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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 Mac OS X.


On Ubuntu 14.04 LTS:

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

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 ..

Optionally, you can specify the install location by providing the desired install path prefix:

cmake .. -DCMAKE_INSTALL_PREFIX=/install/path

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 execute the tests for this library, run:

make check