mcl

A portable and fast pairing-based cryptography library.

Abstract

mcl is a library for pairing-based cryptography, which supports the optimal Ate pairing over BN curves and BLS12-381 curves.

News

add new hash functions corresponding to python-impl of algorand/bls_sig_ref.

• mclBn_ethMsgToFp2(resp. Hp2)
• mclBn_ethFp2ToG2(resp. opt_swu2_map)
• mclBn_ethMsgToG2(resp. map2curve_osswu2)

Support architecture

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

Support curves

• BN curve ; p(z) = 36z^4 + 36z^3 + 24z^2 + 6z + 1.
  • BN254 ; a BN curve over the 254-bit prime p(z) where z = -(2^62 + 2^55 + 1).
  • BN_SNARK1 ; a BN curve over a 254-bit prime p such that n := p + 1 - t has high 2-adicity.
  • BN381_1 ; a BN curve over the 381-bit prime p(z) where z = -(2^94 + 2^76 + 2^72 + 1).
  • BN462 ; a BN curve over the 462-bit prime p(z) where z = 2^114 + 2^101 - 2^14 - 1.
• BLS12_381 ; a BLS12-381 curve

C-API

see api.md

How to build on Linux and macOS

x86-64/ARM/ARM64 Linux, macOS and mingw64 are supported.

Installation Requirements

GMP is necessary (default setting).

apt install libgmp-dev # on Ubuntu

How to build with Makefile

git clone git://github.com/herumi/mcl
cd mcl
make -j4

• lib/libmcl.* ; core library
• lib/libmclbn384_256.* ; library to use C-API of BLS12-381 pairing

How to test of BLS12-381 pairing

# C
make bin/bn_c384_256_test.exe && bin/bn_c384_256_test.exe

# C++
make bin/bls12_test.exe && bin/bls12_test.exe

How to build without GMP

make MCL_USE_GMP=0

Define MCL_USE_VINT if using C++ header files.

How to build on 32-bit x86 Linux

Build GMP and for 32-bit mode and install <lib32> at yourself.

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

How to build on 64-bit Windows with Visual Studio

Clone cybozulib_ext, which provides compiled binaries of MPIR.

mkdir work
cd work
git clone git://github.com/herumi/mcl
git clone git://github.com/herumi/cybozulib_ext
cd work
# static library
mklib
mk -s test\bls12_test.cpp && bin\bls12_test.exe
# dynamic library
mklib dll
mk -d test\bls12_test.cpp && bin\bls12_test.exe

(not maintenanced) Open mcl.sln and build or if you have msbuild.exe

msbuild /p:Configuration=Release

How to build with CMake

For Linux, macOS, etc.

mkdir build
cd build
cmake ..
make

For Visual Studio,

mkdir build
cd build
cmake .. -A x64
msbuild mcl.sln /p:Configuration=Release /m

options

cmake .. USE_GMP=OFF ; without GMP

see cmake .. -LA.

How to build for wasm(WebAssembly)

mcl supports emcc (Emscripten) and test/bn_test.cpp runs on browers such as Firefox, Chrome and Edge.

• IBE on browser
• SHE on browser
• BLS signature on brower

The timing of a pairing on BN254 is 2.8msec on 64-bit Firefox with Skylake 3.4GHz.

Node.js

• mcl-wasm pairing library
• bls-wasm BLS signature library
• she-wasm 2 Level Homomorphic Encryption library

Benchmark

The latest benchmark(2018/11/7)

Intel Core i7-6700 3.4GHz(Skylake), Ubuntu 18.04.1 LTS

curveType	binary	clang-6.0.0	gcc-7.3.0
BN254	bin/bn_test.exe	882Kclk	933Kclk
BLS12-381	bin/bls12_test.exe	2290Kclk	2630Kclk

Intel Core i7-7700 3.6GHz(Kaby Lake), Ubuntu 18.04.1 LTS on Windows 10 Vmware

curveType	binary	clang-6.0.0	gcc-7.3.0
BN254	bin/bn_test.exe	900Kclk	954Kclk
BLS12-381	bin/bls12_test.exe	2340Kclk	2680Kclk

• now investigating the reason why gcc is slower than clang.

