index 98fb798d82..27d694a703 100644
--- a/src/bench_ecmult.c
+++ b/src/bench_ecmult.c
@@ -113,7 +113,7 @@ static void bench_ecmult_const(void* arg, int iters) {
     int i;
 
     for (i = 0; i < iters; ++i) {
-        secp256k1_ecmult_const(&data->output[i], &data->pubkeys[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS], 256);
+        secp256k1_ecmult_const(&data->output[i], &data->pubkeys[(data->offset1+i) % POINTS], &data->scalars[(data->offset2+i) % POINTS]);
     }
 }
 
diff --git a/src/bench_internal.c b/src/bench_internal.c
index c248ab8ebc..f3686dd289 100644
--- a/src/bench_internal.c
+++ b/src/bench_internal.c
@@ -65,10 +65,10 @@ static void bench_setup(void* arg) {
 
     secp256k1_scalar_set_b32(&data->scalar[0], init[0], NULL);
     secp256k1_scalar_set_b32(&data->scalar[1], init[1], NULL);
-    secp256k1_fe_set_b32(&data->fe[0], init[0]);
-    secp256k1_fe_set_b32(&data->fe[1], init[1]);
-    secp256k1_fe_set_b32(&data->fe[2], init[2]);
-    secp256k1_fe_set_b32(&data->fe[3], init[3]);
+    secp256k1_fe_set_b32_limit(&data->fe[0], init[0]);
+    secp256k1_fe_set_b32_limit(&data->fe[1], init[1]);
+    secp256k1_fe_set_b32_limit(&data->fe[2], init[2]);
+    secp256k1_fe_set_b32_limit(&data->fe[3], init[3]);
     CHECK(secp256k1_ge_set_xo_var(&data->ge[0], &data->fe[0], 0));
     CHECK(secp256k1_ge_set_xo_var(&data->ge[1], &data->fe[1], 1));
     secp256k1_gej_set_ge(&data->gej[0], &data->ge[0]);
diff --git a/src/ecdsa_impl.h b/src/ecdsa_impl.h
index 90b4b22b77..48e30851b5 100644
--- a/src/ecdsa_impl.h
+++ b/src/ecdsa_impl.h
@@ -239,7 +239,8 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar *sigr, const secp25
 }
 #else
     secp256k1_scalar_get_b32(c, sigr);
-    secp256k1_fe_set_b32(&xr, c);
+    /* we can ignore the fe_set_b32_limit return value, because we know the input is in range */
+    (void)secp256k1_fe_set_b32_limit(&xr, c);
 
     /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
      *  in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
diff --git a/src/eckey_impl.h b/src/eckey_impl.h
index e0506d3e2b..b2fe36fe93 100644
--- a/src/eckey_impl.h
+++ b/src/eckey_impl.h
@@ -17,10 +17,10 @@
 static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
     if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) {
         secp256k1_fe x;
-        return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD);
+        return secp256k1_fe_set_b32_limit(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD);
     } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) {
         secp256k1_fe x, y;
-        if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
+        if (!secp256k1_fe_set_b32_limit(&x, pub+1) || !secp256k1_fe_set_b32_limit(&y, pub+33)) {
             return 0;
         }
         secp256k1_ge_set_xy(elem, &x, &y);
diff --git a/src/ecmult_const.h b/src/ecmult_const.h
index 417f328535..080e04bc88 100644
--- a/src/ecmult_const.h
+++ b/src/ecmult_const.h
@@ -11,12 +11,9 @@
 #include "group.h"
 
 /**
- * Multiply: R = q*A (in constant-time)
- * Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus
- * one because we internally sometimes add 2 to the number during the WNAF conversion.
- * A must not be infinity.
+ * Multiply: R = q*A (in constant-time for q)
  */
-static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits);
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
 
 /**
  * Same as secp256k1_ecmult_const, but takes in an x coordinate of the base point
@@ -35,7 +32,6 @@ static int secp256k1_ecmult_const_xonly(
     const secp256k1_fe *n,
     const secp256k1_fe *d,
     const secp256k1_scalar *q,
-    int bits,
     int known_on_curve
 );
 
diff --git a/src/ecmult_const_impl.h b/src/ecmult_const_impl.h
index f23e0ec89d..26b3e238d8 100644
--- a/src/ecmult_const_impl.h
+++ b/src/ecmult_const_impl.h
@@ -29,7 +29,7 @@ static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *p
 #define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
     int m = 0; \
     /* Extract the sign-bit for a constant time absolute-value. */ \
-    int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \
+    int volatile mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \
     int abs_n = ((n) + mask) ^ mask; \
     int idx_n = abs_n >> 1; \
     secp256k1_fe neg_y; \
@@ -130,7 +130,7 @@ static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w
     return skew;
 }
 
-static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
     secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
     secp256k1_ge tmpa;
     secp256k1_fe Z;
@@ -144,20 +144,17 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
 
     int i;
 
-    /* build wnaf representation for q. */
-    int rsize = size;
-    if (size > 128) {
-        rsize = 128;
-        /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
-        secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar);
-        skew_1   = secp256k1_wnaf_const(wnaf_1,   &q_1,   WINDOW_A - 1, 128);
-        skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
-    } else
-    {
-        skew_1   = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size);
-        skew_lam = 0;
+    if (secp256k1_ge_is_infinity(a)) {
+        secp256k1_gej_set_infinity(r);
+        return;
     }
 
+    /* build wnaf representation for q. */
+    /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+    secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar);
+    skew_1   = secp256k1_wnaf_const(wnaf_1,   &q_1,   WINDOW_A - 1, 128);
+    skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
+
     /* Calculate odd multiples of a.
      * All multiples are brought to the same Z 'denominator', which is stored
      * in Z. Due to secp256k1' isomorphism we can do all operations pretending
@@ -170,28 +167,23 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
     for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
         secp256k1_fe_normalize_weak(&pre_a[i].y);
     }
-    if (size > 128) {
-        for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
-            secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
-        }
-
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
     }
 
     /* first loop iteration (separated out so we can directly set r, rather
      * than having it start at infinity, get doubled several times, then have
      * its new value added to it) */
-    i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
+    i = wnaf_1[WNAF_SIZE_BITS(128, WINDOW_A - 1)];
     VERIFY_CHECK(i != 0);
     ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
     secp256k1_gej_set_ge(r, &tmpa);
-    if (size > 128) {
-        i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
-        VERIFY_CHECK(i != 0);
-        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
-        secp256k1_gej_add_ge(r, r, &tmpa);
-    }
+    i = wnaf_lam[WNAF_SIZE_BITS(128, WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+    secp256k1_gej_add_ge(r, r, &tmpa);
     /* remaining loop iterations */
-    for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
+    for (i = WNAF_SIZE_BITS(128, WINDOW_A - 1) - 1; i >= 0; i--) {
         int n;
         int j;
         for (j = 0; j < WINDOW_A - 1; ++j) {
@@ -202,12 +194,10 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
         VERIFY_CHECK(n != 0);
         secp256k1_gej_add_ge(r, r, &tmpa);
-        if (size > 128) {
-            n = wnaf_lam[i];
-            ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
-            VERIFY_CHECK(n != 0);
-            secp256k1_gej_add_ge(r, r, &tmpa);
-        }
+        n = wnaf_lam[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
     }
 
     {
@@ -218,17 +208,15 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         secp256k1_gej_add_ge(&tmpj, r, &tmpa);
         secp256k1_gej_cmov(r, &tmpj, skew_1);
 
-        if (size > 128) {
-            secp256k1_ge_neg(&tmpa, &pre_a_lam[0]);
-            secp256k1_gej_add_ge(&tmpj, r, &tmpa);
-            secp256k1_gej_cmov(r, &tmpj, skew_lam);
-        }
+        secp256k1_ge_neg(&tmpa, &pre_a_lam[0]);
+        secp256k1_gej_add_ge(&tmpj, r, &tmpa);
+        secp256k1_gej_cmov(r, &tmpj, skew_lam);
     }
 
     secp256k1_fe_mul(&r->z, &r->z, &Z);
 }
 
-static int secp256k1_ecmult_const_xonly(secp256k1_fe* r, const secp256k1_fe *n, const secp256k1_fe *d, const secp256k1_scalar *q, int bits, int known_on_curve) {
+static int secp256k1_ecmult_const_xonly(secp256k1_fe* r, const secp256k1_fe *n, const secp256k1_fe *d, const secp256k1_scalar *q, int known_on_curve) {
 
     /* This algorithm is a generalization of Peter Dettman's technique for
      * avoiding the square root in a random-basepoint x-only multiplication
@@ -346,7 +334,7 @@ static int secp256k1_ecmult_const_xonly(secp256k1_fe* r, const secp256k1_fe *n,
 #ifdef VERIFY
     VERIFY_CHECK(!secp256k1_scalar_is_zero(q));
 #endif
-    secp256k1_ecmult_const(&rj, &p, q, bits);
+    secp256k1_ecmult_const(&rj, &p, q);
 #ifdef VERIFY
     VERIFY_CHECK(!secp256k1_gej_is_infinity(&rj));
 #endif
diff --git a/src/ecmult_gen_compute_table_impl.h b/src/ecmult_gen_compute_table_impl.h
index ff6a2992dc..7d672b9950 100644
--- a/src/ecmult_gen_compute_table_impl.h
+++ b/src/ecmult_gen_compute_table_impl.h
@@ -31,7 +31,7 @@ static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, cons
         secp256k1_fe nums_x;
         secp256k1_ge nums_ge;
         int r;
-        r = secp256k1_fe_set_b32(&nums_x, nums_b32);
+        r = secp256k1_fe_set_b32_limit(&nums_x, nums_b32);
         (void)r;
         VERIFY_CHECK(r);
         r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
diff --git a/src/ecmult_gen_impl.h b/src/ecmult_gen_impl.h
index 4f5ea9f3c0..deb0323b7a 100644
--- a/src/ecmult_gen_impl.h
+++ b/src/ecmult_gen_impl.h
@@ -108,7 +108,7 @@ static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const
     memset(keydata, 0, sizeof(keydata));
     /* Accept unobservably small non-uniformity. */
     secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
-    overflow = !secp256k1_fe_set_b32(&s, nonce32);
+    overflow = !secp256k1_fe_set_b32_limit(&s, nonce32);
     overflow |= secp256k1_fe_is_zero(&s);
     secp256k1_fe_cmov(&s, &secp256k1_fe_one, overflow);
     /* Randomize the projection to defend against multiplier sidechannels.
diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h
index a9a63850ef..72fadf6e3a 100644
--- a/src/ecmult_impl.h
+++ b/src/ecmult_impl.h
@@ -279,9 +279,6 @@ static void secp256k1_ecmult_strauss_wnaf(const struct secp256k1_strauss_state *
          */
         tmp = a[np];
         if (no) {
-#ifdef VERIFY
-            secp256k1_fe_normalize_var(&Z);
-#endif
             secp256k1_gej_rescale(&tmp, &Z);
         }
         secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->pre_a + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &Z, &tmp);
@@ -683,7 +680,7 @@ static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_call
     }
     state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps));
     state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int));
-    buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, (1<<bucket_window) * sizeof(*buckets));
+    buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, ((size_t)1 << bucket_window) * sizeof(*buckets));
     if (state_space->ps == NULL || state_space->wnaf_na == NULL || buckets == NULL) {
         secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
         return 0;
diff --git a/src/field.h b/src/field.h
index 64ceead4d2..bbc836b199 100644
--- a/src/field.h
+++ b/src/field.h
@@ -7,19 +7,36 @@
 #ifndef SECP256K1_FIELD_H
 #define SECP256K1_FIELD_H
 
-/** Field element module.
- *
- *  Field elements can be represented in several ways, but code accessing
- *  it (and implementations) need to take certain properties into account:
- *  - Each field element can be normalized or not.
- *  - Each field element has a magnitude, which represents how far away
- *    its representation is away from normalization. Normalized elements
- *    always have a magnitude of 0 or 1, but a magnitude of 1 doesn't
- *    imply normality.
- */
-
 #include "util.h"
 
+/* This file defines the generic interface for working with secp256k1_fe
+ * objects, which represent field elements (integers modulo 2^256 - 2^32 - 977).
+ *
+ * The actual definition of the secp256k1_fe type depends on the chosen field
+ * implementation; see the field_5x52.h and field_10x26.h files for details.
+ *
+ * All secp256k1_fe objects have implicit properties that determine what
+ * operations are permitted on it. These are purely a function of what
+ * secp256k1_fe_ operations are applied on it, generally (implicitly) fixed at
+ * compile time, and do not depend on the chosen field implementation. Despite
+ * that, what these properties actually entail for the field representation
+ * values depends on the chosen field implementation. These properties are:
+ * - magnitude: an integer in [0,32]
+ * - normalized: 0 or 1; normalized=1 implies magnitude <= 1.
+ *
+ * In VERIFY mode, they are materialized explicitly as fields in the struct,
+ * allowing run-time verification of these properties. In that case, the field
+ * implementation also provides a secp256k1_fe_verify routine to verify that
+ * these fields match the run-time value and perform internal consistency
+ * checks. */
+#ifdef VERIFY
+#  define SECP256K1_FE_VERIFY_FIELDS \
+    int magnitude; \
+    int normalized;
+#else
+#  define SECP256K1_FE_VERIFY_FIELDS
+#endif
+
 #if defined(SECP256K1_WIDEMUL_INT128)
 #include "field_5x52.h"
 #elif defined(SECP256K1_WIDEMUL_INT64)
@@ -28,117 +45,295 @@
 #error "Please select wide multiplication implementation"
 #endif
 
+#ifdef VERIFY
+/* Magnitude and normalized value for constants. */
+#define SECP256K1_FE_VERIFY_CONST(d7, d6, d5, d4, d3, d2, d1, d0) \
+    /* Magnitude is 0 for constant 0; 1 otherwise. */ \
+    , (((d7) | (d6) | (d5) | (d4) | (d3) | (d2) | (d1) | (d0)) != 0) \
+    /* Normalized is 1 unless sum(d_i<<(32*i) for i=0..7) exceeds field modulus. */ \
+    , (!(((d7) & (d6) & (d5) & (d4) & (d3) & (d2)) == 0xfffffffful && ((d1) == 0xfffffffful || ((d1) == 0xfffffffe && (d0 >= 0xfffffc2f)))))
+#else
+#define SECP256K1_FE_VERIFY_CONST(d7, d6, d5, d4, d3, d2, d1, d0)
+#endif
+
+/** This expands to an initializer for a secp256k1_fe valued sum((i*32) * d_i, i=0..7) mod p.
+ *
+ * It has magnitude 1, unless d_i are all 0, in which case the magnitude is 0.
+ * It is normalized, unless sum(2^(i*32) * d_i, i=0..7) >= p.
+ *
+ * SECP256K1_FE_CONST_INNER is provided by the implementation.
+ */
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)) SECP256K1_FE_VERIFY_CONST((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)) }
+
 static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
 static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST(
     0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
     0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
 );
 
