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C++ library for Finite Fields and Elliptic Curves

libff is a C++ library for finite fields and elliptic curves. The library is developed by SCIPR Lab and contributors (see AUTHORS file) and is released under the MIT License (see LICENSE file).

Table of contents

Directory structure

The directory structure is as follows:

  • libff: C++ source code, containing the following modules:
    • algebra: fields and elliptic curve groups
    • common: miscellaneous utilities
  • depends: dependency libraries

Elliptic curve choices

The libsnark library currently provides three options:

  • edwards: an instantiation based on an Edwards curve, providing 80 bits of security.

  • bn128: an instantiation based on a Barreto-Naehrig curve, providing 128 bits of security. The underlying curve implementation is [ate-pairing], which has incorporated our patch that changes the BN curve to one suitable for SNARK applications.

    • This implementation uses dynamically-generated machine code for the curve arithmetic. Some modern systems disallow execution of code on the heap, and will thus block this implementation.

      For example, on Fedora 20 at its default settings, you will get the error zmInit ERR:can't protect when running this code. To solve this, run sudo setsebool -P allow_execheap 1 to allow execution, or use make CURVE=ALT_BN128 instead.

  • alt_bn128: an alternative to bn128, somewhat slower but avoids dynamic code generation.

Note that bn128 requires an x86-64 CPU while the other curve choices should be architecture-independent.

Build guide

The library has the following dependencies:

The library has been tested on Linux, but it is compatible with Windows and MacOS.


On Ubuntu 14.04 LTS:

sudo apt-get install build-essential git libboost-all-dev cmake libgmp3-dev libssl-dev libprocps3-dev pkg-config libsodium-dev

On MacOS, all of the libraries from the previous section can be installed with brew, except for libprocps, which is turned off by default.

Fetch dependencies from their GitHub repos:

git submodule init && git submodule update


To compile, starting at the project root directory, create the build directory and Makefile:

mkdir build && cd build
cmake ..

If you are on macOS, change the cmake command to be

cmake .. -DOPENSSL_ROOT_DIR=$(brew --prefix openssl)

Other build flags include:

Flag Value Description
MAKE_INSTALL_PREFIX (your path) Specifies the desired install location.
CMAKE_BUILD_TYPE Debug Enables asserts. Note that tests now use gtest instead of asserts.
WITH_PROCPS ON Enables libprocps, which is by default turned off since it is not supported on some systems such as MacOS.

Then, to compile and install the library, run this within the build directory:

make install

This will install libff.a into /install/path/lib; so your application should be linked using -L/install/path/lib -lff. It also installs the requisite headers into /install/path/include; so your application should be compiled using -I/install/path/include.


To build and execute the tests for this library, run:

make check

Code formatting and linting

To run clang-tidy on this library, specify the variable USE_CLANG_TIDY (eg. cmake .. -D USE_CLANG_TIDY=ON). Then, run:

make clang-tidy

One can specify which clang-tidy checks to run and which files to run clang-tidy on using the .clang-tidy file in the root directory of the project.


To compile the multi-exponentiation profiler in this library, run:

make profile

The resulting profiler is named multiexp_profile and can be found in the libff folder under the build directory.