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<span class="pre noprint docinfo">[<a href="https://www.rfc-editor.org" title="RFC Editor">RFC Home</a>] [<a href="/rfc/rfc6234.txt">TEXT</a>|<a href="/rfc/pdfrfc/rfc6234.txt.pdf">PDF</a>|<a href="/rfc/rfc6234.html">HTML</a>] [<a href='https://datatracker.ietf.org/doc/rfc6234' title='IETF Datatracker information for this document'>Tracker</a>] [<a href="https://datatracker.ietf.org/ipr/search/?rfc=6234&submit=rfc" title="IPR disclosures related to this document">IPR</a>] [<a class="boldtext" href="/errata/rfc6234" target="_blank">Errata</a>] [<a href='https://www.rfc-editor.org/info/rfc6234' title='Info page'>Info page</a>] </span><br/><span class="pre noprint docinfo"> </span><br /><span class="pre noprint docinfo"> INFORMATIONAL</span><br /><span class="pre noprint docinfo"> <span style='color: #C00;'>Errata Exist</span></span><pre>Internet Engineering Task Force (IETF) D. Eastlake 3rd
Request for Comments: 6234 Huawei
Obsoletes: <a href="./rfc4634">4634</a> T. Hansen
Updates: <a href="./rfc3174">3174</a> AT&T Labs
Category: Informational May 2011
ISSN: 2070-1721
<span class="h1">US Secure Hash Algorithms</span>
<span class="h1">(SHA and SHA-based HMAC and HKDF)</span>
Abstract
The United States of America has adopted a suite of Secure Hash
Algorithms (SHAs), including four beyond SHA-1, as part of a Federal
Information Processing Standard (FIPS), namely SHA-224, SHA-256,
SHA-384, and SHA-512. This document makes open source code
performing these SHA hash functions conveniently available to the
Internet community. The sample code supports input strings of
arbitrary bit length. Much of the text herein was adapted by the
authors from FIPS 180-2.
This document replaces <a href="./rfc4634">RFC 4634</a>, fixing errata and adding code for an
HMAC-based extract-and-expand Key Derivation Function, HKDF (<a href="./rfc5869">RFC</a>
<a href="./rfc5869">5869</a>). As with <a href="./rfc4634">RFC 4634</a>, code to perform SHA-based Hashed Message
Authentication Codes (HMACs) is also included.
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are a candidate for any level of Internet
Standard; see <a href="./rfc5741#section-2">Section 2 of RFC 5741</a>.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
<a href="https://www.rfc-editor.org/info/rfc6234">http://www.rfc-editor.org/info/rfc6234</a>.
<span class="grey">Eastlake & Hansen Informational [Page 1]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-2" ></span>
<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
Copyright Notice
Copyright (c) 2011 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to <a href="https://www.rfc-editor.org/bcp/bcp78">BCP 78</a> and the IETF Trust's Legal
Provisions Relating to IETF Documents
(<a href="http://trustee.ietf.org/license-info">http://trustee.ietf.org/license-info</a>) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
<span class="grey">Eastlake & Hansen Informational [Page 2]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-3" ></span>
<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
Table of Contents
<a href="#section-1">1</a>. Overview of Contents ............................................<a href="#page-4">4</a>
<a href="#section-2">2</a>. Notation for Bit Strings and Integers ...........................<a href="#page-5">5</a>
<a href="#section-3">3</a>. Operations on Words .............................................<a href="#page-6">6</a>
<a href="#section-4">4</a>. Message Padding and Parsing .....................................<a href="#page-8">8</a>
<a href="#section-4.1">4.1</a>. SHA-224 and SHA-256 ........................................<a href="#page-8">8</a>
<a href="#section-4.2">4.2</a>. SHA-384 and SHA-512 ........................................<a href="#page-9">9</a>
<a href="#section-5">5</a>. Functions and Constants Used ...................................<a href="#page-10">10</a>
<a href="#section-5.1">5.1</a>. SHA-224 and SHA-256 .......................................<a href="#page-10">10</a>
<a href="#section-5.2">5.2</a>. SHA-384 and SHA-512 .......................................<a href="#page-11">11</a>