-/** Normalize a field element. This brings the field element to a canonical representation, reduces
- *  its magnitude to 1, and reduces it modulo field size `p`.
+#ifndef VERIFY
+/* In non-VERIFY mode, we #define the fe operations to be identical to their
+ * internal field implementation, to avoid the potential overhead of a
+ * function call (even though presumably inlinable). */
+#  define secp256k1_fe_normalize secp256k1_fe_impl_normalize
+#  define secp256k1_fe_normalize_weak secp256k1_fe_impl_normalize_weak
+#  define secp256k1_fe_normalize_var secp256k1_fe_impl_normalize_var
+#  define secp256k1_fe_normalizes_to_zero secp256k1_fe_impl_normalizes_to_zero
+#  define secp256k1_fe_normalizes_to_zero_var secp256k1_fe_impl_normalizes_to_zero_var
+#  define secp256k1_fe_set_int secp256k1_fe_impl_set_int
+#  define secp256k1_fe_clear secp256k1_fe_impl_clear
+#  define secp256k1_fe_is_zero secp256k1_fe_impl_is_zero
+#  define secp256k1_fe_is_odd secp256k1_fe_impl_is_odd
+#  define secp256k1_fe_cmp_var secp256k1_fe_impl_cmp_var
+#  define secp256k1_fe_set_b32_mod secp256k1_fe_impl_set_b32_mod
+#  define secp256k1_fe_set_b32_limit secp256k1_fe_impl_set_b32_limit
+#  define secp256k1_fe_get_b32 secp256k1_fe_impl_get_b32
+#  define secp256k1_fe_negate secp256k1_fe_impl_negate
+#  define secp256k1_fe_mul_int secp256k1_fe_impl_mul_int
+#  define secp256k1_fe_add secp256k1_fe_impl_add
+#  define secp256k1_fe_mul secp256k1_fe_impl_mul
+#  define secp256k1_fe_sqr secp256k1_fe_impl_sqr
+#  define secp256k1_fe_cmov secp256k1_fe_impl_cmov
+#  define secp256k1_fe_to_storage secp256k1_fe_impl_to_storage
+#  define secp256k1_fe_from_storage secp256k1_fe_impl_from_storage
+#  define secp256k1_fe_inv secp256k1_fe_impl_inv
+#  define secp256k1_fe_inv_var secp256k1_fe_impl_inv_var
+#  define secp256k1_fe_get_bounds secp256k1_fe_impl_get_bounds
+#  define secp256k1_fe_half secp256k1_fe_impl_half
+#  define secp256k1_fe_add_int secp256k1_fe_impl_add_int
+#  define secp256k1_fe_is_square_var secp256k1_fe_impl_is_square_var
+#endif /* !defined(VERIFY) */
+
+/** Normalize a field element.
+ *
+ * On input, r must be a valid field element.
+ * On output, r represents the same value but has normalized=1 and magnitude=1.
  */
 static void secp256k1_fe_normalize(secp256k1_fe *r);
 
-/** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */
+/** Give a field element magnitude 1.
+ *
+ * On input, r must be a valid field element.
+ * On output, r represents the same value but has magnitude=1. Normalized is unchanged.
+ */
 static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
 
-/** Normalize a field element, without constant-time guarantee. */
+/** Normalize a field element, without constant-time guarantee.
+ *
+ * Identical in behavior to secp256k1_fe_normalize, but not constant time in r.
+ */
 static void secp256k1_fe_normalize_var(secp256k1_fe *r);
 
-/** Verify whether a field element represents zero i.e. would normalize to a zero value. */
+/** Determine whether r represents field element 0.
+ *
+ * On input, r must be a valid field element.
+ * Returns whether r = 0 (mod p).
+ */
 static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r);
 
-/** Verify whether a field element represents zero i.e. would normalize to a zero value,
- *  without constant-time guarantee. */
+/** Determine whether r represents field element 0, without constant-time guarantee.
+ *
+ * Identical in behavior to secp256k1_normalizes_to_zero, but not constant time in r.
+ */
 static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r);
 
-/** Set a field element equal to a small (not greater than 0x7FFF), non-negative integer.
- *  Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise.
+/** Set a field element to an integer in range [0,0x7FFF].
+ *
+ * On input, r does not need to be initialized, a must be in [0,0x7FFF].
+ * On output, r represents value a, is normalized and has magnitude (a!=0).
  */
 static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
 
-/** Sets a field element equal to zero, initializing all fields. */
+/** Set a field element to 0.
+ *
+ * On input, a does not need to be initialized.
+ * On output, a represents 0, is normalized and has magnitude 0.
+ */
 static void secp256k1_fe_clear(secp256k1_fe *a);
 
-/** Verify whether a field element is zero. Requires the input to be normalized. */
+/** Determine whether a represents field element 0.
+ *
+ * On input, a must be a valid normalized field element.
+ * Returns whether a = 0 (mod p).
+ *
+ * This behaves identical to secp256k1_normalizes_to_zero{,_var}, but requires
+ * normalized input (and is much faster).
+ */
 static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 
-/** Check the "oddness" of a field element. Requires the input to be normalized. */
+/** Determine whether a (mod p) is odd.
+ *
+ * On input, a must be a valid normalized field element.
+ * Returns (int(a) mod p) & 1.
+ */
 static int secp256k1_fe_is_odd(const secp256k1_fe *a);
 
-/** Compare two field elements. Requires magnitude-1 inputs. */
+/** Determine whether two field elements are equal.
+ *
+ * On input, a and b must be valid field elements with magnitudes not exceeding
+ * 1 and 31, respectively.
+ * Returns a = b (mod p).
+ */
 static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
 
-/** Same as secp256k1_fe_equal, but may be variable time. */
+/** Determine whether two field elements are equal, without constant-time guarantee.
+ *
+ * Identical in behavior to secp256k1_fe_equal, but not constant time in either a or b.
+ */
 static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
-/** Compare two field elements. Requires both inputs to be normalized */
+/** Compare the values represented by 2 field elements, without constant-time guarantee.
+ *
+ * On input, a and b must be valid normalized field elements.
+ * Returns 1 if a > b, -1 if a < b, and 0 if a = b (comparisons are done as integers
+ * in range 0..p-1).
+ */
 static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
-/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
-static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
+/** Set a field element equal to a provided 32-byte big endian value, reducing it.
+ *
+ * On input, r does not need to be initalized. a must be a pointer to an initialized 32-byte array.
+ * On output, r = a (mod p). It will have magnitude 1, and not be normalized.
+ */
+static void secp256k1_fe_set_b32_mod(secp256k1_fe *r, const unsigned char *a);
+
+/** Set a field element equal to a provided 32-byte big endian value, checking for overflow.
+ *
+ * On input, r does not need to be initalized. a must be a pointer to an initialized 32-byte array.
+ * On output, r = a if (a < p), it will be normalized with magnitude 1, and 1 is returned.
+ * If a >= p, 0 is returned, and r will be made invalid (and must not be used without overwriting).
+ */
+static int secp256k1_fe_set_b32_limit(secp256k1_fe *r, const unsigned char *a);
 
-/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+/** Convert a field element to 32-byte big endian byte array.
+ * On input, a must be a valid normalized field element, and r a pointer to a 32-byte array.
+ * On output, r = a (mod p).
+ */
 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
 
-/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
- *  as an argument. The magnitude of the output is one higher. */
+/** Negate a field element.
+ *
+ * On input, r does not need to be initialized. a must be a valid field element with
+ * magnitude not exceeding m. m must be an integer in [0,31].
+ * Performs {r = -a}.
+ * On output, r will not be normalized, and will have magnitude m+1.
+ */
 static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
 
-/** Adds a small integer (up to 0x7FFF) to r. The resulting magnitude increases by one. */
+/** Add a small integer to a field element.
+ *
+ * Performs {r += a}. The magnitude of r increases by 1, and normalized is cleared.
+ * a must be in range [0,0xFFFF].
+ */
 static void secp256k1_fe_add_int(secp256k1_fe *r, int a);
 
-/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
- *  small integer. */
+/** Multiply a field element with a small integer.
+ *
+ * On input, r must be a valid field element. a must be an integer in [0,32].
+ * The magnitude of r times a must not exceed 32.
+ * Performs {r *= a}.
+ * On output, r's magnitude is multiplied by a, and r will not be normalized.
+ */
 static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
 
-/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
+/** Increment a field element by another.
+ *
+ * On input, r and a must be valid field elements, not necessarily normalized.
+ * The sum of their magnitudes must not exceed 32.
+ * Performs {r += a}.
+ * On output, r will not be normalized, and will have magnitude incremented by a's.
+ */
 static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
 
-/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
- *  The output magnitude is 1 (but not guaranteed to be normalized). */
+/** Multiply two field elements.
+ *
+ * On input, a and b must be valid field elements; r does not need to be initialized.
+ * r and a may point to the same object, but neither can be equal to b. The magnitudes
+ * of a and b must not exceed 8.
+ * Performs {r = a * b}
+ * On output, r will have magnitude 1, but won't be normalized.
+ */
 static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
 
-/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
- *  The output magnitude is 1 (but not guaranteed to be normalized). */
+/** Square a field element.
+ *
+ * On input, a must be a valid field element; r does not need to be initialized. The magnitude
+ * of a must not exceed 8.
+ * Performs {r = a**2}
+ * On output, r will have magnitude 1, but won't be normalized.
+ */
 static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
 
-/** If a has a square root, it is computed in r and 1 is returned. If a does not
- *  have a square root, the root of its negation is computed and 0 is returned.
- *  The input's magnitude can be at most 8. The output magnitude is 1 (but not
- *  guaranteed to be normalized). The result in r will always be a square
- *  itself. */
-static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a);
+/** Compute a square root of a field element.
+ *
+ * On input, a must be a valid field element with magnitude<=8; r need not be initialized.
+ * Performs {r = sqrt(a)} or {r = sqrt(-a)}, whichever exists. The resulting value
+ * represented by r will be a square itself. Variables r and a must not point to the same object.
+ * On output, r will have magnitude 1 but will not be normalized.
+ */
+static int secp256k1_fe_sqrt(secp256k1_fe * SECP256K1_RESTRICT r, const secp256k1_fe * SECP256K1_RESTRICT a);
 
-/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
- *  at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
+/** Compute the modular inverse of a field element.
+ *
+ * On input, a must be a valid field element; r need not be initialized.
+ * Performs {r = a**(p-2)} (which maps 0 to 0, and every other element to its
+ * inverse).
+ * On output, r will have magnitude (a.magnitude != 0) and be normalized.
+ */
 static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
 
-/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
+/** Compute the modular inverse of a field element, without constant-time guarantee.
+ *
+ * Behaves identically to secp256k1_fe_inv, but is not constant-time in a.
+ */
 static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
 
-/** Convert a field element to the storage type. */
+/** Convert a field element to secp256k1_fe_storage.
+ *
+ * On input, a must be a valid normalized field element.
+ * Performs {r = a}.
+ */
 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
 
-/** Convert a field element back from the storage type. */
+/** Convert a field element back from secp256k1_fe_storage.
+ *
+ * On input, r need not be initialized.
+ * Performs {r = a}.
+ * On output, r will be normalized and will have magnitude 1.
+ */
 static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
 
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
 
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
+/** Conditionally move a field element in constant time.
+ *
+ * On input, both r and a must be valid field elements. Flag must be 0 or 1.
+ * Performs {r = flag ? a : r}.
+ * On output, r's magnitude and normalized will equal a's in case of flag=1, unchanged otherwise.
+ */
 static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
 
-/** Halves the value of a field element modulo the field prime. Constant-time.
- *  For an input magnitude 'm', the output magnitude is set to 'floor(m/2) + 1'.
- *  The output is not guaranteed to be normalized, regardless of the input. */
+/** Halve the value of a field element modulo the field prime in constant-time.
+ *
+ * On input, r must be a valid field element.
+ * On output, r will be normalized and have magnitude floor(m/2) + 1 where m is
+ * the magnitude of r on input.
+ */
 static void secp256k1_fe_half(secp256k1_fe *r);
 
-/** Sets each limb of 'r' to its upper bound at magnitude 'm'. The output will also have its
- *  magnitude set to 'm' and is normalized if (and only if) 'm' is zero. */
+/** Sets r to a field element with magnitude m, normalized if (and only if) m==0.
+ *  The value is chosen so that it is likely to trigger edge cases related to
+ *  internal overflows. */
 static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m);
 
-/** Determine whether a is a square (modulo p). */
+/** Determine whether a is a square (modulo p).
+ *
+ * On input, a must be a valid field element.
+ */
 static int secp256k1_fe_is_square_var(const secp256k1_fe *a);
 
+/** Check invariants on a field element (no-op unless VERIFY is enabled). */
+static void secp256k1_fe_verify(const secp256k1_fe *a);
+
 #endif /* SECP256K1_FIELD_H */
diff --git a/src/field_10x26.h b/src/field_10x26.h
index 9eb65607f1..203c10167c 100644
--- a/src/field_10x26.h
+++ b/src/field_10x26.h
@@ -9,15 +9,28 @@
 
 #include <stdint.h>
 
+/** This field implementation represents the value as 10 uint32_t limbs in base
+ *  2^26. */
 typedef struct {
-    /* X = sum(i=0..9, n[i]*2^(i*26)) mod p
-     * where p = 2^256 - 0x1000003D1
-     */
+   /* A field element f represents the sum(i=0..9, f.n[i] << (i*26)) mod p,
+    * where p is the field modulus, 2^256 - 2^32 - 977.
+    *
+    * The individual limbs f.n[i] can exceed 2^26; the field's magnitude roughly
+    * corresponds to how much excess is allowed. The value
+    * sum(i=0..9, f.n[i] << (i*26)) may exceed p, unless the field element is
+    * normalized. */
     uint32_t n[10];
-#ifdef VERIFY
-    int magnitude;
-    int normalized;
-#endif
+    /*
+     * Magnitude m requires:
+     *     n[i] <= 2 * m * (2^26 - 1) for i=0..8
+     *     n[9] <= 2 * m * (2^22 - 1)
+     *
+     * Normalized requires:
+     *     n[i] <= (2^26 - 1) for i=0..8
+     *     sum(i=0..9, n[i] << (i*26)) < p
+     *     (together these imply n[9] <= 2^22 - 1)
+     */
+    SECP256K1_FE_VERIFY_FIELDS
 } secp256k1_fe;
 
 /* Unpacks a constant into a overlapping multi-limbed FE element. */
@@ -34,12 +47,6 @@ typedef struct {
     (((uint32_t)d7) >> 10) \
 }
 
-#ifdef VERIFY
-#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
-#else
-#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
-#endif
-
 typedef struct {
     uint32_t n[8];
 } secp256k1_fe_storage;
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 3b7f4d2480..c1b32b80a8 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -12,47 +12,32 @@
 #include "field.h"
 #include "modinv32_impl.h"
 
-/** See the comment at the top of field_5x52_impl.h for more details.
- *
- *  Here, we represent field elements as 10 uint32_t's in base 2^26, least significant first,
- *  where limbs can contain >26 bits.
- *  A magnitude M means:
- *  - 2*M*(2^22-1) is the max (inclusive) of the most significant limb
- *  - 2*M*(2^26-1) is the max (inclusive) of the remaining limbs
- */
-
 #ifdef VERIFY
-static void secp256k1_fe_verify(const secp256k1_fe *a) {
+static void secp256k1_fe_impl_verify(const secp256k1_fe *a) {
     const uint32_t *d = a->n;
-    int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
-    r &= (d[0] <= 0x3FFFFFFUL * m);
-    r &= (d[1] <= 0x3FFFFFFUL * m);
-    r &= (d[2] <= 0x3FFFFFFUL * m);
-    r &= (d[3] <= 0x3FFFFFFUL * m);
-    r &= (d[4] <= 0x3FFFFFFUL * m);
-    r &= (d[5] <= 0x3FFFFFFUL * m);
-    r &= (d[6] <= 0x3FFFFFFUL * m);
-    r &= (d[7] <= 0x3FFFFFFUL * m);
-    r &= (d[8] <= 0x3FFFFFFUL * m);
-    r &= (d[9] <= 0x03FFFFFUL * m);
-    r &= (a->magnitude >= 0);
-    r &= (a->magnitude <= 32);
+    int m = a->normalized ? 1 : 2 * a->magnitude;
+    VERIFY_CHECK(d[0] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[1] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[2] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[3] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[4] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[5] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[6] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[7] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[8] <= 0x3FFFFFFUL * m);
+    VERIFY_CHECK(d[9] <= 0x03FFFFFUL * m);
     if (a->normalized) {
-        r &= (a->magnitude <= 1);
-        if (r && (d[9] == 0x03FFFFFUL)) {
+        if (d[9] == 0x03FFFFFUL) {
             uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
             if (mid == 0x3FFFFFFUL) {
-                r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
+                VERIFY_CHECK((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
             }
         }
     }
-    VERIFY_CHECK(r == 1);
 }
 #endif
 
-static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
-    VERIFY_CHECK(m >= 0);
-    VERIFY_CHECK(m <= 2048);
+static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m) {
     r->n[0] = 0x3FFFFFFUL * 2 * m;
     r->n[1] = 0x3FFFFFFUL * 2 * m;
     r->n[2] = 0x3FFFFFFUL * 2 * m;
@@ -63,14 +48,9 @@ static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
     r->n[7] = 0x3FFFFFFUL * 2 * m;
     r->n[8] = 0x3FFFFFFUL * 2 * m;
     r->n[9] = 0x03FFFFFUL * 2 * m;
-#ifdef VERIFY
-    r->magnitude = m;
-    r->normalized = (m == 0);
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_normalize(secp256k1_fe *r) {
+static void secp256k1_fe_impl_normalize(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -117,15 +97,9 @@ static void secp256k1_fe_normalize(secp256k1_fe *r) {
 
