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Latest commit

04af0ba Replace ge_equals_ge[,j] calls with group.h equality calls (Pieter Wuille)
60525f6 Add unit tests for group.h equality functions (Pieter Wuille)
a47cd97 Add group.h ge/gej equality functions (Pieter Wuille)

Pull request description:

  This pull requests removes the test-only functions `ge_equals_ge` and `ge_equals_gej`, and replaces them with proper group.h functions `secp256k1_ge_eq_var` and `secp256k1_gej_eq_ge_var` (mimicking the existing `secp256k1_gej_eq_var` function).

  This drops some of the arbitrary and undocumented magnitude restristrictions these functions have, makes them properly tested on their own, and makes their semantics cleaner (I'm always left checking whether `ge_equals_ge` does a `CHECK` internally or whether it returns a value...).

ACKs for top commit:
    utACK 04af0ba
    ACK 04af0ba.

Tree-SHA512: 49bc409ffa980144d1305c9389a846af45f0a97bfec19d016929056aa918c6a9f020dbe8549f5318fa8e6a4108621cc3cce60331aa0634f84619a1104d20a62a

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Dependencies: None #secp256k1

Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1.

This library is intended to be the highest quality publicly available library for cryptography on the secp256k1 curve. However, the primary focus of its development has been for usage in the Bitcoin system and usage unlike Bitcoin's may be less well tested, verified, or suffer from a less well thought out interface. Correct usage requires some care and consideration that the library is fit for your application's purpose.


  • secp256k1 ECDSA signing/verification and key generation.
  • Additive and multiplicative tweaking of secret/public keys.
  • Serialization/parsing of secret keys, public keys, signatures.
  • Constant time, constant memory access signing and public key generation.
  • Derandomized ECDSA (via RFC6979 or with a caller provided function.)
  • Very efficient implementation.
  • Suitable for embedded systems.
  • No runtime dependencies.
  • Optional module for public key recovery.
  • Optional module for ECDH key exchange.
  • Optional module for Schnorr signatures according to BIP-340.

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.
    • 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
      • Using 10 26-bit limbs (including hand-optimized assembly for 32-bit ARM, by Wladimir J. van der Laan).
        • This is an experimental feature that has not received enough scrutiny to satisfy the standard of quality of this library but is made available for testing and review by the community.
  • 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.
  • Modular inverses (both field elements and scalars) based on safegcd with some modifications, and a variable-time variant (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.
    • 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.
    • 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 (secret key) is known, preventing even an attacker with control over the secret key used to control the data internally.

Building with Autotools

$ ./
$ ./configure
$ make
$ make check  # run the test suite
$ sudo make install  # optional

To compile optional modules (such as Schnorr signatures), you need to run ./configure with additional flags (such as --enable-module-schnorrsig). Run ./configure --help to see the full list of available flags.

Building with CMake (experimental)

To maintain a pristine source tree, CMake encourages to perform an out-of-source build by using a separate dedicated build tree.

Building on POSIX systems

$ mkdir build && cd build
$ cmake ..
$ make
$ make check  # run the test suite
$ sudo make install  # optional

To compile optional modules (such as Schnorr signatures), you need to run cmake with additional flags (such as -DSECP256K1_ENABLE_MODULE_SCHNORRSIG=ON). Run cmake .. -LH to see the full list of available flags.

Cross compiling

To alleviate issues with cross compiling, preconfigured toolchain files are available in the cmake directory. For example, to cross compile for Windows:

$ cmake .. -DCMAKE_TOOLCHAIN_FILE=../cmake/x86_64-w64-mingw32.toolchain.cmake

To cross compile for Android with NDK (using NDK's toolchain file, and assuming the ANDROID_NDK_ROOT environment variable has been set):

$ cmake .. -DCMAKE_TOOLCHAIN_FILE="${ANDROID_NDK_ROOT}/build/cmake/android.toolchain.cmake" -DANDROID_ABI=arm64-v8a -DANDROID_PLATFORM=28

Building on Windows

To build on Windows with Visual Studio, a proper generator must be specified for a new build tree.

The following example assumes using of Visual Studio 2022 and CMake v3.21+.

In "Developer Command Prompt for VS 2022":

>cmake -G "Visual Studio 17 2022" -A x64 -S . -B build
>cmake --build build --config RelWithDebInfo

Usage examples

Usage examples can be found in the examples directory. To compile them you need to configure with --enable-examples.

To compile the Schnorr signature and ECDH examples, you also need to configure with --enable-module-schnorrsig and --enable-module-ecdh.

Test coverage

This library aims to have full coverage of the reachable lines and branches.

To create a test coverage report, configure with --enable-coverage (use of GCC is necessary):

$ ./configure --enable-coverage

Run the tests:

$ make check

To create a report, gcovr is recommended, as it includes branch coverage reporting:

$ gcovr --exclude 'src/bench*' --print-summary

To create a HTML report with coloured and annotated source code:

$ mkdir -p coverage
$ gcovr --exclude 'src/bench*' --html --html-details -o coverage/coverage.html


If configured with --enable-benchmark (which is the default), binaries for benchmarking the libsecp256k1 functions will be present in the root directory after the build.

To print the benchmark result to the command line:

$ ./bench_name

To create a CSV file for the benchmark result :

$ ./bench_name | sed '2d;s/ \{1,\}//g' > bench_name.csv

Reporting a vulnerability