<a href="#section-6">6</a>. Computing the Message Digest ...................................<a href="#page-12">12</a>
<a href="#section-6.1">6.1</a>. SHA-224 and SHA-256 Initialization ........................<a href="#page-12">12</a>
<a href="#section-6.2">6.2</a>. SHA-224 and SHA-256 Processing ............................<a href="#page-13">13</a>
<a href="#section-6.3">6.3</a>. SHA-384 and SHA-512 Initialization ........................<a href="#page-14">14</a>
<a href="#section-6.4">6.4</a>. SHA-384 and SHA-512 Processing ............................<a href="#page-15">15</a>
<a href="#section-7">7</a>. HKDF- and SHA-Based HMACs ......................................<a href="#page-17">17</a>
<a href="#section-7.1">7.1</a>. SHA-Based HMACs ...........................................<a href="#page-17">17</a>
<a href="#section-7.2">7.2</a>. HKDF ......................................................<a href="#page-17">17</a>
<a href="#section-8">8</a>. C Code for SHAs, HMAC, and HKDF ................................<a href="#page-17">17</a>
<a href="#section-8.1">8.1</a>. The Header Files ..........................................<a href="#page-21">21</a>
<a href="#section-8.1.1">8.1.1</a>. The .h file ........................................<a href="#page-21">21</a>
<a href="#section-8.1.2">8.1.2</a>. stdint-example.h ...................................<a href="#page-29">29</a>
<a href="#section-8.1.3">8.1.3</a>. sha-private.h ......................................<a href="#page-29">29</a>
<a href="#section-8.2">8.2</a>. The SHA Code ..............................................<a href="#page-30">30</a>
<a href="#section-8.2.1">8.2.1</a>. sha1.c .............................................<a href="#page-30">30</a>
<a href="#section-8.2.2">8.2.2</a>. sha224-256.c .......................................<a href="#page-39">39</a>
<a href="#section-8.2.3">8.2.3</a>. sha384-512.c .......................................<a href="#page-51">51</a>
<a href="#section-8.2.4">8.2.4</a>. usha.c .............................................<a href="#page-73">73</a>
<a href="#section-8.3">8.3</a>. The HMAC Code .............................................<a href="#page-79">79</a>
<a href="#section-8.4">8.4</a>. The HKDF Code .............................................<a href="#page-84">84</a>
<a href="#section-8.5">8.5</a>. The Test Driver ...........................................<a href="#page-91">91</a>
<a href="#section-9">9</a>. Security Considerations .......................................<a href="#page-123">123</a>
<a href="#section-10">10</a>. Acknowledgements .............................................<a href="#page-123">123</a>
<a href="#section-11">11</a>. References ...................................................<a href="#page-124">124</a>
<a href="#section-11.1">11.1</a>. Normative References ....................................<a href="#page-124">124</a>
<a href="#section-11.2">11.2</a>. Informative References ..................................<a href="#page-124">124</a>
Appendix: Changes from <a href="./rfc4634">RFC 4634</a>...................................<a href="#page-126">126</a>
<span class="grey">Eastlake & Hansen Informational [Page 3]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-4" ></span>
<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>. Overview of Contents</span>
This document includes specifications for the United States of
America (USA) Federal Information Processing Standard (FIPS) Secure
Hash Algorithms (SHAs), code to implement the SHAs, code to implement
HMAC (Hashed Message Authentication Code, [<a href="./rfc2104" title=""HMAC: Keyed- Hashing for Message Authentication"">RFC2104</a>]) based on the
SHAs, and code to implement HKDF (HMAC-based Key Derivation Function,
[<a href="./rfc5869" title=""HMAC-based Extract-and-Expand Key Derivation Function (HKDF)"">RFC5869</a>]) based on HMAC. Specifications for HMAC and HKDF are not
included as they appear elsewhere in the RFC series [<a href="./rfc2104" title=""HMAC: Keyed- Hashing for Message Authentication"">RFC2104</a>]
[<a href="./rfc5869" title=""HMAC-based Extract-and-Expand Key Derivation Function (HKDF)"">RFC5869</a>].