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
     r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -149,14 +123,9 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
 
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
     r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -204,15 +173,9 @@ static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
 
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
     r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
+static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -241,7 +204,7 @@ static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
+static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r) {
     uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
     uint32_t z0, z1;
     uint32_t x;
@@ -293,53 +256,29 @@ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
-    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
+SECP256K1_INLINE static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a) {
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
-#ifdef VERIFY
-    r->magnitude = (a != 0);
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+SECP256K1_INLINE static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a) {
     const uint32_t *t = a->n;
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    secp256k1_fe_verify(a);
-#endif
     return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    secp256k1_fe_verify(a);
-#endif
+SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
     return a->n[0] & 1;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+SECP256K1_INLINE static void secp256k1_fe_impl_clear(secp256k1_fe *a) {
     int i;
-#ifdef VERIFY
-    a->magnitude = 0;
-    a->normalized = 1;
-#endif
     for (i=0; i<10; i++) {
         a->n[i] = 0;
     }
 }
 
-static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     int i;
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    VERIFY_CHECK(b->normalized);
-    secp256k1_fe_verify(a);
-    secp256k1_fe_verify(b);
-#endif
     for (i = 9; i >= 0; i--) {
         if (a->n[i] > b->n[i]) {
             return 1;
@@ -351,8 +290,7 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     return 0;
 }
 
-static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
-    int ret;
+static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
     r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
     r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22);
     r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20);
@@ -363,26 +301,15 @@ static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
     r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
     r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
     r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
+}
 
-    ret = !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
-#ifdef VERIFY
-    r->magnitude = 1;
-    if (ret) {
-        r->normalized = 1;
-        secp256k1_fe_verify(r);
-    } else {
-        r->normalized = 0;
-    }
-#endif
-    return ret;
+static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
+    secp256k1_fe_impl_set_b32_mod(r, a);
+    return !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
 }
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    secp256k1_fe_verify(a);
-#endif
+static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
     r[0] = (a->n[9] >> 14) & 0xff;
     r[1] = (a->n[9] >> 6) & 0xff;
     r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
@@ -417,15 +344,15 @@ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
     r[31] = a->n[0] & 0xff;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->magnitude <= m);
-    secp256k1_fe_verify(a);
+SECP256K1_INLINE static void secp256k1_fe_impl_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+    /* For all legal values of m (0..31), the following properties hold: */
     VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
     VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
     VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
     VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m);
-#endif
+
+    /* Due to the properties above, the left hand in the subtractions below is never less than
+     * the right hand. */
     r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
     r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
     r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
@@ -436,14 +363,9 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k
     r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
     r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
     r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
-#ifdef VERIFY
-    r->magnitude = m + 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_impl_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
@@ -454,17 +376,9 @@ SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
     r->n[7] *= a;
     r->n[8] *= a;
     r->n[9] *= a;
-#ifdef VERIFY
-    r->magnitude *= a;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    secp256k1_fe_verify(a);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
     r->n[0] += a->n[0];
     r->n[1] += a->n[1];
     r->n[2] += a->n[2];
@@ -475,25 +389,10 @@ SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_f
     r->n[7] += a->n[7];
     r->n[8] += a->n[8];
     r->n[9] += a->n[9];
-#ifdef VERIFY
-    r->magnitude += a->magnitude;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) {
-#ifdef VERIFY
-    secp256k1_fe_verify(r);
-    VERIFY_CHECK(a >= 0);
-    VERIFY_CHECK(a <= 0x7FFF);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
     r->n[0] += a;
-#ifdef VERIFY
-    r->magnitude += 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 #if defined(USE_EXTERNAL_ASM)
@@ -1115,37 +1014,15 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t
 }
 #endif
 
-static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->magnitude <= 8);
-    VERIFY_CHECK(b->magnitude <= 8);
-    secp256k1_fe_verify(a);
-    secp256k1_fe_verify(b);
-    VERIFY_CHECK(r != b);
-    VERIFY_CHECK(a != b);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
     secp256k1_fe_mul_inner(r->n, a->n, b->n);
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->magnitude <= 8);
-    secp256k1_fe_verify(a);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
     secp256k1_fe_sqr_inner(r->n, a->n);
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
     uint32_t mask0, mask1;
     volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
@@ -1161,25 +1038,14 @@ static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_
     r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
     r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
     r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
-#ifdef VERIFY
-    if (flag) {
-        r->magnitude = a->magnitude;
-        r->normalized = a->normalized;
-    }
-#endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
+static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
     uint32_t one = (uint32_t)1;
     uint32_t mask = -(t0 & one) >> 6;
 
-#ifdef VERIFY
-    secp256k1_fe_verify(r);
-    VERIFY_CHECK(r->magnitude < 32);
-#endif
-
     /* Bounds analysis (over the rationals).
      *
      * Let m = r->magnitude
@@ -1226,10 +1092,8 @@ static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
      *
      * Current bounds: t0..t8 <= C * (m/2 + 1/2)
      *                     t9 <= D * (m/2 + 1/4)
-     */
-
-#ifdef VERIFY
-    /* Therefore the output magnitude (M) has to be set such that:
+     *
+     * Therefore the output magnitude (M) has to be set such that:
      *     t0..t8: C * M >= C * (m/2 + 1/2)
      *         t9: D * M >= D * (m/2 + 1/4)
      *
@@ -1239,10 +1103,6 @@ static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
      * and since we want the smallest such integer value for M:
      *     M == floor(m/2) + 1
      */
-    r->magnitude = (r->magnitude >> 1) + 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
@@ -1261,10 +1121,7 @@ static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r,
     r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
 }
 
-static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-#endif
+static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
     r->n[0] = a->n[0] | a->n[1] << 26;
     r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
     r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
@@ -1275,7 +1132,7 @@ static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe
     r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
 }
 
-static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
     r->n[0] = a->n[0] & 0x3FFFFFFUL;
     r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
     r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
@@ -1286,11 +1143,6 @@ static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const se
     r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
     r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
     r->n[9] = a->n[7] >> 10;
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) {
@@ -1321,12 +1173,6 @@ static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32
     r->n[7] = (a6 >>  2           ) & M26;
     r->n[8] = (a6 >> 28 | a7 <<  2) & M26;
     r->n[9] = (a7 >> 24 | a8 <<  6);
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) {
@@ -1334,10 +1180,6 @@ static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp2
     const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4],
                    a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9];
 
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-#endif
-
     r->v[0] = (a0       | a1 << 26) & M30;
     r->v[1] = (a1 >>  4 | a2 << 22) & M30;
     r->v[2] = (a2 >>  8 | a3 << 18) & M30;
@@ -1355,37 +1197,27 @@ static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = {
     0x2DDACACFL
 };
 
-static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
-    secp256k1_fe tmp;
+static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x) {
+    secp256k1_fe tmp = *x;
     secp256k1_modinv32_signed30 s;
 
-    tmp = *x;
     secp256k1_fe_normalize(&tmp);
     secp256k1_fe_to_signed30(&s, &tmp);
     secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe);
     secp256k1_fe_from_signed30(r, &s);
-
-#ifdef VERIFY
-    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
-#endif
 }
 
-static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
-    secp256k1_fe tmp;
+static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
+    secp256k1_fe tmp = *x;
     secp256k1_modinv32_signed30 s;
 
-    tmp = *x;
     secp256k1_fe_normalize_var(&tmp);
     secp256k1_fe_to_signed30(&s, &tmp);
     secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe);
     secp256k1_fe_from_signed30(r, &s);
-
-#ifdef VERIFY
-    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
-#endif
 }
 
-static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
+static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
     secp256k1_fe tmp;
     secp256k1_modinv32_signed30 s;
     int jac, ret;
@@ -1403,10 +1235,6 @@ static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
         secp256k1_fe dummy;
         ret = secp256k1_fe_sqrt(&dummy, &tmp);
     } else {
-#ifdef VERIFY
-        secp256k1_fe dummy;
-        VERIFY_CHECK(jac == 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1);
-#endif
         ret = jac >= 0;
     }
     return ret;
diff --git a/src/field_5x52.h b/src/field_5x52.h
index 50ee3f9ec9..f20c246fdd 100644
--- a/src/field_5x52.h
+++ b/src/field_5x52.h
@@ -9,15 +9,28 @@
 
 #include <stdint.h>
 
+/** This field implementation represents the value as 5 uint64_t limbs in base
+ *  2^52. */
 typedef struct {
-    /* X = sum(i=0..4, n[i]*2^(i*52)) mod p
-     * where p = 2^256 - 0x1000003D1
-     */
+   /* A field element f represents the sum(i=0..4, f.n[i] << (i*52)) mod p,
+    * where p is the field modulus, 2^256 - 2^32 - 977.
+    *
+    * The individual limbs f.n[i] can exceed 2^52; the field's magnitude roughly
+    * corresponds to how much excess is allowed. The value
+    * sum(i=0..4, f.n[i] << (i*52)) may exceed p, unless the field element is
+    * normalized. */
     uint64_t n[5];
-#ifdef VERIFY
-    int magnitude;
-    int normalized;
-#endif
+    /*
+     * Magnitude m requires:
+     *     n[i] <= 2 * m * (2^52 - 1) for i=0..3
+     *     n[4] <= 2 * m * (2^48 - 1)
+     *
+     * Normalized requires:
+     *     n[i] <= (2^52 - 1) for i=0..3
+     *     sum(i=0..4, n[i] << (i*52)) < p
+     *     (together these imply n[4] <= 2^48 - 1)
+     */
+    SECP256K1_FE_VERIFY_FIELDS
 } secp256k1_fe;
 
 /* Unpacks a constant into a overlapping multi-limbed FE element. */
@@ -29,12 +42,6 @@ typedef struct {
     ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
 }
 
-#ifdef VERIFY
-#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
-#else
-#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
-#endif
-
 typedef struct {
     uint64_t n[4];
 } secp256k1_fe_storage;
diff --git a/src/field_5x52_asm_impl.h b/src/field_5x52_asm_impl.h
index a2118044ab..04a9af2105 100644
--- a/src/field_5x52_asm_impl.h
+++ b/src/field_5x52_asm_impl.h
@@ -14,6 +14,8 @@
 #ifndef SECP256K1_FIELD_INNER5X52_IMPL_H
 #define SECP256K1_FIELD_INNER5X52_IMPL_H
 
+#include "util.h"
+
 SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
 /**
  * Registers: rdx:rax = multiplication accumulator
@@ -278,7 +280,7 @@ __asm__ __volatile__(
     "addq %%rsi,%%r8\n"
     /* r[4] = c */
     "movq %%r8,32(%%rdi)\n"
-: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
+: "+S"(a), "=&m"(tmp1), "=&m"(tmp2), "=&m"(tmp3)
 : "b"(b), "D"(r)
 : "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
 );
@@ -493,7 +495,7 @@ __asm__ __volatile__(
     "addq %%rsi,%%r8\n"
     /* r[4] = c */
     "movq %%r8,32(%%rdi)\n"
-: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
+: "+S"(a), "=&m"(tmp1), "=&m"(tmp2), "=&m"(tmp3)
 : "D"(r)
 : "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
 );
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index 6b97157d0f..0a4cc1a630 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -18,59 +18,33 @@
 #include "field_5x52_int128_impl.h"
 #endif
 
-/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
- *  represented as 5 uint64_t's in base 2^52, least significant first. Note that the limbs are allowed to
- *  contain >52 bits each.
- *
- *  Each field element has a 'magnitude' associated with it. Internally, a magnitude M means:
- *  - 2*M*(2^48-1) is the max (inclusive) of the most significant limb
- *  - 2*M*(2^52-1) is the max (inclusive) of the remaining limbs
- *
- *  Operations have different rules for propagating magnitude to their outputs. If an operation takes a
- *  magnitude M as a parameter, that means the magnitude of input field elements can be at most M (inclusive).
- *
- *  Each field element also has a 'normalized' flag. A field element is normalized if its magnitude is either
- *  0 or 1, and its value is already reduced modulo the order of the field.
- */
-
 #ifdef VERIFY
-static void secp256k1_fe_verify(const secp256k1_fe *a) {
+static void secp256k1_fe_impl_verify(const secp256k1_fe *a) {
     const uint64_t *d = a->n;
-    int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
+    int m = a->normalized ? 1 : 2 * a->magnitude;
    /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
-    r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
-    r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
-    r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
-    r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
-    r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
-    r &= (a->magnitude >= 0);
-    r &= (a->magnitude <= 2048);
+    VERIFY_CHECK(d[0] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[1] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[2] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[3] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[4] <= 0x0FFFFFFFFFFFFULL * m);
     if (a->normalized) {
-        r &= (a->magnitude <= 1);
-        if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
-            r &= (d[0] < 0xFFFFEFFFFFC2FULL);
+        if ((d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
+            VERIFY_CHECK(d[0] < 0xFFFFEFFFFFC2FULL);
         }
     }
-    VERIFY_CHECK(r == 1);
 }
 #endif
 
-static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
-    VERIFY_CHECK(m >= 0);
-    VERIFY_CHECK(m <= 2048);
+static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m) {
     r->n[0] = 0xFFFFFFFFFFFFFULL * 2 * m;
     r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * m;
     r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * m;
     r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * m;
     r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * m;
-#ifdef VERIFY
-    r->magnitude = m;
-    r->normalized = (m == 0);
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_normalize(secp256k1_fe *r) {
+static void secp256k1_fe_impl_normalize(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -105,15 +79,9 @@ static void secp256k1_fe_normalize(secp256k1_fe *r) {
     t4 &= 0x0FFFFFFFFFFFFULL;
 
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -130,14 +98,9 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
     VERIFY_CHECK(t4 >> 49 == 0);
 
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -173,15 +136,9 @@ static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
     }
 
     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
+static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
@@ -204,7 +161,7 @@ static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
+static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r) {
     uint64_t t0, t1, t2, t3, t4;
     uint64_t z0, z1;
     uint64_t x;
@@ -245,53 +202,29 @@ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
-    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
+SECP256K1_INLINE static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a) {
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
-#ifdef VERIFY
-    r->magnitude = (a != 0);
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+SECP256K1_INLINE static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a) {
     const uint64_t *t = a->n;
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    secp256k1_fe_verify(a);
-#endif
     return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    secp256k1_fe_verify(a);
-#endif
+SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
     return a->n[0] & 1;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+SECP256K1_INLINE static void secp256k1_fe_impl_clear(secp256k1_fe *a) {
     int i;
-#ifdef VERIFY
-    a->magnitude = 0;
-    a->normalized = 1;
-#endif
     for (i=0; i<5; i++) {
         a->n[i] = 0;
     }
 }
 
-static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     int i;
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    VERIFY_CHECK(b->normalized);
-    secp256k1_fe_verify(a);
-    secp256k1_fe_verify(b);
-#endif
     for (i = 4; i >= 0; i--) {
         if (a->n[i] > b->n[i]) {
             return 1;
@@ -303,8 +236,7 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     return 0;
 }
 
