Note this is taken from Bitcoin-ABC

Bitcoin-ABC commit dc0adb7b18f854a6b076824e4edb8b02ce62e5bd

It is recommended you go to the above link for specific issues/PRs/feedback, related to libsecp256k1.

The purpose of this fork is to provide a stand-alone repository of just libsecp256k1 (based off the Bitcoin ABC "Schnorr module enabled" fork of the secp256k1 codebase) for Electron Cash to pull in and build from. As such, this repository mostly lives as a submodule of the Electron Cash sources, and is accessed using Electron Cash's contrib/make_secp script.

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libsecp256k1

Optimized C library for EC operations on curve secp256k1.

This library is a work in progress and is being used to research best practices. Use at your own risk.

Features:

• secp256k1 ECDSA signing/verification and key generation.
• Adding/multiplying private/public keys.
• Serialization/parsing of private keys, public keys, signatures.
• Constant time, constant memory access signing and pubkey generation.
• Derandomized DSA (via RFC6979 or with a caller provided function.)
• Very efficient implementation.

Implementation details

• General
  • No runtime heap allocation.
  • Extensive testing infrastructure.
  • Structured to facilitate review and analysis.
  • Intended to be portable to any system with a C89 compiler and uint64_t support.
  • Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
• Field operations
  • Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).
    • Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys).
    • Using 10 26-bit limbs.
  • Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman).
• Scalar operations
  • Optimized implementation without data-dependent branches of arithmetic modulo the curve's order.
    • Using 4 64-bit limbs (relying on __int128 support in the compiler).
    • Using 8 32-bit limbs.
• Group operations
  • Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7).
  • Use addition between points in Jacobian and affine coordinates where possible.
  • Use a unified addition/doubling formula where necessary to avoid data-dependent branches.
  • Point/x comparison without a field inversion by comparison in the Jacobian coordinate space.
• Point multiplication for verification (aP + bG).
  • Use wNAF notation for point multiplicands.
  • Use a much larger window for multiples of G, using precomputed multiples.
  • Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
  • Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
• Point multiplication for signing
  • Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
  • Access the table with branch-free conditional moves so memory access is uniform.
  • No data-dependent branches
  • The precomputed tables add and eventually subtract points for which no known scalar (private key) is known, preventing even an attacker with control over the private key used to control the data internally.

Build steps

libsecp256k1 is built using autotools:

$ ./autogen.sh
$ ./configure
$ make
$ ./tests
$ sudo make install  # optional