NOTE: Much of the text below is taken from [<a href="#ref-SHS" title=""Secure Hash Standard"">SHS</a>], and the assertions
of the security of the hash algorithms described therein are made by
the US Government, the author of [<a href="#ref-SHS" title=""Secure Hash Standard"">SHS</a>], not by the listed authors of
this document. See also [<a href="./rfc6194" title=""Security Considerations for the SHA-0 and SHA-1 Message-Digest Algorithms"">RFC6194</a>] concerning the security of SHA-1.
The text below specifies Secure Hash Algorithms, SHA-224 [<a href="./rfc3874" title=""A 224-bit One-way Hash Function: SHA-224"">RFC3874</a>],
SHA-256, SHA-384, and SHA-512, for computing a condensed
representation of a message or a data file. (SHA-1 is specified in
[<a href="./rfc3174" title=""US Secure Hash Algorithm 1 (SHA1)"">RFC3174</a>].) When a message of any length < 2^64 bits (for SHA-224 and
SHA-256) or < 2^128 bits (for SHA-384 and SHA-512) is input to one of
these algorithms, the result is an output called a message digest.
The message digests range in length from 224 to 512 bits, depending
on the algorithm. Secure Hash Algorithms are typically used with
other cryptographic algorithms, such as digital signature algorithms
and keyed-hash authentication codes, the generation of random numbers
[<a href="./rfc4086" title=""Randomness Requirements for Security"">RFC4086</a>], or in key derivation functions.
The algorithms specified in this document are called secure because
it is computationally infeasible to (1) find a message that
corresponds to a given message digest, or (2) find two different
messages that produce the same message digest. Any change to a
message in transit will, with very high probability, result in a
different message digest. This will result in a verification failure
when the Secure Hash Algorithm is used with a digital signature
algorithm or a keyed-hash message authentication algorithm.
The code provided herein supports input strings of arbitrary bit
length. SHA-1's sample code from [<a href="./rfc3174" title=""US Secure Hash Algorithm 1 (SHA1)"">RFC3174</a>] has also been updated to
handle input strings of arbitrary bit length. Permission is granted
for all uses, commercial and non-commercial, of this code.
This document obsoletes [<a href="./rfc4634" title=""US Secure Hash Algorithms (SHA and HMAC-SHA)"">RFC4634</a>], and the changes from that RFC are
summarized in the Appendix.
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
ASN.1 OIDs (Object Identifiers) for the SHA algorithms, taken from
[<a href="./rfc4055" title=""Additional Algorithms and Identifiers for RSA Cryptography for use in the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile"">RFC4055</a>], are as follows:
id-sha1 OBJECT IDENTIFIER ::= { iso(1)
identified-organization(3) oiw(14)
secsig(3) algorithms(2) 26 }
id-sha224 OBJECT IDENTIFIER ::= {{ joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101)
csor(3) nistalgorithm(4) hashalgs(2) 4 }
id-sha256 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101)
csor(3) nistalgorithm(4) hashalgs(2) 1 }
id-sha384 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101)
csor(3) nistalgorithm(4) hashalgs(2) 2 }
id-sha512 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101)
csor(3) nistalgorithm(4) hashalgs(2) 3 }
<a href="#section-2">Section 2</a> below defines the terminology and functions used as
building blocks to form these algorithms. <a href="#section-3">Section 3</a> describes the
fundamental operations on words from which these algorithms are
built. <a href="#section-4">Section 4</a> describes how messages are padded up to an integral
multiple of the required block size and then parsed into blocks.
<a href="#section-5">Section 5</a> defines the constants and the composite functions used to
specify the hash algorithms. <a href="#section-6">Section 6</a> gives the actual
specification for the SHA-224, SHA-256, SHA-384, and SHA-512
functions. <a href="#section-7">Section 7</a> provides pointers to the specification of HMAC
keyed message authentication codes and to the specification of an
extract-and-expand key derivation function based on HMAC.
