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

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

Installation Requirements

• GMP must

apt install libgmp-dev

• OpenSSL must
• LLVM optional

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

mkdir work
cd work
git clone git://github.com/herumi/mcl.git
git clone git://github.com/herumi/cybozulib.git
git clone git://github.com/herumi/xbyak.git
git clone git://github.com/herumi/cybozulib_ext.git

• Xbyak is a prerequisite for optimizing the operations in the finite field on x86-64.
• Cybozulib_ext is a prerequisite for running OpenSSL and GMP on VC (Visual C++).

Build and test

To make lib/libmcl.a and test, run

make test

To measure pairing, run

bin/bn_test.exe

To make sample programs, run

make sample

If LLVM is installed, then

make MCL_USE_LLVM=1 LLVM_VER=-3.8

Change LLVM_VER=-3.8 to LLVM_VER=-3.7 if the version of LLVM is 3.7.

Build for 32-bit Linux

Build openssl and gmp for 32-bit mode and install

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

Build for ARM64 Linux

make MCL_USE_LLVM=1 LLVM_VER=-3.7 ARCH=aarch64

Build for ARM Linux

make MCL_USE_LLVM=1 LLVM_VER=-3.8 ARCH=arm

Benchmark

A benchmark of a BN curve over the 254-bit prime.

• 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	0.35	2.0	27	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	-

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)