Skip to content
Optimized C library for EC operations on curve secp256k1
C C++ Python Java M4 Assembly Other
Branch: master
Clone or download
jonasnick Merge #678: Preventing compiler optimizations in benchmarks without a…
… memory fence

362bb25 Modified bench_scalar_split so it won't get optimized out (Elichai Turkel)
73a30c6 Added accumulators and checks on benchmarks so they won't get optimized out (Elichai Turkel)

Pull request description:

  As asked #667 (comment) this is the parts of #667 that don't require an assembly memory fence.

  I splitted them to 2 commits, one with obvious easy ones. and another that changes the logic a bit to achieve this (See #667 (comment) )

ACKs for top commit:
    ACK 362bb25
    ACK 362bb25 I read the diff and I ran the benchmarks

Tree-SHA512: d5e47f5d64c3b035155276f057671ceb7f5852f24c7102fee4d0141aabebf882039f3eae0d152bae89d0603bc09fa6ad9f7bc6b8c0f74a668ee252c727517804
Latest commit 544002c Nov 18, 2019
Type Name Latest commit message Commit time
Failed to load latest commit information.
build-aux/m4 Merge #460: [build] Update ax_jni_include_dir.m4 macro Feb 6, 2018
include Remove mention of ec_privkey_export because it doesn't exist Sep 15, 2019
obj Add obj/ directory Apr 11, 2013
.gitignore Add bench_ecmult to .gitignore Dec 31, 2017
.travis.yml Fix ASM setting in travis Nov 5, 2019
TODO variable signing precompute table Sep 5, 2019 Correct order of libs returned on pkg-config --libs --static libsecp2… Oct 23, 2018


Build Status

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.


  • 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.
    • No use of floating types, except in benchmarks.
    • 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.
    • Intended to be completely free of timing sidechannels for secret-key operations (on reasonable hardware/toolchains)
      • Access the table with branch-free conditional moves so memory access is uniform.
      • No data-dependent branches
    • Optional runtime blinding which attempts to frustrate differential power analysis.
    • 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:

$ ./
$ ./configure
$ make
$ make check
$ sudo make install  # optional

Exhaustive tests

$ ./exhaustive_tests

With valgrind, you might need to increase the max stack size:

$ valgrind --max-stackframe=2500000 ./exhaustive_tests
You can’t perform that action at this time.