-static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
-    int ret;
+static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
     r->n[0] = (uint64_t)a[31]
             | ((uint64_t)a[30] << 8)
             | ((uint64_t)a[29] << 16)
@@ -339,25 +271,15 @@ static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
             | ((uint64_t)a[2] << 24)
             | ((uint64_t)a[1] << 32)
             | ((uint64_t)a[0] << 40);
-    ret = !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL));
-#ifdef VERIFY
-    r->magnitude = 1;
-    if (ret) {
-        r->normalized = 1;
-        secp256k1_fe_verify(r);
-    } else {
-        r->normalized = 0;
-    }
-#endif
-    return ret;
+}
+
+static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
+    secp256k1_fe_impl_set_b32_mod(r, a);
+    return !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL));
 }
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-    secp256k1_fe_verify(a);
-#endif
+static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
     r[0] = (a->n[4] >> 40) & 0xFF;
     r[1] = (a->n[4] >> 32) & 0xFF;
     r[2] = (a->n[4] >> 24) & 0xFF;
@@ -392,100 +314,50 @@ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
     r[31] = a->n[0] & 0xFF;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->magnitude <= m);
-    secp256k1_fe_verify(a);
+SECP256K1_INLINE static void secp256k1_fe_impl_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+    /* For all legal values of m (0..31), the following properties hold: */
     VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
     VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
     VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m);
-#endif
+
+    /* Due to the properties above, the left hand in the subtractions below is never less than
+     * the right hand. */
     r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
     r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
     r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
     r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
     r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
-#ifdef VERIFY
-    r->magnitude = m + 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_impl_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
     r->n[3] *= a;
     r->n[4] *= a;
-#ifdef VERIFY
-    r->magnitude *= a;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) {
-#ifdef VERIFY
-    secp256k1_fe_verify(r);
-    VERIFY_CHECK(a >= 0);
-    VERIFY_CHECK(a <= 0x7FFF);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
     r->n[0] += a;
-#ifdef VERIFY
-    r->magnitude += 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    secp256k1_fe_verify(a);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
     r->n[0] += a->n[0];
     r->n[1] += a->n[1];
     r->n[2] += a->n[2];
     r->n[3] += a->n[3];
     r->n[4] += a->n[4];
-#ifdef VERIFY
-    r->magnitude += a->magnitude;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->magnitude <= 8);
-    VERIFY_CHECK(b->magnitude <= 8);
-    secp256k1_fe_verify(a);
-    secp256k1_fe_verify(b);
-    VERIFY_CHECK(r != b);
-    VERIFY_CHECK(a != b);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
     secp256k1_fe_mul_inner(r->n, a->n, b->n);
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->magnitude <= 8);
-    secp256k1_fe_verify(a);
-#endif
+SECP256K1_INLINE static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
     secp256k1_fe_sqr_inner(r->n, a->n);
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
     uint64_t mask0, mask1;
     volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
@@ -496,24 +368,13 @@ static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_
     r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
     r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
-#ifdef VERIFY
-    if (flag) {
-        r->magnitude = a->magnitude;
-        r->normalized = a->normalized;
-    }
-#endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
+static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
     uint64_t one = (uint64_t)1;
     uint64_t mask = -(t0 & one) >> 12;
 
-#ifdef VERIFY
-    secp256k1_fe_verify(r);
-    VERIFY_CHECK(r->magnitude < 32);
-#endif
-
     /* Bounds analysis (over the rationals).
      *
      * Let m = r->magnitude
@@ -550,10 +411,8 @@ static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
      *
      * Current bounds: t0..t3 <= C * (m/2 + 1/2)
      *                     t4 <= D * (m/2 + 1/4)
-     */
-
-#ifdef VERIFY
-    /* Therefore the output magnitude (M) has to be set such that:
+     *
+     * Therefore the output magnitude (M) has to be set such that:
      *     t0..t3: C * M >= C * (m/2 + 1/2)
      *         t4: D * M >= D * (m/2 + 1/4)
      *
@@ -563,10 +422,6 @@ static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
      * and since we want the smallest such integer value for M:
      *     M == floor(m/2) + 1
      */
-    r->magnitude = (r->magnitude >> 1) + 1;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
@@ -581,27 +436,19 @@ static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r,
     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
 }
 
-static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-#endif
+static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
     r->n[0] = a->n[0] | a->n[1] << 52;
     r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
     r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
     r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
 }
 
-static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
     r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
     r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
     r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
     r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
     r->n[4] = a->n[3] >> 16;
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64_signed62 *a) {
@@ -622,22 +469,12 @@ static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64
     r->n[2] = (a1 >> 42 | a2 << 20) & M52;
     r->n[3] = (a2 >> 32 | a3 << 30) & M52;
     r->n[4] = (a3 >> 22 | a4 << 40);
-
-#ifdef VERIFY
-    r->magnitude = 1;
-    r->normalized = 1;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 static void secp256k1_fe_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_fe *a) {
     const uint64_t M62 = UINT64_MAX >> 2;
     const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4];
 
-#ifdef VERIFY
-    VERIFY_CHECK(a->normalized);
-#endif
-
     r->v[0] = (a0       | a1 << 52) & M62;
     r->v[1] = (a1 >> 10 | a2 << 42) & M62;
     r->v[2] = (a2 >> 20 | a3 << 32) & M62;
@@ -650,37 +487,27 @@ static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_fe = {
     0x27C7F6E22DDACACFLL
 };
 
-static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
-    secp256k1_fe tmp;
+static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x) {
+    secp256k1_fe tmp = *x;
     secp256k1_modinv64_signed62 s;
 
-    tmp = *x;
     secp256k1_fe_normalize(&tmp);
     secp256k1_fe_to_signed62(&s, &tmp);
     secp256k1_modinv64(&s, &secp256k1_const_modinfo_fe);
     secp256k1_fe_from_signed62(r, &s);
-
-#ifdef VERIFY
-    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
-#endif
 }
 
-static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
-    secp256k1_fe tmp;
+static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
+    secp256k1_fe tmp = *x;
     secp256k1_modinv64_signed62 s;
 
-    tmp = *x;
     secp256k1_fe_normalize_var(&tmp);
     secp256k1_fe_to_signed62(&s, &tmp);
     secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_fe);
     secp256k1_fe_from_signed62(r, &s);
-
-#ifdef VERIFY
-    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
-#endif
 }
 
-static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
+static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
     secp256k1_fe tmp;
     secp256k1_modinv64_signed62 s;
     int jac, ret;
@@ -698,10 +525,6 @@ static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
         secp256k1_fe dummy;
         ret = secp256k1_fe_sqrt(&dummy, &tmp);
     } else {
-#ifdef VERIFY
-        secp256k1_fe dummy;
-        VERIFY_CHECK(jac == 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1);
-#endif
         ret = jac >= 0;
     }
     return ret;
diff --git a/src/field_5x52_int128_impl.h b/src/field_5x52_int128_impl.h
index 18567b95f3..b2a391dec9 100644
--- a/src/field_5x52_int128_impl.h
+++ b/src/field_5x52_int128_impl.h
@@ -10,6 +10,7 @@
 #include <stdint.h>
 
 #include "int128.h"
+#include "util.h"
 
 #ifdef VERIFY
 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
diff --git a/src/field_impl.h b/src/field_impl.h
index 0a03076bbc..7270375007 100644
--- a/src/field_impl.h
+++ b/src/field_impl.h
@@ -7,6 +7,7 @@
 #ifndef SECP256K1_FIELD_IMPL_H
 #define SECP256K1_FIELD_IMPL_H
 
+#include "field.h"
 #include "util.h"
 
 #if defined(SECP256K1_WIDEMUL_INT128)
@@ -19,6 +20,12 @@
 
 SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
     secp256k1_fe na;
+#ifdef VERIFY
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(a->magnitude <= 1);
+    VERIFY_CHECK(b->magnitude <= 31);
+#endif
     secp256k1_fe_negate(&na, a, 1);
     secp256k1_fe_add(&na, b);
     return secp256k1_fe_normalizes_to_zero(&na);
@@ -26,6 +33,12 @@ SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp
 
 SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     secp256k1_fe na;
+#ifdef VERIFY
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(a->magnitude <= 1);
+    VERIFY_CHECK(b->magnitude <= 31);
+#endif
     secp256k1_fe_negate(&na, a, 1);
     secp256k1_fe_add(&na, b);
     return secp256k1_fe_normalizes_to_zero_var(&na);
@@ -42,9 +55,13 @@ static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
      *  itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
      */
     secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
-    int j;
+    int j, ret;
 
+#ifdef VERIFY
     VERIFY_CHECK(r != a);
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(a->magnitude <= 8);
+#endif
 
     /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
      *  { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
@@ -128,7 +145,288 @@ static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
     /* Check that a square root was actually calculated */
 
     secp256k1_fe_sqr(&t1, r);
-    return secp256k1_fe_equal(&t1, a);
+    ret = secp256k1_fe_equal(&t1, a);
+
+#ifdef VERIFY
+    if (!ret) {
+        secp256k1_fe_negate(&t1, &t1, 1);
+        secp256k1_fe_normalize_var(&t1);
+        VERIFY_CHECK(secp256k1_fe_equal_var(&t1, a));
+    }
+#endif
+    return ret;
+}
+
+#ifndef VERIFY
+static void secp256k1_fe_verify(const secp256k1_fe *a) { (void)a; }
+#else
+static void secp256k1_fe_impl_verify(const secp256k1_fe *a);
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
+    /* Magnitude between 0 and 32. */
+    VERIFY_CHECK((a->magnitude >= 0) && (a->magnitude <= 32));
+    /* Normalized is 0 or 1. */
+    VERIFY_CHECK((a->normalized == 0) || (a->normalized == 1));
+    /* If normalized, magnitude must be 0 or 1. */
+    if (a->normalized) VERIFY_CHECK(a->magnitude <= 1);
+    /* Invoke implementation-specific checks. */
+    secp256k1_fe_impl_verify(a);
+}
+
+static void secp256k1_fe_impl_normalize(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_normalize(secp256k1_fe *r) {
+    secp256k1_fe_verify(r);
+    secp256k1_fe_impl_normalize(r);
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+    secp256k1_fe_verify(r);
+    secp256k1_fe_impl_normalize_weak(r);
+    r->magnitude = 1;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+    secp256k1_fe_verify(r);
+    secp256k1_fe_impl_normalize_var(r);
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+}
+
+static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r);
+SECP256K1_INLINE static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
+    secp256k1_fe_verify(r);
+    return secp256k1_fe_impl_normalizes_to_zero(r);
+}
+
+static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r);
+SECP256K1_INLINE static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
+    secp256k1_fe_verify(r);
+    return secp256k1_fe_impl_normalizes_to_zero_var(r);
+}
+
+static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
+    secp256k1_fe_impl_set_int(r, a);
+    r->magnitude = (a != 0);
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
+    secp256k1_fe_verify(r);
+    secp256k1_fe_impl_add_int(r, a);
+    r->magnitude += 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_clear(secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+    a->magnitude = 0;
+    a->normalized = 1;
+    secp256k1_fe_impl_clear(a);
+    secp256k1_fe_verify(a);
+}
+
+static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a);
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(a->normalized);
+    return secp256k1_fe_impl_is_zero(a);
+}
+
+static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a);
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(a->normalized);
+    return secp256k1_fe_impl_is_odd(a);
+}
+
+static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
+SECP256K1_INLINE static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(a->normalized);
+    VERIFY_CHECK(b->normalized);
+    return secp256k1_fe_impl_cmp_var(a, b);
+}
+
+static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a);
+SECP256K1_INLINE static void secp256k1_fe_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
+    secp256k1_fe_impl_set_b32_mod(r, a);
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
 }
 
+static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a);
+SECP256K1_INLINE static int secp256k1_fe_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
+    if (secp256k1_fe_impl_set_b32_limit(r, a)) {
+        r->magnitude = 1;
+        r->normalized = 1;
+        secp256k1_fe_verify(r);
+        return 1;
+    } else {
+        /* Mark the output field element as invalid. */
+        r->magnitude = -1;
+        return 0;
+    }
+}
+
+static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_impl_get_b32(r, a);
+}
+
+static void secp256k1_fe_impl_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(m >= 0 && m <= 31);
+    VERIFY_CHECK(a->magnitude <= m);
+    secp256k1_fe_impl_negate(r, a, m);
+    r->magnitude = m + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_mul_int(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+    secp256k1_fe_verify(r);
+    VERIFY_CHECK(a >= 0 && a <= 32);
+    VERIFY_CHECK(a*r->magnitude <= 32);
+    secp256k1_fe_impl_mul_int(r, a);
+    r->magnitude *= a;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe_verify(r);
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(r->magnitude + a->magnitude <= 32);
+    secp256k1_fe_impl_add(r, a);
+    r->magnitude += a->magnitude;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
+SECP256K1_INLINE static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(b);
+    VERIFY_CHECK(a->magnitude <= 8);
+    VERIFY_CHECK(b->magnitude <= 8);
+    VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
+    secp256k1_fe_impl_mul(r, a, b);
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(a->magnitude <= 8);
+    secp256k1_fe_impl_sqr(r, a);
+    r->magnitude = 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
+SECP256K1_INLINE static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    VERIFY_CHECK(flag == 0 || flag == 1);
+    secp256k1_fe_verify(a);
+    secp256k1_fe_verify(r);
+    secp256k1_fe_impl_cmov(r, a, flag);
+    if (flag) {
+        r->magnitude = a->magnitude;
+        r->normalized = a->normalized;
+    }
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
+    secp256k1_fe_verify(a);
+    VERIFY_CHECK(a->normalized);
+    secp256k1_fe_impl_to_storage(r, a);
+}
+
+static void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
+SECP256K1_INLINE static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+    secp256k1_fe_impl_from_storage(r, a);
+    r->magnitude = 1;
+    r->normalized = 1;
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x);
+SECP256K1_INLINE static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
+    int input_is_zero = secp256k1_fe_normalizes_to_zero(x);
+    secp256k1_fe_verify(x);
+    secp256k1_fe_impl_inv(r, x);
+    r->magnitude = x->magnitude > 0;
+    r->normalized = 1;
+    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == input_is_zero);
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x);
+SECP256K1_INLINE static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
+    int input_is_zero = secp256k1_fe_normalizes_to_zero(x);
+    secp256k1_fe_verify(x);
+    secp256k1_fe_impl_inv_var(r, x);
+    r->magnitude = x->magnitude > 0;
+    r->normalized = 1;
+    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == input_is_zero);
+    secp256k1_fe_verify(r);
+}
+
+static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x);
+SECP256K1_INLINE static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
+    int ret;
+    secp256k1_fe tmp = *x, sqrt;
+    secp256k1_fe_verify(x);
+    ret = secp256k1_fe_impl_is_square_var(x);
+    secp256k1_fe_normalize_weak(&tmp);
+    VERIFY_CHECK(ret == secp256k1_fe_sqrt(&sqrt, &tmp));
+    return ret;
+}
+
+static void secp256k1_fe_impl_get_bounds(secp256k1_fe* r, int m);
+SECP256K1_INLINE static void secp256k1_fe_get_bounds(secp256k1_fe* r, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 32);
+    secp256k1_fe_impl_get_bounds(r, m);
+    r->magnitude = m;
+    r->normalized = (m == 0);
+    secp256k1_fe_verify(r);
+}
+
+static void secp256k1_fe_impl_half(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_half(secp256k1_fe *r) {
+    secp256k1_fe_verify(r);
+    VERIFY_CHECK(r->magnitude < 32);
+    secp256k1_fe_impl_half(r);
+    r->magnitude = (r->magnitude >> 1) + 1;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
+
+#endif /* defined(VERIFY) */
+
 #endif /* SECP256K1_FIELD_IMPL_H */
diff --git a/src/group.h b/src/group.h
index b79ba597db..77ad7435f8 100644
--- a/src/group.h
+++ b/src/group.h
@@ -164,4 +164,10 @@ static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
  */
 static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge);
 
+/** Check invariants on an affine group element (no-op unless VERIFY is enabled). */
+static void secp256k1_ge_verify(const secp256k1_ge *a);
+
+/** Check invariants on a Jacobian group element (no-op unless VERIFY is enabled). */
+static void secp256k1_gej_verify(const secp256k1_gej *a);
+
 #endif /* SECP256K1_GROUP_H */
diff --git a/src/group_impl.h b/src/group_impl.h
index 82ce3f8d8b..44d98434ca 100644
--- a/src/group_impl.h
+++ b/src/group_impl.h
@@ -9,6 +9,7 @@
 
 #include "field.h"
 #include "group.h"
+#include "util.h"
 
 /* Begin of section generated by sage/gen_exhaustive_groups.sage. */
 #define SECP256K1_G_ORDER_7 SECP256K1_GE_CONST(\
@@ -72,37 +73,80 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G;
 #endif
 /* End of section generated by sage/gen_exhaustive_groups.sage. */
 
-static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, SECP256K1_B);
+static void secp256k1_ge_verify(const secp256k1_ge *a) {
+#ifdef VERIFY
+    secp256k1_fe_verify(&a->x);
+    secp256k1_fe_verify(&a->y);
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+#endif
+    (void)a;
+}
+
+static void secp256k1_gej_verify(const secp256k1_gej *a) {
+#ifdef VERIFY
+    secp256k1_fe_verify(&a->x);
+    secp256k1_fe_verify(&a->y);
+    secp256k1_fe_verify(&a->z);
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+#endif
+    (void)a;
+}
 