<a href="#section-8">Section 8</a> gives sample code for the SHA algorithms, for SHA-based
HMACs, and for HMAC-based extract-and-expand key derivation function.
<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>. Notation for Bit Strings and Integers</span>
The following terminology related to bit strings and integers will be
used:
a. A hex digit is an element of the set {0, 1, ... , 9, A, ... , F}.
A hex digit is the representation of a 4-bit string. Examples: 7
= 0111, A = 1010.
b. A word equals a 32-bit or 64-bit string that may be represented
as a sequence of 8 or 16 hex digits, respectively. To convert a
word to hex digits, each 4-bit string is converted to its hex
equivalent as described in (a) above. Example:
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
1010 0001 0000 0011 1111 1110 0010 0011 = A103FE23.
Throughout this document, the "big-endian" convention is used when
expressing both 32-bit and 64-bit words, so that within each word
the most significant bit is shown in the leftmost bit position.
c. An integer may be represented as a word or pair of words.
An integer between 0 and 2^32 - 1 inclusive may be represented as
a 32-bit word. The least significant four bits of the integer are
represented by the rightmost hex digit of the word representation.
Example: the integer 291 = 2^8+2^5+2^1+2^0 = 256+32+2+1 is
represented by the hex word 00000123.
The same holds true for an integer between 0 and 2^64-1 inclusive,
which may be represented as a 64-bit word.
If Z is an integer, 0 <= z < 2^64, then z = (2^32)x + y where
0 <= x < 2^32 and 0 <= y < 2^32. Since x and y can be represented
as words X and Y, respectively, z can be represented as the pair
of words (X,Y).
Again, the "big-endian" convention is used and the most
significant word is in the leftmost word position for values
represented by multiple-words.
d. block = 512-bit or 1024-bit string. A block (e.g., B) may be
represented as a sequence of 32-bit or 64-bit words.
<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>. Operations on Words</span>
The following logical operators will be applied to words in all four
hash operations specified herein. SHA-224 and SHA-256 operate on
32-bit words while SHA-384 and SHA-512 operate on 64-bit words.
In the operations below, x<<n is obtained as follows: discard the
leftmost n bits of x and then pad the result with n zeroed bits on
the right (the result will still be the same number of bits).
Similarly, x>>n is obtained as follows: discard the rightmost n bits
of x and then prepend the result with n zeroed bits on the left (the
result will still be the same number of bits).
a. Bitwise logical word operations
X AND Y = bitwise logical "and" of X and Y.
X OR Y = bitwise logical "inclusive-or" of X and Y.
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
X XOR Y = bitwise logical "exclusive-or" of X and Y.
NOT X = bitwise logical "complement" of X.
Example:
01101100101110011101001001111011
XOR 01100101110000010110100110110111
--------------------------------
= 00001001011110001011101111001100
b. The operation X + Y is defined as follows: words X and Y represent
w-bit integers x and y, where 0 <= x < 2^w and 0 <= y < 2^w. For
positive integers n and m, let
n mod m
be the remainder upon dividing n by m. Compute
z = (x + y) mod 2^w.
Then 0 <= z < 2^w. Convert z to a word, Z, and define Z = X + Y.
c. The right shift operation SHR^n(x), where x is a w-bit word and n
is an integer with 0 <= n < w, is defined by
SHR^n(x) = x>>n
d. The rotate right (circular right shift) operation ROTR^n(x), where
x is a w-bit word and n is an integer with 0 <= n < w, is defined
by
ROTR^n(x) = (x>>n) OR (x<<(w-n))
e. The rotate left (circular left shift) operation ROTL^n(x), where x
is a w-bit word and n is an integer with 0 <= n < w, is defined by
ROTL^n(X) = (x<<n) OR (x>>(w-n))
Note the following equivalence relationships, where w is fixed in
each relationship:
ROTL^n(x) = ROTR^(w-n)(x)
ROTR^n(x) = ROTL^(w-n)(x)
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>. Message Padding and Parsing</span>
The hash functions specified herein are used to compute a message
digest for a message or data file that is provided as input. The
message or data file should be considered to be a bit string. The
length of the message is the number of bits in the message (the empty
message has length 0). If the number of bits in a message is a
multiple of 8, for compactness we can represent the message in hex.
