libsecp256k1

Optimized C library for EC operations on curve secp256k1

This library is experimental, so use at your own risk.

Implementation details

• General
  • Avoid dynamic memory usage almost everywhere.
• 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.
    • Using GMP.
  • Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman).
• 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.
• 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 use secp256k1's efficiently-computable endomorphism to split the multiplicands into 4 half-sized ones first.
• 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.
  • Slice the precomputed table in memory per byte, so memory access to the table becomes uniform.