+/* Set r to the affine coordinates of Jacobian point (a.x, a.y, 1/zi). */
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
     secp256k1_fe zi2;
     secp256k1_fe zi3;
+    secp256k1_gej_verify(a);
+    secp256k1_fe_verify(zi);
+    VERIFY_CHECK(!a->infinity);
+    secp256k1_fe_sqr(&zi2, zi);
+    secp256k1_fe_mul(&zi3, &zi2, zi);
+    secp256k1_fe_mul(&r->x, &a->x, &zi2);
+    secp256k1_fe_mul(&r->y, &a->y, &zi3);
+    r->infinity = a->infinity;
+    secp256k1_ge_verify(r);
+}
+
+/* Set r to the affine coordinates of Jacobian point (a.x, a.y, 1/zi). */
+static void secp256k1_ge_set_ge_zinv(secp256k1_ge *r, const secp256k1_ge *a, const secp256k1_fe *zi) {
+    secp256k1_fe zi2;
+    secp256k1_fe zi3;
+    secp256k1_ge_verify(a);
+    secp256k1_fe_verify(zi);
     VERIFY_CHECK(!a->infinity);
     secp256k1_fe_sqr(&zi2, zi);
     secp256k1_fe_mul(&zi3, &zi2, zi);
     secp256k1_fe_mul(&r->x, &a->x, &zi2);
     secp256k1_fe_mul(&r->y, &a->y, &zi3);
     r->infinity = a->infinity;
+    secp256k1_ge_verify(r);
 }
 
 static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
+    secp256k1_fe_verify(x);
+    secp256k1_fe_verify(y);
     r->infinity = 0;
     r->x = *x;
     r->y = *y;
+    secp256k1_ge_verify(r);
 }
 
 static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
+    secp256k1_ge_verify(a);
     return a->infinity;
 }
 
 static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
+    secp256k1_ge_verify(a);
     *r = *a;
     secp256k1_fe_normalize_weak(&r->y);
     secp256k1_fe_negate(&r->y, &r->y, 1);
+    secp256k1_ge_verify(r);
 }
 
 static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe z2, z3;
+    secp256k1_gej_verify(a);
     r->infinity = a->infinity;
     secp256k1_fe_inv(&a->z, &a->z);
     secp256k1_fe_sqr(&z2, &a->z);
@@ -112,14 +156,17 @@ static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe_set_int(&a->z, 1);
     r->x = a->x;
     r->y = a->y;
+    secp256k1_ge_verify(r);
 }
 
 static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe z2, z3;
-    if (a->infinity) {
+    secp256k1_gej_verify(a);
+    if (secp256k1_gej_is_infinity(a)) {
         secp256k1_ge_set_infinity(r);
         return;
     }
+    r->infinity = 0;
     secp256k1_fe_inv_var(&a->z, &a->z);
     secp256k1_fe_sqr(&z2, &a->z);
     secp256k1_fe_mul(&z3, &a->z, &z2);
@@ -127,6 +174,7 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe_mul(&a->y, &a->y, &z3);
     secp256k1_fe_set_int(&a->z, 1);
     secp256k1_ge_set_xy(r, &a->x, &a->y);
+    secp256k1_ge_verify(r);
 }
 
 static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len) {
@@ -135,6 +183,7 @@ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a
     size_t last_i = SIZE_MAX;
 
     for (i = 0; i < len; i++) {
+        secp256k1_gej_verify(&a[i]);
         if (a[i].infinity) {
             secp256k1_ge_set_infinity(&r[i]);
         } else {
@@ -168,6 +217,7 @@ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a
         if (!a[i].infinity) {
             secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x);
         }
+        secp256k1_ge_verify(&r[i]);
     }
 }
 
@@ -176,21 +226,25 @@ static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const se
     secp256k1_fe zs;
 
     if (len > 0) {
+        /* Verify inputs a[len-1] and zr[len-1]. */
+        secp256k1_ge_verify(&a[i]);
+        secp256k1_fe_verify(&zr[i]);
         /* Ensure all y values are in weak normal form for fast negation of points */
         secp256k1_fe_normalize_weak(&a[i].y);
         zs = zr[i];
 
         /* Work our way backwards, using the z-ratios to scale the x/y values. */
         while (i > 0) {
-            secp256k1_gej tmpa;
+            /* Verify all inputs a[i] and zr[i]. */
+            secp256k1_fe_verify(&zr[i]);
+            secp256k1_ge_verify(&a[i]);
             if (i != len - 1) {
                 secp256k1_fe_mul(&zs, &zs, &zr[i]);
             }
             i--;
-            tmpa.x = a[i].x;
-            tmpa.y = a[i].y;
-            tmpa.infinity = 0;
-            secp256k1_ge_set_gej_zinv(&a[i], &tmpa, &zs);
+            secp256k1_ge_set_ge_zinv(&a[i], &a[i], &zs);
+            /* Verify the output a[i]. */
+            secp256k1_ge_verify(&a[i]);
         }
     }
 }
@@ -200,12 +254,14 @@ static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
     secp256k1_fe_clear(&r->z);
+    secp256k1_gej_verify(r);
 }
 
 static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
     r->infinity = 1;
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
+    secp256k1_ge_verify(r);
 }
 
 static void secp256k1_gej_clear(secp256k1_gej *r) {
@@ -223,31 +279,35 @@ static void secp256k1_ge_clear(secp256k1_ge *r) {
 
 static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
     secp256k1_fe x2, x3;
+    int ret;
+    secp256k1_fe_verify(x);
     r->x = *x;
     secp256k1_fe_sqr(&x2, x);
     secp256k1_fe_mul(&x3, x, &x2);
     r->infinity = 0;
     secp256k1_fe_add_int(&x3, SECP256K1_B);
-    if (!secp256k1_fe_sqrt(&r->y, &x3)) {
-        return 0;
-    }
+    ret = secp256k1_fe_sqrt(&r->y, &x3);
     secp256k1_fe_normalize_var(&r->y);
     if (secp256k1_fe_is_odd(&r->y) != odd) {
         secp256k1_fe_negate(&r->y, &r->y, 1);
     }
-    return 1;
-
+    secp256k1_ge_verify(r);
+    return ret;
 }
 
 static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
+   secp256k1_ge_verify(a);
    r->infinity = a->infinity;
    r->x = a->x;
    r->y = a->y;
    secp256k1_fe_set_int(&r->z, 1);
+   secp256k1_gej_verify(r);
 }
 
 static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b) {
     secp256k1_gej tmp;
+    secp256k1_gej_verify(b);
+    secp256k1_gej_verify(a);
     secp256k1_gej_neg(&tmp, a);
     secp256k1_gej_add_var(&tmp, &tmp, b, NULL);
     return secp256k1_gej_is_infinity(&tmp);
@@ -255,6 +315,8 @@ static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b)
 
 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
     secp256k1_fe r, r2;
+    secp256k1_fe_verify(x);
+    secp256k1_gej_verify(a);
     VERIFY_CHECK(!a->infinity);
     secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
     r2 = a->x; secp256k1_fe_normalize_weak(&r2);
@@ -262,20 +324,24 @@ static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a)
 }
 
 static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
+    secp256k1_gej_verify(a);
     r->infinity = a->infinity;
     r->x = a->x;
     r->y = a->y;
     r->z = a->z;
     secp256k1_fe_normalize_weak(&r->y);
     secp256k1_fe_negate(&r->y, &r->y, 1);
+    secp256k1_gej_verify(r);
 }
 
 static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
+    secp256k1_gej_verify(a);
     return a->infinity;
 }
 
 static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
     secp256k1_fe y2, x3;
+    secp256k1_ge_verify(a);
     if (a->infinity) {
         return 0;
     }
@@ -291,6 +357,7 @@ static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp25
     /* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */
     secp256k1_fe l, s, t;
 
+    secp256k1_gej_verify(a);
     r->infinity = a->infinity;
 
     /* Formula used:
@@ -317,6 +384,7 @@ static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp25
     secp256k1_fe_mul(&r->y, &t, &l);       /* Y3 = L*(X3 + T) (1) */
     secp256k1_fe_add(&r->y, &s);           /* Y3 = L*(X3 + T) + S^2 (2) */
     secp256k1_fe_negate(&r->y, &r->y, 2);  /* Y3 = -(L*(X3 + T) + S^2) (3) */
+    secp256k1_gej_verify(r);
 }
 
 static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
@@ -330,6 +398,7 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
      *  the infinity flag even though the point doubles to infinity, and the result
      *  point will be gibberish (z = 0 but infinity = 0).
      */
+    secp256k1_gej_verify(a);
     if (a->infinity) {
         secp256k1_gej_set_infinity(r);
         if (rzr != NULL) {
@@ -344,12 +413,15 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
     }
 
     secp256k1_gej_double(r, a);
+    secp256k1_gej_verify(r);
 }
 
 static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
     /* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
     secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
+    secp256k1_gej_verify(a);
+    secp256k1_gej_verify(b);
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         *r = *b;
@@ -404,11 +476,14 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
     secp256k1_fe_mul(&r->y, &t, &i);
     secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
+    secp256k1_gej_verify(r);
 }
 
 static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
     /* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
     secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t;
+    secp256k1_gej_verify(a);
+    secp256k1_ge_verify(b);
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         secp256k1_gej_set_ge(r, b);
@@ -461,12 +536,16 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
     secp256k1_fe_mul(&r->y, &t, &i);
     secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
+    secp256k1_gej_verify(r);
+    if (rzr != NULL) secp256k1_fe_verify(rzr);
 }
 
 static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
     /* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
     secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
+    secp256k1_ge_verify(b);
+    secp256k1_fe_verify(bzinv);
     if (a->infinity) {
         secp256k1_fe bzinv2, bzinv3;
         r->infinity = b->infinity;
@@ -525,6 +604,7 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
     secp256k1_fe_mul(&r->y, &t, &i);
     secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
+    secp256k1_gej_verify(r);
 }
 
 
@@ -533,6 +613,8 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
     secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
     secp256k1_fe m_alt, rr_alt;
     int degenerate;
+    secp256k1_gej_verify(a);
+    secp256k1_ge_verify(b);
     VERIFY_CHECK(!b->infinity);
     VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
 
@@ -658,21 +740,28 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
      * We have degenerate = false, r->z = (y1 + y2) * Z.
      * Then r->infinity = ((y1 + y2)Z == 0) = (y1 == -y2) = false. */
     r->infinity = secp256k1_fe_normalizes_to_zero(&r->z);
+    secp256k1_gej_verify(r);
 }
 
 static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
     /* Operations: 4 mul, 1 sqr */
     secp256k1_fe zz;
-    VERIFY_CHECK(!secp256k1_fe_is_zero(s));
+    secp256k1_gej_verify(r);
+    secp256k1_fe_verify(s);
+#ifdef VERIFY
+    VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero_var(s));
+#endif
     secp256k1_fe_sqr(&zz, s);
     secp256k1_fe_mul(&r->x, &r->x, &zz);                /* r->x *= s^2 */
     secp256k1_fe_mul(&r->y, &r->y, &zz);
     secp256k1_fe_mul(&r->y, &r->y, s);                  /* r->y *= s^3 */
     secp256k1_fe_mul(&r->z, &r->z, s);                  /* r->z *= s   */
+    secp256k1_gej_verify(r);
 }
 
 static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
     secp256k1_fe x, y;
+    secp256k1_ge_verify(a);
     VERIFY_CHECK(!a->infinity);
     x = a->x;
     secp256k1_fe_normalize(&x);
@@ -686,14 +775,18 @@ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storag
     secp256k1_fe_from_storage(&r->x, &a->x);
     secp256k1_fe_from_storage(&r->y, &a->y);
     r->infinity = 0;
+    secp256k1_ge_verify(r);
 }
 
 static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) {
+    secp256k1_gej_verify(r);
+    secp256k1_gej_verify(a);
     secp256k1_fe_cmov(&r->x, &a->x, flag);
     secp256k1_fe_cmov(&r->y, &a->y, flag);
     secp256k1_fe_cmov(&r->z, &a->z, flag);
 
     r->infinity ^= (r->infinity ^ a->infinity) & flag;
+    secp256k1_gej_verify(r);
 }
 
 static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
@@ -703,7 +796,9 @@ static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r,
 
 static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
     *r = *a;
+    secp256k1_ge_verify(a);
     secp256k1_fe_mul(&r->x, &r->x, &secp256k1_const_beta);
+    secp256k1_ge_verify(r);
 }
 
 static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
@@ -711,6 +806,7 @@ static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
     secp256k1_gej out;
     int i;
 
+    secp256k1_ge_verify(ge);
     /* A very simple EC multiplication ladder that avoids a dependency on ecmult. */
     secp256k1_gej_set_infinity(&out);
     for (i = 0; i < 32; ++i) {
diff --git a/src/int128_native_impl.h b/src/int128_native_impl.h
index 996e542cf9..7f02e1590b 100644
--- a/src/int128_native_impl.h
+++ b/src/int128_native_impl.h
@@ -2,6 +2,7 @@
 #define SECP256K1_INT128_NATIVE_IMPL_H
 
 #include "int128.h"
+#include "util.h"
 
 static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) {
     *r = (((uint128_t)hi) << 64) + lo;
diff --git a/src/int128_struct_impl.h b/src/int128_struct_impl.h
index cc17bad167..990982da84 100644
--- a/src/int128_struct_impl.h
+++ b/src/int128_struct_impl.h
@@ -2,6 +2,7 @@
 #define SECP256K1_INT128_STRUCT_IMPL_H
 
 #include "int128.h"
+#include "util.h"
 
 #if defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) /* MSVC */
 #    include <intrin.h>
diff --git a/src/modinv32_impl.h b/src/modinv32_impl.h
index 8e400b697b..0ea2699863 100644
--- a/src/modinv32_impl.h
+++ b/src/modinv32_impl.h
@@ -64,7 +64,7 @@ static void secp256k1_modinv32_normalize_30(secp256k1_modinv32_signed30 *r, int3
     const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
     int32_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4],
             r5 = r->v[5], r6 = r->v[6], r7 = r->v[7], r8 = r->v[8];
-    int32_t cond_add, cond_negate;
+    volatile int32_t cond_add, cond_negate;
 
 #ifdef VERIFY
     /* Verify that all limbs are in range (-2^30,2^30). */
@@ -186,7 +186,8 @@ static int32_t secp256k1_modinv32_divsteps_30(int32_t zeta, uint32_t f0, uint32_
      * being inside [-2^31,2^31) means that casting to signed works correctly.
      */
     uint32_t u = 1, v = 0, q = 0, r = 1;
-    uint32_t c1, c2, f = f0, g = g0, x, y, z;
+    volatile uint32_t c1, c2;
+    uint32_t mask1, mask2, f = f0, g = g0, x, y, z;
     int i;
 
     for (i = 0; i < 30; ++i) {
@@ -195,23 +196,25 @@ static int32_t secp256k1_modinv32_divsteps_30(int32_t zeta, uint32_t f0, uint32_
         VERIFY_CHECK((q * f0 + r * g0) == g << i);
         /* Compute conditional masks for (zeta < 0) and for (g & 1). */
         c1 = zeta >> 31;
-        c2 = -(g & 1);
+        mask1 = c1;
+        c2 = g & 1;
+        mask2 = -c2;
         /* Compute x,y,z, conditionally negated versions of f,u,v. */
-        x = (f ^ c1) - c1;
-        y = (u ^ c1) - c1;
-        z = (v ^ c1) - c1;
+        x = (f ^ mask1) - mask1;
+        y = (u ^ mask1) - mask1;
+        z = (v ^ mask1) - mask1;
         /* Conditionally add x,y,z to g,q,r. */
-        g += x & c2;
-        q += y & c2;
-        r += z & c2;
-        /* In what follows, c1 is a condition mask for (zeta < 0) and (g & 1). */
-        c1 &= c2;
+        g += x & mask2;
+        q += y & mask2;
+        r += z & mask2;
+        /* In what follows, mask1 is a condition mask for (zeta < 0) and (g & 1). */
+        mask1 &= mask2;
         /* Conditionally change zeta into -zeta-2 or zeta-1. */
-        zeta = (zeta ^ c1) - 1;
+        zeta = (zeta ^ mask1) - 1;
         /* Conditionally add g,q,r to f,u,v. */
-        f += g & c1;
-        u += q & c1;
-        v += r & c1;
+        f += g & mask1;
+        u += q & mask1;
+        v += r & mask1;
         /* Shifts */
         g >>= 1;
         u <<= 1;
diff --git a/src/modinv64_impl.h b/src/modinv64_impl.h
index e33727d385..c7cef872a4 100644
--- a/src/modinv64_impl.h
+++ b/src/modinv64_impl.h
@@ -88,7 +88,7 @@ static int secp256k1_modinv64_det_check_pow2(const secp256k1_modinv64_trans2x2 *
 static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int64_t sign, const secp256k1_modinv64_modinfo *modinfo) {
     const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
     int64_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4];
-    int64_t cond_add, cond_negate;
+    volatile int64_t cond_add, cond_negate;
 