The purpose of message padding is to make the total length of a
padded message a multiple of 512 for SHA-224 and SHA-256 or a
multiple of 1024 for SHA-384 and SHA-512.
The following specifies how this padding shall be performed. As a
summary, a "1" followed by m "0"s followed by a 64-bit or 128-bit
integer are appended to the end of the message to produce a padded
message of length 512*n or 1024*n. The appended integer is the
length of the original message. The padded message is then processed
by the hash function as n 512-bit or 1024-bit blocks.
<span class="h3"><a class="selflink" id="section-4.1" href="#section-4.1">4.1</a>. SHA-224 and SHA-256</span>
Suppose a message has length L < 2^64. Before it is input to the
hash function, the message is padded on the right as follows:
a. "1" is appended. Example: if the original message is "01010000",
this is padded to "010100001".
b. K "0"s are appended where K is the smallest, non-negative solution
to the equation
( L + 1 + K ) mod 512 = 448
c. Then append the 64-bit block that is L in binary representation.
After appending this block, the length of the message will be a
multiple of 512 bits.
Example: Suppose the original message is the bit string
01100001 01100010 01100011 01100100 01100101
After step (a) this gives
01100001 01100010 01100011 01100100 01100101 1
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
Since L = 40, the number of bits in the above is 41 and K = 407
"0"s are appended, making the total now 448. This gives the
following in hex:
61626364 65800000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000
The 64-bit representation of L = 40 is hex 00000000 00000028.
Hence the final padded message is the following hex
61626364 65800000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000028
<span class="h3"><a class="selflink" id="section-4.2" href="#section-4.2">4.2</a>. SHA-384 and SHA-512</span>
Suppose a message has length L < 2^128. Before it is input to the
hash function, the message is padded on the right as follows:
a. "1" is appended. Example: if the original message is "01010000",
this is padded to "010100001".
b. K "0"s are appended where K is the smallest, non-negative solution
to the equation
( L + 1 + K ) mod 1024 = 896
c. Then append the 128-bit block that is L in binary representation.
After appending this block, the length of the message will be a
multiple of 1024 bits.
Example: Suppose the original message is the bit string
01100001 01100010 01100011 01100100 01100101
After step (a) this gives
01100001 01100010 01100011 01100100 01100101 1
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
Since L = 40, the number of bits in the above is 41 and K = 855
"0"s are appended, making the total now 896. This gives the
following in hex:
61626364 65800000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
The 128-bit representation of L = 40 is hex 00000000 00000000
00000000 00000028. Hence the final padded message is the
following hex:
61626364 65800000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000028
<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>. Functions and Constants Used</span>
The following subsections give the six logical functions and the
table of constants used in each of the hash functions.
<span class="h3"><a class="selflink" id="section-5.1" href="#section-5.1">5.1</a>. SHA-224 and SHA-256</span>
SHA-224 and SHA-256 use six logical functions, where each function
operates on 32-bit words, which are represented as x, y, and z. The
result of each function is a new 32-bit word.
