8l/secp256k1

Optimized C library for EC operations on curve secp256k1

libsecp256k1

Optimized C library for EC operations on curve secp256k1.

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

Features:

• Low-level field and group operations on secp256k1.
• ECDSA signing/verification and key generation.
• Adding/multiplying private/public keys.
• Serialization/parsing of private keys, public keys, signatures.
• Very efficient implementation.

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).
• 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 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.
  • 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
$ sudo make install  # optional