 #ifdef VERIFY
     /* Verify that all limbs are in range (-2^62,2^62). */
@@ -175,7 +175,8 @@ static int64_t secp256k1_modinv64_divsteps_59(int64_t zeta, uint64_t f0, uint64_
      * being inside [-2^63,2^63) means that casting to signed works correctly.
      */
     uint64_t u = 8, v = 0, q = 0, r = 8;
-    uint64_t c1, c2, f = f0, g = g0, x, y, z;
+    volatile uint64_t c1, c2;
+    uint64_t mask1, mask2, f = f0, g = g0, x, y, z;
     int i;
 
     for (i = 3; i < 62; ++i) {
@@ -184,23 +185,25 @@ static int64_t secp256k1_modinv64_divsteps_59(int64_t zeta, uint64_t f0, uint64_
         VERIFY_CHECK((q * f0 + r * g0) == g << i);
         /* Compute conditional masks for (zeta < 0) and for (g & 1). */
         c1 = zeta >> 63;
-        c2 = -(g & 1);
+        mask1 = c1;
+        c2 = g & 1;
+        mask2 = -c2;
         /* Compute x,y,z, conditionally negated versions of f,u,v. */
-        x = (f ^ c1) - c1;
-        y = (u ^ c1) - c1;
-        z = (v ^ c1) - c1;
+        x = (f ^ mask1) - mask1;
+        y = (u ^ mask1) - mask1;
+        z = (v ^ mask1) - mask1;
         /* Conditionally add x,y,z to g,q,r. */
-        g += x & c2;
-        q += y & c2;
-        r += z & c2;
+        g += x & mask2;
+        q += y & mask2;
+        r += z & mask2;
         /* In what follows, c1 is a condition mask for (zeta < 0) and (g & 1). */
-        c1 &= c2;
+        mask1 &= mask2;
         /* Conditionally change zeta into -zeta-2 or zeta-1. */
-        zeta = (zeta ^ c1) - 1;
+        zeta = (zeta ^ mask1) - 1;
         /* Conditionally add g,q,r to f,u,v. */
-        f += g & c1;
-        u += q & c1;
-        v += r & c1;
+        f += g & mask1;
+        u += q & mask1;
+        v += r & mask1;
         /* Shifts */
         g >>= 1;
         u <<= 1;
diff --git a/src/modules/ecdh/main_impl.h b/src/modules/ecdh/main_impl.h
index 5408c9de70..82b082a9f0 100644
--- a/src/modules/ecdh/main_impl.h
+++ b/src/modules/ecdh/main_impl.h
@@ -50,7 +50,7 @@ int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const se
     overflow |= secp256k1_scalar_is_zero(&s);
     secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow);
 
-    secp256k1_ecmult_const(&res, &pt, &s, 256);
+    secp256k1_ecmult_const(&res, &pt, &s);
     secp256k1_ge_set_gej(&pt, &res);
 
     /* Compute a hash of the point */
diff --git a/src/modules/extrakeys/main_impl.h b/src/modules/extrakeys/main_impl.h
index e1003052f4..0c7e266777 100644
--- a/src/modules/extrakeys/main_impl.h
+++ b/src/modules/extrakeys/main_impl.h
@@ -9,6 +9,7 @@
 
 #include "../../../include/secp256k1.h"
 #include "../../../include/secp256k1_extrakeys.h"
+#include "../../util.h"
 
 static SECP256K1_INLINE int secp256k1_xonly_pubkey_load(const secp256k1_context* ctx, secp256k1_ge *ge, const secp256k1_xonly_pubkey *pubkey) {
     return secp256k1_pubkey_load(ctx, ge, (const secp256k1_pubkey *) pubkey);
@@ -27,7 +28,7 @@ int secp256k1_xonly_pubkey_parse(const secp256k1_context* ctx, secp256k1_xonly_p
     memset(pubkey, 0, sizeof(*pubkey));
     ARG_CHECK(input32 != NULL);
 
-    if (!secp256k1_fe_set_b32(&x, input32)) {
+    if (!secp256k1_fe_set_b32_limit(&x, input32)) {
         return 0;
     }
     if (!secp256k1_ge_set_xo_var(&pk, &x, 0)) {
diff --git a/src/modules/extrakeys/tests_exhaustive_impl.h b/src/modules/extrakeys/tests_exhaustive_impl.h
index 5ecc90d50f..d3d817a131 100644
--- a/src/modules/extrakeys/tests_exhaustive_impl.h
+++ b/src/modules/extrakeys/tests_exhaustive_impl.h
@@ -47,7 +47,7 @@ static void test_exhaustive_extrakeys(const secp256k1_context *ctx, const secp25
         CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0);
 
         /* Compare the xonly_pubkey bytes against the precomputed group. */
-        secp256k1_fe_set_b32(&fe, xonly_pubkey_bytes[i - 1]);
+        secp256k1_fe_set_b32_mod(&fe, xonly_pubkey_bytes[i - 1]);
         CHECK(secp256k1_fe_equal_var(&fe, &group[i].x));
 
         /* Check the parity against the precomputed group. */
diff --git a/src/modules/frost/main_impl.h b/src/modules/frost/main_impl.h
index c630b9ffdd..228aecd01d 100644
--- a/src/modules/frost/main_impl.h
+++ b/src/modules/frost/main_impl.h
@@ -20,7 +20,6 @@ static const unsigned char hash_context_prefix_h5[29] = "FROST-secp256k1-SHA256-
 #define SHA256_SIZE (32U)
 #define SERIALIZED_PUBKEY_X_ONLY_SIZE (32U)
 #define SERIALIZED_PUBKEY_XY_SIZE (64U)
-#define ECMULT_CONST_256_BIT_SIZE 256
 
 typedef struct {
     uint32_t index;
@@ -62,7 +61,7 @@ static void secp256k1_gej_mul_scalar(secp256k1_gej *result, const secp256k1_gej
         return;
     }
     secp256k1_ge_set_gej_safe(&pt_ge, pt);
-    secp256k1_ecmult_const(result, &pt_ge, sc, ECMULT_CONST_256_BIT_SIZE);
+    secp256k1_ecmult_const(result, &pt_ge, sc);
 }
 
 static SECP256K1_WARN_UNUSED_RESULT int secp256k1_gej_eq(const secp256k1_gej *a, const secp256k1_gej *b) {
@@ -100,8 +99,8 @@ static void serialize_point(const secp256k1_gej *point, unsigned char *output64)
 
 static void deserialize_point(secp256k1_gej *output, const unsigned char *point64) {
     secp256k1_ge normalized_point;
-    secp256k1_fe_set_b32(&normalized_point.x, point64);
-    secp256k1_fe_set_b32(&normalized_point.y, point64 + SERIALIZED_PUBKEY_X_ONLY_SIZE);
+    secp256k1_fe_set_b32_mod(&normalized_point.x, point64);
+    secp256k1_fe_set_b32_mod(&normalized_point.y, point64 + SERIALIZED_PUBKEY_X_ONLY_SIZE);
     normalized_point.infinity = 0;
     secp256k1_gej_set_ge(output, &normalized_point);
 }
@@ -129,7 +128,9 @@ static SECP256K1_WARN_UNUSED_RESULT int deserialize_frost_signature(secp256k1_fr
                                                                     const unsigned char *serialized_signature) {
     secp256k1_fe x;
     secp256k1_ge deserialized_point;
-    secp256k1_fe_set_b32(&x, serialized_signature);
+    if (secp256k1_fe_set_b32_limit(&x, serialized_signature) == 0){
+        return 0;
+    }
     if (secp256k1_ge_set_xo_var(&deserialized_point, &x, 0) == 0) {
         return 0;
     }
@@ -274,10 +275,10 @@ SECP256K1_API int secp256k1_frost_pubkey_save(unsigned char *pubkey33,
     }
     compressed = 1;
 
-    if (secp256k1_fe_set_b32(&pk.x, pubkey->public_key) == 0) {
+    if (secp256k1_fe_set_b32_limit(&pk.x, pubkey->public_key) == 0) {
         return 0;
     }
-    if (secp256k1_fe_set_b32(&pk.y, pubkey->public_key + SERIALIZED_PUBKEY_X_ONLY_SIZE) == 0) {
+    if (secp256k1_fe_set_b32_limit(&pk.y, pubkey->public_key + SERIALIZED_PUBKEY_X_ONLY_SIZE) == 0) {
         return 0;
     }
 
@@ -295,10 +296,10 @@ SECP256K1_API int secp256k1_frost_pubkey_save(unsigned char *pubkey33,
     }
     secp256k1_ge_clear(&pk);
 
-    if (secp256k1_fe_set_b32(&gpk.x, pubkey->group_public_key) == 0) {
+    if (secp256k1_fe_set_b32_limit(&gpk.x, pubkey->group_public_key) == 0) {
         return 0;
     }
-    if (secp256k1_fe_set_b32(&gpk.y, pubkey->group_public_key + SERIALIZED_PUBKEY_X_ONLY_SIZE) == 0) {
+    if (secp256k1_fe_set_b32_limit(&gpk.y, pubkey->group_public_key + SERIALIZED_PUBKEY_X_ONLY_SIZE) == 0) {
         return 0;
     }
 
diff --git a/src/modules/recovery/main_impl.h b/src/modules/recovery/main_impl.h
index e7906eb62e..76a005e017 100644
--- a/src/modules/recovery/main_impl.h
+++ b/src/modules/recovery/main_impl.h
@@ -98,7 +98,7 @@ static int secp256k1_ecdsa_sig_recover(const secp256k1_scalar *sigr, const secp2
     }
 
     secp256k1_scalar_get_b32(brx, sigr);
-    r = secp256k1_fe_set_b32(&fx, brx);
+    r = secp256k1_fe_set_b32_limit(&fx, brx);
     (void)r;
     VERIFY_CHECK(r); /* brx comes from a scalar, so is less than the order; certainly less than p */
     if (recid & 2) {
diff --git a/src/modules/schnorrsig/main_impl.h b/src/modules/schnorrsig/main_impl.h
index cd651591c4..4e7b45a045 100644
--- a/src/modules/schnorrsig/main_impl.h
+++ b/src/modules/schnorrsig/main_impl.h
@@ -232,7 +232,7 @@ int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned cha
     ARG_CHECK(msg != NULL || msglen == 0);
     ARG_CHECK(pubkey != NULL);
 
-    if (!secp256k1_fe_set_b32(&rx, &sig64[0])) {
+    if (!secp256k1_fe_set_b32_limit(&rx, &sig64[0])) {
         return 0;
     }
 
diff --git a/src/modules/schnorrsig/tests_impl.h b/src/modules/schnorrsig/tests_impl.h
index 062005ee63..ddcb8a599b 100644
--- a/src/modules/schnorrsig/tests_impl.h
+++ b/src/modules/schnorrsig/tests_impl.h
@@ -215,28 +215,36 @@ static void test_schnorrsig_sha256_tagged(void) {
 
 /* Helper function for schnorrsig_bip_vectors
  * Signs the message and checks that it's the same as expected_sig. */
-static void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, const unsigned char *aux_rand, const unsigned char *msg32, const unsigned char *expected_sig) {
+static void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, const unsigned char *aux_rand, const unsigned char *msg, size_t msglen, const unsigned char *expected_sig) {
     unsigned char sig[64];
     secp256k1_keypair keypair;
     secp256k1_xonly_pubkey pk, pk_expected;
 
+    secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT;
+    extraparams.ndata = (unsigned char*)aux_rand;
+
     CHECK(secp256k1_keypair_create(CTX, &keypair, sk));
-    CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg32, &keypair, aux_rand));
+    CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, msglen, &keypair, &extraparams));
     CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0);
+    if (msglen == 32) {
+        memset(sig, 0, 64);
+        CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypair, aux_rand));
+        CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0);
+    }
 
     CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk_expected, pk_serialized));
     CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair));
     CHECK(secp256k1_memcmp_var(&pk, &pk_expected, sizeof(pk)) == 0);
-    CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg32, 32, &pk));
+    CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, msglen, &pk));
 }
 
 /* Helper function for schnorrsig_bip_vectors
  * Checks that both verify and verify_batch (TODO) return the same value as expected. */
-static void test_schnorrsig_bip_vectors_check_verify(const unsigned char *pk_serialized, const unsigned char *msg32, const unsigned char *sig, int expected) {
+static void test_schnorrsig_bip_vectors_check_verify(const unsigned char *pk_serialized, const unsigned char *msg, size_t msglen, const unsigned char *sig, int expected) {
     secp256k1_xonly_pubkey pk;
 
     CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk, pk_serialized));
-    CHECK(expected == secp256k1_schnorrsig_verify(CTX, sig, msg32, 32, &pk));
+    CHECK(expected == secp256k1_schnorrsig_verify(CTX, sig, msg, msglen, &pk));
 }
 