CH( x, y, z) = (x AND y) XOR ( (NOT x) AND z)
MAJ( x, y, z) = (x AND y) XOR (x AND z) XOR (y AND z)
BSIG0(x) = ROTR^2(x) XOR ROTR^13(x) XOR ROTR^22(x)
BSIG1(x) = ROTR^6(x) XOR ROTR^11(x) XOR ROTR^25(x)
SSIG0(x) = ROTR^7(x) XOR ROTR^18(x) XOR SHR^3(x)
SSIG1(x) = ROTR^17(x) XOR ROTR^19(x) XOR SHR^10(x)
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
SHA-224 and SHA-256 use the same sequence of sixty-four constant
32-bit words, K0, K1, ..., K63. These words represent the first 32
bits of the fractional parts of the cube roots of the first sixty-
four prime numbers. In hex, these constant words are as follows
(from left to right):
428a2f98 71374491 b5c0fbcf e9b5dba5
3956c25b 59f111f1 923f82a4 ab1c5ed5
d807aa98 12835b01 243185be 550c7dc3
72be5d74 80deb1fe 9bdc06a7 c19bf174
e49b69c1 efbe4786 0fc19dc6 240ca1cc
2de92c6f 4a7484aa 5cb0a9dc 76f988da
983e5152 a831c66d b00327c8 bf597fc7
c6e00bf3 d5a79147 06ca6351 14292967
27b70a85 2e1b2138 4d2c6dfc 53380d13
650a7354 766a0abb 81c2c92e 92722c85
a2bfe8a1 a81a664b c24b8b70 c76c51a3
d192e819 d6990624 f40e3585 106aa070
19a4c116 1e376c08 2748774c 34b0bcb5
391c0cb3 4ed8aa4a 5b9cca4f 682e6ff3
748f82ee 78a5636f 84c87814 8cc70208
90befffa a4506ceb bef9a3f7 c67178f2
<span class="h3"><a class="selflink" id="section-5.2" href="#section-5.2">5.2</a>. SHA-384 and SHA-512</span>
SHA-384 and SHA-512 each use six logical functions, where each
function operates on 64-bit words, which are represented as x, y, and
z. The result of each function is a new 64-bit word.
CH( x, y, z) = (x AND y) XOR ( (NOT x) AND z)
MAJ( x, y, z) = (x AND y) XOR (x AND z) XOR (y AND z)
BSIG0(x) = ROTR^28(x) XOR ROTR^34(x) XOR ROTR^39(x)
BSIG1(x) = ROTR^14(x) XOR ROTR^18(x) XOR ROTR^41(x)
SSIG0(x) = ROTR^1(x) XOR ROTR^8(x) XOR SHR^7(x)
SSIG1(x) = ROTR^19(x) XOR ROTR^61(x) XOR SHR^6(x)
SHA-384 and SHA-512 use the same sequence of eighty constant 64-bit
words, K0, K1, ... K79. These words represent the first 64 bits of
the fractional parts of the cube roots of the first eighty prime
numbers. In hex, these constant words are as follows (from left to
right):
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
428a2f98d728ae22 7137449123ef65cd b5c0fbcfec4d3b2f e9b5dba58189dbbc
3956c25bf348b538 59f111f1b605d019 923f82a4af194f9b ab1c5ed5da6d8118
d807aa98a3030242 12835b0145706fbe 243185be4ee4b28c 550c7dc3d5ffb4e2
72be5d74f27b896f 80deb1fe3b1696b1 9bdc06a725c71235 c19bf174cf692694
e49b69c19ef14ad2 efbe4786384f25e3 0fc19dc68b8cd5b5 240ca1cc77ac9c65
2de92c6f592b0275 4a7484aa6ea6e483 5cb0a9dcbd41fbd4 76f988da831153b5
983e5152ee66dfab a831c66d2db43210 b00327c898fb213f bf597fc7beef0ee4
c6e00bf33da88fc2 d5a79147930aa725 06ca6351e003826f 142929670a0e6e70
27b70a8546d22ffc 2e1b21385c26c926 4d2c6dfc5ac42aed 53380d139d95b3df
650a73548baf63de 766a0abb3c77b2a8 81c2c92e47edaee6 92722c851482353b
a2bfe8a14cf10364 a81a664bbc423001 c24b8b70d0f89791 c76c51a30654be30
d192e819d6ef5218 d69906245565a910 f40e35855771202a 106aa07032bbd1b8
19a4c116b8d2d0c8 1e376c085141ab53 2748774cdf8eeb99 34b0bcb5e19b48a8
391c0cb3c5c95a63 4ed8aa4ae3418acb 5b9cca4f7763e373 682e6ff3d6b2b8a3
748f82ee5defb2fc 78a5636f43172f60 84c87814a1f0ab72 8cc702081a6439ec