Higher-bit BN curve benchmark

For JavaScript(WebAssembly), see ID based encryption demo.

paramter	x64	Firefox on x64	Safari on iPhone7
BN254	0.25	2.48	4.78
BN381_1	0.95	7.91	11.74
BN462	2.16	14.73	22.77

• x64 : 'Kaby Lake Core i7-7700(3.6GHz)'.
• Firefox : 64-bit version 58.
• iPhone7 : iOS 11.2.1.
• BN254 is by test/bn_test.cpp.
• BN381_1 and BN462 are by test/bn512_test.cpp.
• All the timings are given in ms(milliseconds).

The other benchmark results are bench.txt.

An old benchmark of a BN curve BN254(2016/12/25).

• 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	3.9
TEPLA	1.76	3.7	37	17.9
RELIC PRIME=254	0.30	3.5	36	-
MIRACL ake12bnx	4.2	-	78	-
NEONabe	-	-	16	-

• compile option for RELIC

cmake -DARITH=x64-asm-254 -DFP_PRIME=254 -DFPX_METHD="INTEG;INTEG;LAZYR" -DPP_METHD="LAZYR;OATEP"

SELinux

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

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.

If you want to use Fp with 1024-bit prime on x86-64, then

make MCL_USE_LLVM=1 LLVM_VER=<llvm-version> UPDATE_ASM=1 MCL_MAX_BIT_SIZE=1024

API for Two level homomorphic encryption

• Efficient Two-level Homomorphic Encryption in Prime-order Bilinear Groups and A Fast Implementation in WebAssembly, N. Attrapadung, G. Hanaoka, S. Mitsunari, Y. Sakai, K. Shimizu, and T. Teruya. ASIACCS 2018
• she-api
• she-api(Japanese)

Java API

See java.md

License

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

This library contains some part of the followings software licensed by BSD-3-Clause.

• xbyak
• cybozulib
• 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, (PDF)
• Skew Frobenius Map and Efficient Scalar Multiplication for Pairing–Based Cryptography, Y. Sakemi, Y. Nogami, K. Okeya, Y. Morikawa, CANS 2008.

compatilibity

• mclBnGT_inv returns a - b w, a conjugate of x for x = a + b w in Fp12 = Fp6[w]
  • use mclBnGT_invGeneric if x is not in GT
• mclBn_setETHserialization(true) (de)serialize acoording to ETH2.0 serialization of BLS12-381 when BLS12-381 is used.
• (Break backward compatibility) libmcl_dy.a is renamed to libmcl.a
  • The option SHARE_BASENAME_SUF is removed
• 2nd argument of mclBn_init is changed from maxUnitSize to compiledTimeVar, which must be MCLBN_COMPILED_TIME_VAR.
• break backward compatibility of mapToGi for BLS12. A map-to-function for BN is used. If MCL_USE_OLD_MAPTO_FOR_BLS12 is defined, then the old function is used, but this will be removed in the future.

History

• 2020/Jan/25 v1.04 add new hash functions
• 2019/Dec/05 v1.03 disable to check the order in setStr
• 2019/Sep/30 v1.00 add some functions to bn.h ; api.md.
• 2019/Sep/22 v0.99 add mclBnG1_mulVec, etc.
• 2019/Sep/08 v0.98 bugfix Ec::add(P, Q, R) when P == R
• 2019/Aug/14 v0.97 add some C api functions
• 2019/Jul/26 v0.96 improved scalar multiplication
• 2019/Jun/03 v0.95 fix a parser of 0b10 with base = 16
• 2019/Apr/29 v0.94 mclBn_setETHserialization supports ETH2.0 serialization of BLS12-381
• 2019/Apr/24 v0.93 support ios
• 2019/Mar/22 v0.92 shortcut for Ec::mul(Px, P, x) if P = 0
• 2019/Mar/21 python binding of she256 for Linux/Mac/Windows
• 2019/Mar/14 v0.91 modp supports mcl-wasm
• 2019/Mar/12 v0.90 fix Vint::setArray(x) for x == this
• 2019/Mar/07 add mclBnFr_setLittleEndianMod, mclBnFp_setLittleEndianMod
• 2019/Feb/20 LagrangeInterpolation sets out = yVec[0] if k = 1
• 2019/Jan/31 add mclBnFp_mapToG1, mclBnFp2_mapToG2
• 2019/Jan/31 fix crash on x64-CPU without AVX (thanks to mortdeus)

Author

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