Merge pull request #15 from AbdelStark/main

📝 init mdbook

.github/workflows/book.yml

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+name: Bitcoin Circle STARK Book
+
+on:
+  push:
+    branches:
+      - main
+  pull_request:
+
+jobs:
+  deploy:
+    runs-on: ubuntu-20.04
+    concurrency:
+      group: ${{ github.workflow }}-${{ github.ref }}
+    steps:
+      - uses: actions/checkout@v2
+
+      - name: Setup mdBook
+        uses: peaceiris/actions-mdbook@v1
+        with:
+          mdbook-version: "0.4.10"
+
+      - name: Build mdBook
+        run: mdbook build
+        working-directory: ./book
+
+      - name: Deploy
+        uses: peaceiris/actions-gh-pages@v3
+        if: ${{ github.ref == 'refs/heads/main' }}
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: ./book/book

book/.gitignore

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+book

book/book.toml

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+[book]
+authors = ["Bitcoin-Wildlife-Sanctuary"]
+language = "en"
+multilingual = false
+src = "src"
+title = "Bitcoin Circle STARK"
+
+[output.html]
+git-repository-url = "https://github.com/Bitcoin-Wildlife-Sanctuary/bitcoin-circle-stark/"
+edit-url-template = "https://github.com/Bitcoin-Wildlife-Sanctuary/bitcoin-circle-stark/book/{path}"
+
+[output.html.playground]
+runnable = false

book/src/README.md

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+
+# Introduction
+
+Bitcoin Circle STARK includes Bitcoin script implementations of various cryptographic primitives for STARK.
+
+Essentially, it's a collection of building blocks of a Circle STARK verifier in Bitcoin script.
+
+- [Circle STARKs paper](https://eprint.iacr.org/2024/278.pdf)

book/src/SUMMARY.md

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+
+# Summary
+
+[Introduction](README.md)
+
+- [Primitives](./primitives.md)

book/src/primitives.md

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+
+# Primitives
+
+## M31, CM31, QM31, Circle Point
+
+- Implementation of add, sub, mul of Mersenne-31 (M31), its complex extension (CM31), and its degree-4 extension (QM31), which is imported from [BitVM/rust-bitcoin-m31-or-babybear](https://github.com/BitVM/rust-bitcoin-m31-or-babybear).
+
+## CirclePoint over QM31
+
+- Implementation of doubling of a circle point over QM31.
+- Implementation of drawing a random point on the circle over QM31, useful for Order-Optimal Data Structures (OODS).
+
+## Fiat-Shamir Transcript
+
+- Also known as "channel," which is the term used in Starkware's [stwo](https://github.com/starkware-libs/stwo) library.
+- Absorbing commitments and QM31 elements through `OP_CAT + OP_SHA256`.
+- Squeezing random elements for Fiat-Shamir transform using hints and `OP_CAT + OP_SHA256`.
+
+## Proof-of-Work Check
+
+- Calculating a proof-of-work nonce for the "channel", based on specified security bits.
+- Verifying the proof-of-work nonce and computing the new "channel" state.
+
+## Merkle Tree
+
+- Implementation of Merkle path verification using hints and `OP_CAT + OP_SHA256`.