 /* Test vectors according to BIP-340 ("Schnorr Signatures for secp256k1"). See
@@ -256,7 +264,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0,
             0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9
         };
-        unsigned char aux_rand[32] = {
+        const unsigned char aux_rand[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
@@ -278,8 +286,8 @@ static void test_schnorrsig_bip_vectors(void) {
             0xEB, 0xEE, 0xE8, 0xFD, 0xB2, 0x17, 0x2F, 0x47,
             0x7D, 0xF4, 0x90, 0x0D, 0x31, 0x05, 0x36, 0xC0
         };
-        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig);
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1);
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
     }
     {
         /* Test vector 1 */
@@ -295,7 +303,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8,
             0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59
         };
-        unsigned char aux_rand[32] = {
+        const unsigned char aux_rand[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
@@ -317,8 +325,8 @@ static void test_schnorrsig_bip_vectors(void) {
             0x89, 0x7E, 0xFC, 0xB6, 0x39, 0xEA, 0x87, 0x1C,
             0xFA, 0x95, 0xF6, 0xDE, 0x33, 0x9E, 0x4B, 0x0A
         };
-        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig);
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1);
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
     }
     {
         /* Test vector 2 */
@@ -334,7 +342,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x01, 0x39, 0x71, 0x53, 0x09, 0xB0, 0x86, 0xC9,
             0x60, 0xE1, 0x8F, 0xD9, 0x69, 0x77, 0x4E, 0xB8
         };
-        unsigned char aux_rand[32] = {
+        const unsigned char aux_rand[32] = {
             0xC8, 0x7A, 0xA5, 0x38, 0x24, 0xB4, 0xD7, 0xAE,
             0x2E, 0xB0, 0x35, 0xA2, 0xB5, 0xBB, 0xBC, 0xCC,
             0x08, 0x0E, 0x76, 0xCD, 0xC6, 0xD1, 0x69, 0x2C,
@@ -356,8 +364,8 @@ static void test_schnorrsig_bip_vectors(void) {
             0x7A, 0xDE, 0xA9, 0x8D, 0x82, 0xF8, 0x48, 0x1E,
             0x0E, 0x1E, 0x03, 0x67, 0x4A, 0x6F, 0x3F, 0xB7
         };
-        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig);
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1);
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
     }
     {
         /* Test vector 3 */
@@ -373,7 +381,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x3A, 0x0D, 0x95, 0xFB, 0xF2, 0x1D, 0x46, 0x8A,
             0x1B, 0x33, 0xF8, 0xC1, 0x60, 0xD8, 0xF5, 0x17
         };
-        unsigned char aux_rand[32] = {
+        const unsigned char aux_rand[32] = {
             0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
             0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
             0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
@@ -395,8 +403,8 @@ static void test_schnorrsig_bip_vectors(void) {
             0xF2, 0x5F, 0xD7, 0x88, 0x81, 0xEB, 0xB3, 0x27,
             0x71, 0xFC, 0x59, 0x22, 0xEF, 0xC6, 0x6E, 0xA3
         };
-        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sig);
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1);
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
     }
     {
         /* Test vector 4 */
@@ -422,7 +430,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x60, 0xCB, 0x71, 0xC0, 0x4E, 0x80, 0xF5, 0x93,
             0x06, 0x0B, 0x07, 0xD2, 0x83, 0x08, 0xD7, 0xF4
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 1);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
     }
     {
         /* Test vector 5 */
@@ -460,7 +468,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x7A, 0x73, 0xC6, 0x43, 0xE1, 0x66, 0xBE, 0x5E,
             0xBE, 0xAF, 0xA3, 0x4B, 0x1A, 0xC5, 0x53, 0xE2
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 7 */
@@ -486,7 +494,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x62, 0x2A, 0x95, 0x4C, 0xFE, 0x54, 0x57, 0x35,
             0xAA, 0xEA, 0x51, 0x34, 0xFC, 0xCD, 0xB2, 0xBD
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 8 */
@@ -512,7 +520,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0xE8, 0xD7, 0xC9, 0x3E, 0x00, 0xC5, 0xED, 0x0C,
             0x18, 0x34, 0xFF, 0x0D, 0x0C, 0x2E, 0x6D, 0xA6
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 9 */
@@ -538,7 +546,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0x4F, 0xB7, 0x34, 0x76, 0xF0, 0xD5, 0x94, 0xDC,
             0xB6, 0x5C, 0x64, 0x25, 0xBD, 0x18, 0x60, 0x51
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 10 */
@@ -564,7 +572,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0xDB, 0xA8, 0x7F, 0x11, 0xAC, 0x67, 0x54, 0xF9,
             0x37, 0x80, 0xD5, 0xA1, 0x83, 0x7C, 0xF1, 0x97
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 11 */
@@ -590,7 +598,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0xD1, 0xD7, 0x13, 0xA8, 0xAE, 0x82, 0xB3, 0x2F,
             0xA7, 0x9D, 0x5F, 0x7F, 0xC4, 0x07, 0xD3, 0x9B
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 12 */
@@ -616,7 +624,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0xD1, 0xD7, 0x13, 0xA8, 0xAE, 0x82, 0xB3, 0x2F,
             0xA7, 0x9D, 0x5F, 0x7F, 0xC4, 0x07, 0xD3, 0x9B
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 13 */
@@ -642,7 +650,7 @@ static void test_schnorrsig_bip_vectors(void) {
             0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B,
             0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41
         };
-        test_schnorrsig_bip_vectors_check_verify(pk, msg, sig, 0);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0);
     }
     {
         /* Test vector 14 */
@@ -656,6 +664,147 @@ static void test_schnorrsig_bip_vectors(void) {
         /* No need to check the signature of the test vector as parsing the pubkey already fails */
         CHECK(!secp256k1_xonly_pubkey_parse(CTX, &pk_parsed, pk));
     }
+    {
+        /* Test vector 15 */
+        const unsigned char sk[32] = {
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+        };
+        const unsigned char pk[32] = {
+            0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4,
+            0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22,
+            0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23,
+            0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17,
+        };
+        const unsigned char aux_rand[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        };
+        /* const unsigned char msg[0] = {}; */
+        const unsigned char sig[64] = {
+            0x71, 0x53, 0x5D, 0xB1, 0x65, 0xEC, 0xD9, 0xFB,
+            0xBC, 0x04, 0x6E, 0x5F, 0xFA, 0xEA, 0x61, 0x18,
+            0x6B, 0xB6, 0xAD, 0x43, 0x67, 0x32, 0xFC, 0xCC,
+            0x25, 0x29, 0x1A, 0x55, 0x89, 0x54, 0x64, 0xCF,
+            0x60, 0x69, 0xCE, 0x26, 0xBF, 0x03, 0x46, 0x62,
+            0x28, 0xF1, 0x9A, 0x3A, 0x62, 0xDB, 0x8A, 0x64,
+            0x9F, 0x2D, 0x56, 0x0F, 0xAC, 0x65, 0x28, 0x27,
+            0xD1, 0xAF, 0x05, 0x74, 0xE4, 0x27, 0xAB, 0x63,
+        };
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, NULL, 0, sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, NULL, 0, sig, 1);
+    }
+    {
+        /* Test vector 16 */
+        const unsigned char sk[32] = {
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+        };
+        const unsigned char pk[32] = {
+            0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4,
+            0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22,
+            0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23,
+            0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17,
+        };
+        const unsigned char aux_rand[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        };
+        const unsigned char msg[] = { 0x11 };
+        const unsigned char sig[64] = {
+            0x08, 0xA2, 0x0A, 0x0A, 0xFE, 0xF6, 0x41, 0x24,
+            0x64, 0x92, 0x32, 0xE0, 0x69, 0x3C, 0x58, 0x3A,
+            0xB1, 0xB9, 0x93, 0x4A, 0xE6, 0x3B, 0x4C, 0x35,
+            0x11, 0xF3, 0xAE, 0x11, 0x34, 0xC6, 0xA3, 0x03,
+            0xEA, 0x31, 0x73, 0xBF, 0xEA, 0x66, 0x83, 0xBD,
+            0x10, 0x1F, 0xA5, 0xAA, 0x5D, 0xBC, 0x19, 0x96,
+            0xFE, 0x7C, 0xAC, 0xFC, 0x5A, 0x57, 0x7D, 0x33,
+            0xEC, 0x14, 0x56, 0x4C, 0xEC, 0x2B, 0xAC, 0xBF,
+        };
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
+    }
+    {
+        /* Test vector 17 */
+        const unsigned char sk[32] = {
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+        };
+        const unsigned char pk[32] = {
+            0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4,
+            0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22,
+            0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23,
+            0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17,
+        };
+        const unsigned char aux_rand[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        };
+        const unsigned char msg[] = {
+            0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08,
+            0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F, 0x10,
+            0x11,
+        };
+        const unsigned char sig[64] = {
+            0x51, 0x30, 0xF3, 0x9A, 0x40, 0x59, 0xB4, 0x3B,
+            0xC7, 0xCA, 0xC0, 0x9A, 0x19, 0xEC, 0xE5, 0x2B,
+            0x5D, 0x86, 0x99, 0xD1, 0xA7, 0x1E, 0x3C, 0x52,
+            0xDA, 0x9A, 0xFD, 0xB6, 0xB5, 0x0A, 0xC3, 0x70,
+            0xC4, 0xA4, 0x82, 0xB7, 0x7B, 0xF9, 0x60, 0xF8,
+            0x68, 0x15, 0x40, 0xE2, 0x5B, 0x67, 0x71, 0xEC,
+            0xE1, 0xE5, 0xA3, 0x7F, 0xD8, 0x0E, 0x5A, 0x51,
+            0x89, 0x7C, 0x55, 0x66, 0xA9, 0x7E, 0xA5, 0xA5,
+        };
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
+    }
+    {
+        /* Test vector 18 */
+        const unsigned char sk[32] = {
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+            0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40,
+        };
+        const unsigned char pk[32] = {
+            0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4,
+            0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22,
+            0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23,
+            0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17,
+        };
+        const unsigned char aux_rand[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        };
+        const unsigned char sig[64] = {
+            0x40, 0x3B, 0x12, 0xB0, 0xD8, 0x55, 0x5A, 0x34,
+            0x41, 0x75, 0xEA, 0x7E, 0xC7, 0x46, 0x56, 0x63,
+            0x03, 0x32, 0x1E, 0x5D, 0xBF, 0xA8, 0xBE, 0x6F,
+            0x09, 0x16, 0x35, 0x16, 0x3E, 0xCA, 0x79, 0xA8,
+            0x58, 0x5E, 0xD3, 0xE3, 0x17, 0x08, 0x07, 0xE7,
+            0xC0, 0x3B, 0x72, 0x0F, 0xC5, 0x4C, 0x7B, 0x23,
+            0x89, 0x7F, 0xCB, 0xA0, 0xE9, 0xD0, 0xB4, 0xA0,
+            0x68, 0x94, 0xCF, 0xD2, 0x49, 0xF2, 0x23, 0x67,
+        };
+        unsigned char msg[100];
+        memset(msg, 0x99, sizeof(msg));
+        test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig);
+        test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1);
+    }
 }
 
 /* Nonce function that returns constant 0 */
diff --git a/src/scalar_4x64_impl.h b/src/scalar_4x64_impl.h
index 1959dae986..0d342fd847 100644
--- a/src/scalar_4x64_impl.h
+++ b/src/scalar_4x64_impl.h
@@ -10,6 +10,7 @@
 #include "checkmem.h"
 #include "int128.h"
 #include "modinv64_impl.h"
+#include "util.h"
 
 /* Limbs of the secp256k1 order. */
 #define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
@@ -110,8 +111,9 @@ static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a,
 
 static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
     secp256k1_uint128 t;
+    volatile int vflag = flag;
     VERIFY_CHECK(bit < 256);
-    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
+    bit += ((uint32_t) vflag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
     secp256k1_u128_from_u64(&t, r->d[0]);
     secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
     r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64);
@@ -188,7 +190,8 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
 static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
     /* If we are flag = 0, mask = 00...00 and this is a no-op;
      * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
-    uint64_t mask = !flag - 1;
+    volatile int vflag = flag;
+    uint64_t mask = -vflag;
     uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
     secp256k1_uint128 t;
     secp256k1_u128_from_u64(&t, r->d[0] ^ mask);
@@ -380,7 +383,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq %%r10, %q5\n"
     /* extract m6 */
     "movq %%r8, %q6\n"
-    : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
+    : "=&g"(m0), "=&g"(m1), "=&g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
     : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
     : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
 
diff --git a/src/scalar_8x32_impl.h b/src/scalar_8x32_impl.h
index a2555cbbcd..da9936dbd9 100644
--- a/src/scalar_8x32_impl.h
+++ b/src/scalar_8x32_impl.h
@@ -9,6 +9,7 @@
 
 #include "checkmem.h"
 #include "modinv32_impl.h"
+#include "util.h"
 
 /* Limbs of the secp256k1 order. */
 #define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
@@ -141,8 +142,9 @@ static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a,
 
 static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
     uint64_t t;
+    volatile int vflag = flag;
     VERIFY_CHECK(bit < 256);
-    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
+    bit += ((uint32_t) vflag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
     t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
     r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
     t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
@@ -241,7 +243,8 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
 static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
     /* If we are flag = 0, mask = 00...00 and this is a no-op;
      * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
-    uint32_t mask = !flag - 1;
+    volatile int vflag = flag;
+    uint32_t mask = -vflag;
     uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
     uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
     r->d[0] = t & nonzero; t >>= 32;
diff --git a/src/scalar_low_impl.h b/src/scalar_low_impl.h
index bfd1139110..428a5deb33 100644
--- a/src/scalar_low_impl.h
+++ b/src/scalar_low_impl.h
@@ -9,6 +9,7 @@
 
 #include "checkmem.h"
 #include "scalar.h"
+#include "util.h"
 
 #include <string.h>
 
diff --git a/src/secp256k1.c b/src/secp256k1.c
index 41281a521f..e8b92d9bd4 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -247,8 +247,8 @@ static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge,
     } else {
         /* Otherwise, fall back to 32-byte big endian for X and Y. */
         secp256k1_fe x, y;
-        secp256k1_fe_set_b32(&x, pubkey->data);
-        secp256k1_fe_set_b32(&y, pubkey->data + 32);
+        secp256k1_fe_set_b32_mod(&x, pubkey->data);
+        secp256k1_fe_set_b32_mod(&y, pubkey->data + 32);
         secp256k1_ge_set_xy(ge, &x, &y);
     }
     ARG_CHECK(!secp256k1_fe_is_zero(&ge->x));
diff --git a/src/testrand.h b/src/testrand.h
index d109bb9f8b..721099d039 100644
--- a/src/testrand.h
+++ b/src/testrand.h
@@ -7,6 +7,8 @@
 #ifndef SECP256K1_TESTRAND_H
 #define SECP256K1_TESTRAND_H
 
+#include "util.h"
+
 /* A non-cryptographic RNG used only for test infrastructure. */
 
 /** Seed the pseudorandom number generator for testing. */
diff --git a/src/testrand_impl.h b/src/testrand_impl.h
index e9b9d7ded4..1b7481a53b 100644
--- a/src/testrand_impl.h
+++ b/src/testrand_impl.h
@@ -13,6 +13,7 @@
 
 #include "testrand.h"
 #include "hash.h"
+#include "util.h"
 
 static uint64_t secp256k1_test_state[4];
 static uint64_t secp256k1_test_rng_integer;
diff --git a/src/tests.c b/src/tests.c
index 3e8c09486b..b65999d304 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -10,7 +10,12 @@
 
 #include <time.h>
 
+#ifdef USE_EXTERNAL_DEFAULT_CALLBACKS
+    #pragma message("Ignoring USE_EXTERNAL_CALLBACKS in tests.")
+    #undef USE_EXTERNAL_DEFAULT_CALLBACKS
+#endif
 #include "secp256k1.c"
+
 #include "../include/secp256k1.h"
 #include "../include/secp256k1_preallocated.h"
 #include "testrand_impl.h"
@@ -85,7 +90,7 @@ static void random_field_element_test(secp256k1_fe *fe) {
     do {
         unsigned char b32[32];
         secp256k1_testrand256_test(b32);
-        if (secp256k1_fe_set_b32(fe, b32)) {
+        if (secp256k1_fe_set_b32_limit(fe, b32)) {
             break;
         }
     } while(1);
@@ -2221,7 +2226,7 @@ static void scalar_test(void) {
         for (i = 0; i < 100; ++i) {
             int low;
             int shift = 1 + secp256k1_testrand_int(15);
-            int expected = r.d[0] % (1 << shift);
+            int expected = r.d[0] % (1ULL << shift);
             low = secp256k1_scalar_shr_int(&r, shift);
             CHECK(expected == low);
         }
@@ -2952,7 +2957,7 @@ static void random_fe(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
         secp256k1_testrand256(bin);
-        if (secp256k1_fe_set_b32(x, bin)) {
+        if (secp256k1_fe_set_b32_limit(x, bin)) {
             return;
         }
     } while(1);
@@ -2962,7 +2967,7 @@ static void random_fe_test(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
         secp256k1_testrand256_test(bin);
-        if (secp256k1_fe_set_b32(x, bin)) {
+        if (secp256k1_fe_set_b32_limit(x, bin)) {
             return;
         }
     } while(1);
@@ -3016,7 +3021,7 @@ static void run_field_convert(void) {
     unsigned char b322[32];
     secp256k1_fe_storage fes2;
     /* Check conversions to fe. */
-    CHECK(secp256k1_fe_set_b32(&fe2, b32));
+    CHECK(secp256k1_fe_set_b32_limit(&fe2, b32));
     CHECK(secp256k1_fe_equal_var(&fe, &fe2));
     secp256k1_fe_from_storage(&fe2, &fes);
     CHECK(secp256k1_fe_equal_var(&fe, &fe2));
@@ -3027,6 +3032,72 @@ static void run_field_convert(void) {
     CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0);
 }
 
