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a portable and fast pairing-based cryptography library

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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

  • Improve the performance of squareRoot.
  • Add batch inversion for Fr and Fp elements, and batch normalization for G1 and G2 points.
  • mulVec is a little improved.
  • mulEach with AVX-512 IFMA is improved slightly and 2.8 times faster than G1::mul on BLS12-381.
  • mulVec (multi scalar multiplication) with AVX-512 IFMA is 1.4 times faster on Xeon w9-3495X
  • a little performance improvement of G1::mulVec of BLS12-381
  • improve performance of Fr::inv on M1 mac
  • add mcl::bn::isValidGT(x) and mclBnGT_isValid(x) to check x in GT for x in Fp12.
  • support BN_P256 (hash-to-curve is not yet standard way.)
  • the performance of {G1,G2}::mulVec(z, xVec, yVec, n) has improved for n >= 256. (about 2x speed up for n = 512).
    • But it changes the type of xVec from const G* to G* because xVec may be normalized when computing.
    • fix mul(G, G, F) for F = Fp at v1.61
  • add set DST functions for hashMapToGi
  • add F::invVec, G::normalizeVec
  • improve SECP256K1 for x64
  • add G1::mulVecMT, G2::mulVecMT (enabled by MCL_USE_OMP=1)
  • improve mulMod of SECP256K1 for wasm
  • fix FpToG1(P, u, v) and Fp2ToG2(P, u, v) when u == v (This bug does not affect mapToG1 and mapToG2).
  • add millerLoopVecMT (enabled if built with MCL_USE_OMP=1)
  • support s390x(systemz)
  • improve M1 mac performance
  • set default MCL_MAX_BIT_SIZE=512 so disable to support NICT_P521.
  • improve performance
  • support M1 mac

Support architecture

  • x86-64 Windows + Visual Studio 2015 (or later)
  • x86, x86-64 Linux + gcc/clang
  • x86-64, M1 macOS
  • ARM / ARM64 Linux
  • WebAssembly : see mcl-wasm
  • Android : see mcl-android
  • iPhone
  • s390x(systemz)
    • install llvm and clang, and make UPDATE_ASM=1 once.
  • (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

BLS signature

See bls if you want mcl for BLS-signature.

C-API

See api.md and FAQ for serialization and hash-to-curve.

How to build on Linux and macOS

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

GMP is necessary only to build test programs.

  • sudo apt install libgmp-dev on Ubuntu
  • brew install gmp on macOS

OpenMP is optional (make MCL_USE_OMP=1 to use OpenMP for mulVec)

  • sudo apt install libomp-dev on Ubuntu
  • brew install libomp

How to build with Makefile

For x86-64 Linux and macOS,

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

clang++ is required except for x86-64 on Linux and Windows.

make -j4 CXX=clang++
  • lib/libmcl.* ; core library
  • lib/libmclbn384_256.* ; library to use C-API of BLS12-381 pairing

How to build with CMake

For x86-64 Linux and macOS.

mkdir build
cd build
cmake ..
make

For the other platform (including mingw), clang++ is required.

mkdir build
cd build
cmake .. -DCMAKE_CXX_COMPILER=clang++
make

Use clang++ instead of gcc on mingw.

For Visual Studio, (REMARK : It is not maintained; use the vcxproj file.)

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

How to build a static library with Visual Studio

Open mcl.sln and build it. src/proj/lib/lib.vcxproj is to build a static library lib/mcl.lib which is defined MCL_MAX_BIT_SIZE=384.

options

see cmake .. -LA.

tests

make test binaries in ./bin.

cmake .. -DBUILD_TESTING=ON
make -j4

How to make from src/{base,bint}{32,64}.ll

clang (clang-cl on Windows) is necessary to build files with a suffix ll.

  • BIT = 64 (if 64-bit CPU) else 32
  • src/base${BIT}.ll is necessary if MCL_USE_LLVM is defined.
    • This code is used if xbyak is not used.
  • src/bint${BIT}.ll is necessary if MCL_BINT_ASM=1.
    • src/bint-x64-{amd64,win}.asm is used instead if MCL_BINT_ASM_X64=1.
    • It is faster than src/bint64.ll because it uses mulx/adox/adcx.

These files may be going to be unified in the future.

