A generic and fast pairing-based cryptography library.
mcl is a library for pairing-based cryptography. The current version supports the optimal Ate pairing over BN curves.
- x86-64 Windows + Visual Studio
- x86, x86-64 Linux + gcc/clang
- ARM Linux
- ARM64 Linux
- (maybe any platform to be supported by LLVM)
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++).
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 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"
- make library
mklib.bat
- 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
mcl uses Xbyak JIT engine if it is available on x64 architecture, otherwise mcl uses a little slower functions generated by LLVM. The default mode enables SELinux security policy on CentOS, then JIT is disabled.
% sudo setenforce 1
% getenforce
Enforcing
% bin/bn_test.exe
JIT 0
pairing 1.496Mclk
finalExp 581.081Kclk
% sudo setenforce 0
% getenforce
Permissive
% bin/bn_test.exe
JIT 1
pairing 1.394Mclk
finalExp 546.259Kclk
Call mcl::bn256::bn256init before calling any operations.
#include <mcl/bn256.hpp>
mcl::bn::CurveParam cp = mcl::bn::CurveFp254BNb; // or mcl::bn::CurveSNARK1
mcl::bn256::bn256init(cp);
mcl::bn256::G1 P(...);
mcl::bn256::G2 Q(...);
mcl::bn256::Fp12 e;
mcl::bn256::BN::pairing(e, Q, P);
- (CurveFp254BNb) a BN curve over the 254-bit prime p = 36z^4 + 36z^3 + 24z^2 + 6z + 1 where z = -(2^62 + 2^55 + 1).
- (CurveSNARK1) a BN curve over a 254-bit prime p such that n := p + 1 - t has high 2-adicity.
See test/bn_test.cpp.
A benchmark of a BN curve CurveFp254BNb.
- x64, x86 ; Inte Core i7-6700 3.4GHz(Skylake) upto 4GHz on Ubuntu 16.04.
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 | 0.31 | 1.6 | 22.6 | 4.0 |
| TEPLA | 1.76 | 3.7 | 37 | 17.9 |
| RELIC PRIME=254 | 1.31 | 3.5 | 36 | - |
| MIRACL ake12bnx | 4.2 | - | 78 | - |
| NEONabe | - | - | 16 | - |
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.
See java.md
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.
- 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)
光成滋生 MITSUNARI Shigeo(herumi@nifty.com)