mcl

A class library of finite field, elliptic curve and pairing

Abstract

mcl is a library for pairing-based cryptography. The current version supports the optimal Ate pairing over BN curves.

Support architecture

• x86-64 Windows + Visual Studio
• x86, x86-64 Linux + gcc/clang
• ARM Linux
• ARM64 Linux
• (maybe any platform to be supported by LLVM)

Installation Requirements

• GMP

apt install libgmp-dev

Create a working directory (e.g., work) and clone the following repositories.

mkdir work
cd work
git clone git://github.com/herumi/mcl
git clone git://github.com/herumi/cybozulib
git clone git://github.com/herumi/xbyak ; for only x86/x64
git clone git://github.com/herumi/cybozulib_ext ; for only Windows

• Cybozulib_ext is a prerequisite for running OpenSSL and GMP on VC (Visual C++).

Build and test on x86-64, ARM and ARM64 Linux

To make lib/libmcl.a and test it:

cod work/mcl
make test

To benchmark a pairing:

bin/bn_test.exe

To make sample programs:

make sample

Build for 32-bit Linux

Build openssl and gmp for 32-bit mode and install <lib32>

make ARCH=x86 CFLAGS_USER="-I <lib32>/include" LDFLAGS_USER="-L <lib32>/lib -Wl,-rpath,<lib32>/lib"

Build for 64-bit Windows

1. make library

mklib.bat

2. make exe binary of sample\pairing.cpp

mk sample\pairing.cpp

open mcl.sln and build or if you have msbuild.exe

msbuild /p:Configuration=Release

Benchmark

A benchmark of a BN curve over the 254-bit prime p = 36z^4 + 36z^3 + 24z^2 + 6z + 1 where z = -(2^62 + 2^55 + 1).

• x64, x86 ; Inte Core i7-6700 3.4GHz(Skylake) upto 4GHz
  • sudo cpufreq-set -g performance
• arm ; 900MHz quad-core ARM Cortex-A7 on Raspberry Pi2, Linux 4.4.11-v7+
• arm64 ; 1.2GHz ARM Cortex-A53 HiKey

software	x64	x86	arm	arm64(msec)
ate-pairing	0.21	-	-	-
mcl	0.34	1.8	25	4.4
TEPLA	1.76	3.7	37	17.9
RELIC PRIME=254	1.31	3.5	36	-
MIRACL ake12bnx	4.2	-	78	-
NEONabe	-	-	16	-

How to make asm files(optional)

The asm files generated by this way are already put in src/asm, then it is not necessary to do this.

Install LLVM.

make MCL_USE_LLVM=1 LLVM_VER=<llvm-version> UPDATE_ASM=1

For example, specify -3.8 for <llvm-version> if opt-3.8 and llc-3.8 are installed.

License

modified new BSD License http://opensource.org/licenses/BSD-3-Clause

The original source of the followings are https://github.com/aistcrypt/Lifted-ElGamal . These files are licensed by BSD-3-Clause and are used for only tests.

include/mcl/elgamal.hpp
include/mcl/window_method.hpp
test/elgamal_test.cpp
test/window_method_test.cpp
sample/vote.cpp

This library contains mie and Lifted-ElGamal.

References

• ate-pairing
• Faster Explicit Formulas for Computing Pairings over Ordinary Curves, D.F. Aranha, K. Karabina, P. Longa, C.H. Gebotys, J. Lopez, EUROCRYPTO 2011, (preprint)
• High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves, Jean-Luc Beuchat, Jorge Enrique González Díaz, Shigeo Mitsunari, Eiji Okamoto, Francisco Rodríguez-Henríquez, Tadanori Teruya, Pairing 2010, (preprint)
• Faster hashing to G2,Laura Fuentes-Castañeda, Edward Knapp, Francisco Rodríguez-Henríquez, SAC 2011, (preprint)

Author

光成滋生 MITSUNARI Shigeo(herumi@nifty.com)