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 make a library for BLS12-381 without Xbyak

On x64 environment, mcl uses JIT code, but if you want to avoid them,

make lib/libmcl.a MCL_STATIC_CODE=1 -j
# test of pairing
make test_static

The generated library supports only BLS12_381 and requires compiler options -DMCL_MAX_BIT_SIZE=384 -DMCL_STATIC_CODE.

How to profile on Linux

Use perf

make MCL_USE_PROF=1 bin/bls12_test.exe
env MCL_PROF=1 bin/bls12_test.exe

Use Intel VTune profiler

Supporse VTune is installed in /opt/intel/vtune_amplifier/.

make MCL_USE_PROF=2 bin/bls12_test.exe
env MCL_PROF=2 bin/bls12_test.exe

How to build on 32-bit x86 Linux

Build GMP for 32-bit mode.

sudo apt install g++-multilib
sudo apt install clang-14
cd <GMP dir>
env ABI=32 ./configure --enable-cxx --prefix=<install dir>
make -j install
cd <mcl dir>
make ARCH=x86 LLVM_VER=-14 GMP_DIR=<install dir>

How to build a library for arm with clang++ on Linux

make -f Makefile.cross BIT=32 TARGET=armv7l
sudo apt install g++-arm-linux-gnueabi
arm-linux-gnueabi-g++ sample/pairing.cpp -O3 -DNDEBUG -I ./include/ lib/libmclbn384_256.a -DMCL_MAX_BIT_SIZE=384
env QEMU_LD_PREFIX=/usr/arm-linux-gnueabi/ qemu-arm ./a.out

The static library libbls384_256.a built by bls/Makefile.onelib in bls contains all mcl functions. So please see the comment of Makefile.onelib if you want to build this library on the other platform such as Mingw64 on Linux.

How to build on 64-bit Windows with Visual Studio

Python3 is necessary. Open a console window, and

git clone https://github.com/herumi/mcl
cd mcl

# 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

C# test

cd mcl
mklib dll
cd ffi/cs
dotnet build mcl.sln
cd ../../bin
../ffi/cs/test/bin/Debug/netcoreapp3.1/test.exe

How to build for wasm(WebAssembly)

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

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

Node.js

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

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.

References

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.

FAQ

How do I set the hash value to Fr?

The behavior of setHashOf function may be a little different from what you want.

Please use the following code:

template<class F>
void setHash(F& x, const void *msg, size_t msgSize)
{
    uint8_t md[32];
    mcl::fp::sha256(md, sizeof(md), msg, msgSize);
    x.setBigEndianMod(md, sizeof(md));
    // or x.setLittleEndianMod(md, sizeof(md));
}

History

  • 2022/Apr/10 v1.60 improve {G1,G2}::mulVec
  • 2022/Mar/25 v1.59 add set DST functions for hashMapToGi
  • 2022/Mar/24 add F::invVec, G::normalizeVec
  • 2022/Mar/08 v1.58 improve SECP256K1 for x64
  • 2022/Feb/13 v1.57 add mulVecMT
  • 2021/Aug/26 v1.52 improve {G1,G2}::isValidOrder() for BLS12-381
  • 2021/May/04 v1.50 support s390x(systemz)
  • 2021/Apr/21 v1.41 fix inner function of mapToGi for large dst (not affect hashAndMapToGi)
  • 2021/May/24 v1.40 fix sigsegv in valgrind
  • 2021/Jan/28 v1.31 fix : call setOrder in init for isValidOrder
  • 2021/Jan/28 v1.30 a little optimization of Fp operations
  • 2020/Nov/14 v1.28 support M1 mac
  • 2020/Jun/07 v1.22 remove old hash-to-curve functions
  • 2020/Jun/04 v1.21 mapToG1 and hashAndMapToG1 are compatible to irtf/eip-2537
  • 2020/May/13 v1.09 support draft-irtf-cfrg-hash-to-curve-07
  • 2020/Mar/26 v1.07 change DST for hash-to-curve-06
  • 2020/Mar/15 v1.06 support hash-to-curve-06
  • 2020/Jan/31 v1.05 mclBn_ethMsgToFp2 has changed to append zero byte at the end of msg
  • 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

MITSUNARI Shigeo([email protected])

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a portable and fast pairing-based cryptography library

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cryptography pairing

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