+static void run_field_be32_overflow(void) {
+    {
+        static const unsigned char zero_overflow[32] = {
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F,
+        };
+        static const unsigned char zero[32] = { 0x00 };
+        unsigned char out[32];
+        secp256k1_fe fe;
+        CHECK(secp256k1_fe_set_b32_limit(&fe, zero_overflow) == 0);
+        secp256k1_fe_set_b32_mod(&fe, zero_overflow);
+        CHECK(secp256k1_fe_normalizes_to_zero(&fe) == 1);
+        secp256k1_fe_normalize(&fe);
+        CHECK(secp256k1_fe_is_zero(&fe) == 1);
+        secp256k1_fe_get_b32(out, &fe);
+        CHECK(secp256k1_memcmp_var(out, zero, 32) == 0);
+    }
+    {
+        static const unsigned char one_overflow[32] = {
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30,
+        };
+        static const unsigned char one[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        unsigned char out[32];
+        secp256k1_fe fe;
+        CHECK(secp256k1_fe_set_b32_limit(&fe, one_overflow) == 0);
+        secp256k1_fe_set_b32_mod(&fe, one_overflow);
+        secp256k1_fe_normalize(&fe);
+        CHECK(secp256k1_fe_cmp_var(&fe, &secp256k1_fe_one) == 0);
+        secp256k1_fe_get_b32(out, &fe);
+        CHECK(secp256k1_memcmp_var(out, one, 32) == 0);
+    }
+    {
+        static const unsigned char ff_overflow[32] = {
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+        };
+        static const unsigned char ff[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x03, 0xD0,
+        };
+        unsigned char out[32];
+        secp256k1_fe fe;
+        const secp256k1_fe fe_ff = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0x01, 0x000003d0);
+        CHECK(secp256k1_fe_set_b32_limit(&fe, ff_overflow) == 0);
+        secp256k1_fe_set_b32_mod(&fe, ff_overflow);
+        secp256k1_fe_normalize(&fe);
+        CHECK(secp256k1_fe_cmp_var(&fe, &fe_ff) == 0);
+        secp256k1_fe_get_b32(out, &fe);
+        CHECK(secp256k1_memcmp_var(out, ff, 32) == 0);
+    }
+}
+
 /* Returns true if two field elements have the same representation. */
 static int fe_identical(const secp256k1_fe *a, const secp256k1_fe *b) {
     int ret = 1;
@@ -3605,7 +3676,7 @@ static void run_inverse_tests(void)
         b32[31] = i & 0xff;
         b32[30] = (i >> 8) & 0xff;
         secp256k1_scalar_set_b32(&x_scalar, b32, NULL);
-        secp256k1_fe_set_b32(&x_fe, b32);
+        secp256k1_fe_set_b32_mod(&x_fe, b32);
         for (var = 0; var <= 1; ++var) {
             test_inverse_scalar(NULL, &x_scalar, var);
             test_inverse_field(NULL, &x_fe, var);
@@ -3622,7 +3693,7 @@ static void run_inverse_tests(void)
         for (i = 0; i < 64 * COUNT; ++i) {
             (testrand ? secp256k1_testrand256_test : secp256k1_testrand256)(b32);
             secp256k1_scalar_set_b32(&x_scalar, b32, NULL);
-            secp256k1_fe_set_b32(&x_fe, b32);
+            secp256k1_fe_set_b32_mod(&x_fe, b32);
             for (var = 0; var <= 1; ++var) {
                 test_inverse_scalar(NULL, &x_scalar, var);
                 test_inverse_field(NULL, &x_fe, var);
@@ -4338,9 +4409,9 @@ static void test_ecmult_target(const secp256k1_scalar* target, int mode) {
         secp256k1_ecmult(&p2j, &pj, &n2, &zero);
         secp256k1_ecmult(&ptj, &pj, target, &zero);
     } else {
-        secp256k1_ecmult_const(&p1j, &p, &n1, 256);
-        secp256k1_ecmult_const(&p2j, &p, &n2, 256);
-        secp256k1_ecmult_const(&ptj, &p, target, 256);
+        secp256k1_ecmult_const(&p1j, &p, &n1);
+        secp256k1_ecmult_const(&p2j, &p, &n2);
+        secp256k1_ecmult_const(&ptj, &p, target);
     }
 
     /* Add them all up: n1*P + n2*P + target*P = (n1+n2+target)*P = (n1+n1-n1-n2)*P = 0. */
@@ -4403,7 +4474,7 @@ static void ecmult_const_random_mult(void) {
         0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
     );
     secp256k1_gej b;
-    secp256k1_ecmult_const(&b, &a, &xn, 256);
+    secp256k1_ecmult_const(&b, &a, &xn);
 
     CHECK(secp256k1_ge_is_valid_var(&a));
     ge_equals_gej(&expected_b, &b);
@@ -4419,12 +4490,12 @@ static void ecmult_const_commutativity(void) {
     random_scalar_order_test(&a);
     random_scalar_order_test(&b);
 
-    secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256);
-    secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256);
+    secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
+    secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
     secp256k1_ge_set_gej(&mid1, &res1);
     secp256k1_ge_set_gej(&mid2, &res2);
-    secp256k1_ecmult_const(&res1, &mid1, &b, 256);
-    secp256k1_ecmult_const(&res2, &mid2, &a, 256);
+    secp256k1_ecmult_const(&res1, &mid1, &b);
+    secp256k1_ecmult_const(&res2, &mid2, &a);
     secp256k1_ge_set_gej(&mid1, &res1);
     secp256k1_ge_set_gej(&mid2, &res2);
     ge_equals_ge(&mid1, &mid2);
@@ -4440,13 +4511,13 @@ static void ecmult_const_mult_zero_one(void) {
     secp256k1_scalar_negate(&negone, &one);
 
     random_group_element_test(&point);
-    secp256k1_ecmult_const(&res1, &point, &zero, 3);
+    secp256k1_ecmult_const(&res1, &point, &zero);
     secp256k1_ge_set_gej(&res2, &res1);
     CHECK(secp256k1_ge_is_infinity(&res2));
-    secp256k1_ecmult_const(&res1, &point, &one, 2);
+    secp256k1_ecmult_const(&res1, &point, &one);
     secp256k1_ge_set_gej(&res2, &res1);
     ge_equals_ge(&res2, &point);
-    secp256k1_ecmult_const(&res1, &point, &negone, 256);
+    secp256k1_ecmult_const(&res1, &point, &negone);
     secp256k1_gej_neg(&res1, &res1);
     secp256k1_ge_set_gej(&res2, &res1);
     ge_equals_ge(&res2, &point);
@@ -4476,7 +4547,7 @@ static void ecmult_const_mult_xonly(void) {
             n = base.x;
         }
         /* Perform x-only multiplication. */
-        res = secp256k1_ecmult_const_xonly(&resx, &n, (i & 1) ? &d : NULL, &q, 256, i & 2);
+        res = secp256k1_ecmult_const_xonly(&resx, &n, (i & 1) ? &d : NULL, &q, i & 2);
         CHECK(res);
         /* Perform normal multiplication. */
         secp256k1_gej_set_ge(&basej, &base);
@@ -4498,7 +4569,7 @@ static void ecmult_const_mult_xonly(void) {
             random_field_element_test(&x);
             secp256k1_fe_sqr(&c, &x);
             secp256k1_fe_mul(&c, &c, &x);
-            secp256k1_fe_add(&c, &secp256k1_fe_const_b);
+            secp256k1_fe_add_int(&c, SECP256K1_B);
         } while (secp256k1_fe_is_square_var(&c));
         /* If i is odd, n=d*x for random non-zero d. */
         if (i & 1) {
@@ -4509,7 +4580,7 @@ static void ecmult_const_mult_xonly(void) {
         } else {
             n = x;
         }
-        res = secp256k1_ecmult_const_xonly(&r, &n, (i & 1) ? &d : NULL, &q, 256, 0);
+        res = secp256k1_ecmult_const_xonly(&r, &n, (i & 1) ? &d : NULL, &q, 0);
         CHECK(res == 0);
     }
 }
@@ -4534,7 +4605,7 @@ static void ecmult_const_chain_multiply(void) {
     for (i = 0; i < 100; ++i) {
         secp256k1_ge tmp;
         secp256k1_ge_set_gej(&tmp, &point);
-        secp256k1_ecmult_const(&point, &tmp, &scalar, 256);
+        secp256k1_ecmult_const(&point, &tmp, &scalar);
     }
     secp256k1_ge_set_gej(&res, &point);
     ge_equals_gej(&res, &expected_point);
@@ -5432,7 +5503,7 @@ static void test_ecmult_accumulate(secp256k1_sha256* acc, const secp256k1_scalar
     secp256k1_ecmult(&rj3, &infj, &zero, x);
     secp256k1_ecmult_multi_var(NULL, scratch, &rj4, x, NULL, NULL, 0);
     secp256k1_ecmult_multi_var(NULL, scratch, &rj5, &zero, test_ecmult_accumulate_cb, (void*)x, 1);
-    secp256k1_ecmult_const(&rj6, &secp256k1_ge_const_g, x, 256);
+    secp256k1_ecmult_const(&rj6, &secp256k1_ge_const_g, x);
     secp256k1_ge_set_gej_var(&r, &rj1);
     ge_equals_gej(&r, &rj2);
     ge_equals_gej(&r, &rj3);
@@ -7699,6 +7770,7 @@ int main(int argc, char **argv) {
     run_field_half();
     run_field_misc();
     run_field_convert();
+    run_field_be32_overflow();
     run_fe_mul();
     run_sqr();
     run_sqrt();
diff --git a/src/tests_exhaustive.c b/src/tests_exhaustive.c
index 63b6ef03af..d35acdd58e 100644
--- a/src/tests_exhaustive.c
+++ b/src/tests_exhaustive.c
@@ -13,13 +13,19 @@
 #define EXHAUSTIVE_TEST_ORDER 13
 #endif
 
+#ifdef USE_EXTERNAL_DEFAULT_CALLBACKS
+    #pragma message("Ignoring USE_EXTERNAL_CALLBACKS in exhaustive_tests.")
+    #undef USE_EXTERNAL_DEFAULT_CALLBACKS
+#endif
 #include "secp256k1.c"
+
 #include "../include/secp256k1.h"
 #include "assumptions.h"
 #include "group.h"
 #include "testrand_impl.h"
 #include "ecmult_compute_table_impl.h"
 #include "ecmult_gen_compute_table_impl.h"
+#include "util.h"
 
 static int count = 2;
 
@@ -54,7 +60,7 @@ static void random_fe(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
         secp256k1_testrand256(bin);
-        if (secp256k1_fe_set_b32(x, bin)) {
+        if (secp256k1_fe_set_b32_limit(x, bin)) {
             return;
         }
     } while(1);
@@ -192,7 +198,7 @@ static void test_exhaustive_ecmult(const secp256k1_ge *group, const secp256k1_ge
     }
 
     for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
-        for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
+        for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
             int ret;
             secp256k1_gej tmp;
             secp256k1_fe xn, xd, tmpf;
@@ -203,19 +209,19 @@ static void test_exhaustive_ecmult(const secp256k1_ge *group, const secp256k1_ge
             secp256k1_scalar_set_int(&ng, j);
 
             /* Test secp256k1_ecmult_const. */
-            secp256k1_ecmult_const(&tmp, &group[i], &ng, 256);
+            secp256k1_ecmult_const(&tmp, &group[i], &ng);
             ge_equals_gej(&group[(i * j) % EXHAUSTIVE_TEST_ORDER], &tmp);
 
-            if (j != 0) {
+            if (i != 0 && j != 0) {
                 /* Test secp256k1_ecmult_const_xonly with all curve X coordinates, and xd=NULL. */
-                ret = secp256k1_ecmult_const_xonly(&tmpf, &group[i].x, NULL, &ng, 256, 0);
+                ret = secp256k1_ecmult_const_xonly(&tmpf, &group[i].x, NULL, &ng, 0);
                 CHECK(ret);
                 CHECK(secp256k1_fe_equal_var(&tmpf, &group[(i * j) % EXHAUSTIVE_TEST_ORDER].x));
 
                 /* Test secp256k1_ecmult_const_xonly with all curve X coordinates, with random xd. */
                 random_fe_non_zero(&xd);
                 secp256k1_fe_mul(&xn, &xd, &group[i].x);
-                ret = secp256k1_ecmult_const_xonly(&tmpf, &xn, &xd, &ng, 256, 0);
+                ret = secp256k1_ecmult_const_xonly(&tmpf, &xn, &xd, &ng, 0);
                 CHECK(ret);
                 CHECK(secp256k1_fe_equal_var(&tmpf, &group[(i * j) % EXHAUSTIVE_TEST_ORDER].x));
             }
diff --git a/src/util.h b/src/util.h
index e75c5ad552..0e3faf0234 100644
--- a/src/util.h
+++ b/src/util.h
@@ -7,6 +7,8 @@
 #ifndef SECP256K1_UTIL_H
 #define SECP256K1_UTIL_H
 
+#include "../include/secp256k1.h"
+
 #include <stdlib.h>
 #include <stdint.h>
 #include <stdio.h>
@@ -17,6 +19,38 @@
 #define DEBUG_CONFIG_MSG(x) "DEBUG_CONFIG: " x
 #define DEBUG_CONFIG_DEF(x) DEBUG_CONFIG_MSG(#x "=" STR(x))
 
+/* Debug helper for printing arrays of unsigned char. */
+#define PRINT_BUF(buf, len) do { \
+    printf("%s[%lu] = ", #buf, (unsigned long)len); \
+    print_buf_plain(buf, len); \
+} while(0)
+
+static void print_buf_plain(const unsigned char *buf, size_t len) {
+    size_t i;
+    printf("{");
+    for (i = 0; i < len; i++) {
+        if (i % 8 == 0) {
+            printf("\n    ");
+        } else {
+            printf(" ");
+        }
+        printf("0x%02X,", buf[i]);
+    }
+    printf("\n}\n");
+}
+
+# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) )
+#  if SECP256K1_GNUC_PREREQ(2,7)
+#   define SECP256K1_INLINE __inline__
+#  elif (defined(_MSC_VER))
+#   define SECP256K1_INLINE __inline
+#  else
+#   define SECP256K1_INLINE
+#  endif
+# else
+#  define SECP256K1_INLINE inline
+# endif
+
 typedef struct {
     void (*fn)(const char *text, void* data);
     const void* data;
diff --git a/tools/tests_wycheproof_generate.py b/tools/tests_wycheproof_generate.py
index 333f6fbef0..b26dfa89d6 100755
--- a/tools/tests_wycheproof_generate.py
+++ b/tools/tests_wycheproof_generate.py
@@ -7,8 +7,6 @@
 '''
 
 import json
-import hashlib
-import urllib.request
 import sys
 
 filename_input = sys.argv[1]
@@ -19,7 +17,8 @@
 num_groups = len(doc['testGroups'])
 
 def to_c_array(x):
-    if x == "": return ""
+    if x == "":
+        return ""
     s = ',0x'.join(a+b for a,b in zip(x[::2], x[1::2]))
     return "0x" + s
 
@@ -43,18 +42,23 @@ def to_c_array(x):
         sig_size = len(test_vector['sig']) // 2
         msg_size = len(test_vector['msg']) // 2
 
-        if test_vector['result'] == "invalid": expected_verify = 0
-        elif test_vector['result'] == "valid": expected_verify = 1
-        else: raise ValueError("invalid result field")
+        if test_vector['result'] == "invalid":
+            expected_verify = 0
+        elif test_vector['result'] == "valid":
+            expected_verify = 1
+        else:
+            raise ValueError("invalid result field")
 
-        if num_vectors != 0 and sig_size != 0: signatures += ",\n  "
+        if num_vectors != 0 and sig_size != 0:
+            signatures += ",\n  "
 
         new_msg = False
         msg = to_c_array(test_vector['msg'])
         msg_offset = offset_msg_running
         # check for repeated msg
-        if msg not in cache_msgs.keys():
-            if num_vectors != 0 and msg_size != 0: messages += ",\n  "
+        if msg not in cache_msgs:
+            if num_vectors != 0 and msg_size != 0:
+                messages += ",\n  "
             cache_msgs[msg] = offset_msg_running
             messages += msg
             new_msg = True
@@ -65,8 +69,9 @@ def to_c_array(x):
         pk = to_c_array(public_key['uncompressed'])
         pk_offset = offset_pk_running
         # check for repeated pk
-        if pk not in cache_public_keys.keys():
-            if num_vectors != 0: public_keys += ",\n  "
+        if pk not in cache_public_keys:
+            if num_vectors != 0:
+                public_keys += ",\n  "
             cache_public_keys[pk] = offset_pk_running
             public_keys += pk
             new_pk = True
@@ -76,15 +81,11 @@ def to_c_array(x):
         signatures += to_c_array(test_vector['sig'])
 
         out += "  /" + "* tcId: " + str(test_vector['tcId']) + ". " + test_vector['comment'] + " *" + "/\n"
-        out += "  {" + "{0}, {1}, {2}, {3}, {4}, {5}".format(
-                pk_offset,
-                msg_offset,
-                msg_size,
-                offset_sig,
-                sig_size,
-                expected_verify) + " },\n"
-        if new_msg: offset_msg_running += msg_size
-        if new_pk: offset_pk_running += 65
+        out += f"  {{{pk_offset}, {msg_offset}, {msg_size}, {offset_sig}, {sig_size}, {expected_verify} }},\n"
+        if new_msg:
+            offset_msg_running += msg_size
+        if new_pk:
+            offset_pk_running += 65
         offset_sig += sig_size
         num_vectors += 1
 
@@ -101,7 +102,7 @@ def to_c_array(x):
 
 
 print("/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */")
-print("#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS ({})".format(num_vectors))
+print(f"#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS ({num_vectors})")
 
 print(struct_definition)