90befffa23631e28 a4506cebde82bde9 bef9a3f7b2c67915 c67178f2e372532b
ca273eceea26619c d186b8c721c0c207 eada7dd6cde0eb1e f57d4f7fee6ed178
06f067aa72176fba 0a637dc5a2c898a6 113f9804bef90dae 1b710b35131c471b
28db77f523047d84 32caab7b40c72493 3c9ebe0a15c9bebc 431d67c49c100d4c
4cc5d4becb3e42b6 597f299cfc657e2a 5fcb6fab3ad6faec 6c44198c4a475817
<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>. Computing the Message Digest</span>
The output of each of the secure hash functions, after being applied
to a message of N blocks, is the hash quantity H(N). For SHA-224 and
SHA-256, H(i) can be considered to be eight 32-bit words, H(i)0,
H(i)1, ... H(i)7. For SHA-384 and SHA-512, it can be considered to
be eight 64-bit words, H(i)0, H(i)1, ..., H(i)7.
As described below, the hash words are initialized, modified as each
message block is processed, and finally concatenated after processing
the last block to yield the output. For SHA-256 and SHA-512, all of
the H(N) variables are concatenated while the SHA-224 and SHA-384
hashes are produced by omitting some from the final concatenation.
<span class="h3"><a class="selflink" id="section-6.1" href="#section-6.1">6.1</a>. SHA-224 and SHA-256 Initialization</span>
For SHA-224, the initial hash value, H(0), consists of the following
32-bit words in hex:
H(0)0 = c1059ed8
H(0)1 = 367cd507
H(0)2 = 3070dd17
H(0)3 = f70e5939
H(0)4 = ffc00b31
H(0)5 = 68581511
H(0)6 = 64f98fa7
H(0)7 = befa4fa4
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
For SHA-256, the initial hash value, H(0), consists of the following
eight 32-bit words, in hex. These words were obtained by taking the
first 32 bits of the fractional parts of the square roots of the
first eight prime numbers.
H(0)0 = 6a09e667
H(0)1 = bb67ae85
H(0)2 = 3c6ef372
H(0)3 = a54ff53a
H(0)4 = 510e527f
H(0)5 = 9b05688c
H(0)6 = 1f83d9ab
H(0)7 = 5be0cd19
<span class="h3"><a class="selflink" id="section-6.2" href="#section-6.2">6.2</a>. SHA-224 and SHA-256 Processing</span>
SHA-224 and SHA-256 perform identical processing on message blocks
and differ only in how H(0) is initialized and how they produce their
final output. They may be used to hash a message, M, having a length
of L bits, where 0 <= L < 2^64. The algorithm uses (1) a message
schedule of sixty-four 32-bit words, (2) eight working variables of
32 bits each, and (3) a hash value of eight 32-bit words.
The words of the message schedule are labeled W0, W1, ..., W63. The
eight working variables are labeled a, b, c, d, e, f, g, and h. The
words of the hash value are labeled H(i)0, H(i)1, ..., H(i)7, which
will hold the initial hash value, H(0), replaced by each successive
intermediate hash value (after each message block is processed),
H(i), and ending with the final hash value, H(N), after all N blocks
are processed. They also use two temporary words, T1 and T2.
The input message is padded as described in <a href="#section-4.1">Section 4.1</a> above, then
parsed into 512-bit blocks that are considered to be composed of
sixteen 32-bit words M(i)0, M(i)1, ..., M(i)15. The following
computations are then performed for each of the N message blocks.
All addition is performed modulo 2^32.
For i = 1 to N
1. Prepare the message schedule W:
For t = 0 to 15
Wt = M(i)t
For t = 16 to 63
Wt = SSIG1(W(t-2)) + W(t-7) + SSIG0(w(t-15)) + W(t-16)
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
2. Initialize the working variables:
a = H(i-1)0
b = H(i-1)1
c = H(i-1)2
d = H(i-1)3
e = H(i-1)4
f = H(i-1)5
g = H(i-1)6
h = H(i-1)7
3. Perform the main hash computation:
For t = 0 to 63
T1 = h + BSIG1(e) + CH(e,f,g) + Kt + Wt
T2 = BSIG0(a) + MAJ(a,b,c)
h = g
g = f
f = e
e = d + T1
d = c
c = b
b = a
a = T1 + T2
4. Compute the intermediate hash value H(i)
H(i)0 = a + H(i-1)0
H(i)1 = b + H(i-1)1
H(i)2 = c + H(i-1)2
H(i)3 = d + H(i-1)3
H(i)4 = e + H(i-1)4
H(i)5 = f + H(i-1)5
H(i)6 = g + H(i-1)6
H(i)7 = h + H(i-1)7
After the above computations have been sequentially performed for all
of the blocks in the message, the final output is calculated. For
SHA-256, this is the concatenation of all of H(N)0, H(N)1, through
H(N)7. For SHA-224, this is the concatenation of H(N)0, H(N)1,
through H(N)6.
<span class="h3"><a class="selflink" id="section-6.3" href="#section-6.3">6.3</a>. SHA-384 and SHA-512 Initialization</span>
For SHA-384, the initial hash value, H(0), consists of the following
eight 64-bit words, in hex. These words were obtained by taking the
first 64 bits of the fractional parts of the square roots of the
ninth through sixteenth prime numbers.
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>
H(0)0 = cbbb9d5dc1059ed8
H(0)1 = 629a292a367cd507
H(0)2 = 9159015a3070dd17
H(0)3 = 152fecd8f70e5939
H(0)4 = 67332667ffc00b31
H(0)5 = 8eb44a8768581511
H(0)6 = db0c2e0d64f98fa7
H(0)7 = 47b5481dbefa4fa4
For SHA-512, the initial hash value, H(0), consists of the following
eight 64-bit words, in hex. These words were obtained by taking the
first 64 bits of the fractional parts of the square roots of the
first eight prime numbers.
H(0)0 = 6a09e667f3bcc908
H(0)1 = bb67ae8584caa73b
H(0)2 = 3c6ef372fe94f82b
H(0)3 = a54ff53a5f1d36f1
H(0)4 = 510e527fade682d1
H(0)5 = 9b05688c2b3e6c1f
H(0)6 = 1f83d9abfb41bd6b
H(0)7 = 5be0cd19137e2179
<span class="h3"><a class="selflink" id="section-6.4" href="#section-6.4">6.4</a>. SHA-384 and SHA-512 Processing</span>
SHA-384 and SHA-512 perform identical processing on message blocks
and differ only in how H(0) is initialized and how they produce their
final output. They may be used to hash a message, M, having a length
of L bits, where 0 <= L < 2^128. The algorithm uses (1) a message
schedule of eighty 64-bit words, (2) eight working variables of 64
bits each, and (3) a hash value of eight 64-bit words.
The words of the message schedule are labeled W0, W1, ..., W79. The
eight working variables are labeled a, b, c, d, e, f, g, and h. The
words of the hash value are labeled H(i)0, H(i)1, ..., H(i)7, which
will hold the initial hash value, H(0), replaced by each successive
intermediate hash value (after each message block is processed),
H(i), and ending with the final hash value, H(N) after all N blocks
are processed.
The input message is padded as described in <a href="#section-4.2">Section 4.2</a> above, then
parsed into 1024-bit blocks that are considered to be composed of
sixteen 64-bit words M(i)0, M(i)1, ..., M(i)15. The following
computations are then performed for each of the N message blocks.
All addition is performed modulo 2^64.
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<span class="grey"><a href="./rfc6234">RFC 6234</a> SHAs, HMAC-SHAs, and HKDF May 2011</span>