[![Build Status](https://travis-ci.org/herumi/mcl.png)](https://travis-ci.org/herumi/mcl) # 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. # 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](https://blog.z.cash/new-snark-curve/) # C-API see [api.md](api.md) # How to build on Linux and macOS x86-64/ARM/ARM64 Linux, macOS and mingw64 are supported. ## Installation Requirements [GMP](https://gmplib.org/) and [OpenSSL](https://www.openssl.org/) are necessary (default setting). ``` apt install libgmp-dev libssl-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 without OpenSSL ``` make MCL_USE_OPENSSL=0 ``` Define `MCL_DONT_USE_OPENSSL` if using C++ header files. ## How to build on 32-bit x86 Linux Build GMP and OpenSSL for 32-bit mode and install `` at yourself. ``` make ARCH=x86 CFLAGS_USER="-I /include" LDFLAGS_USER="-L /lib -Wl,-rpath,/lib" ``` # How to build on 64-bit Windows with Visual Studio Clone cybozulib\_ext, which provides compiled binaries of OpenSSL and [MPIR](http://mpir.org/). ``` 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 cmake .. USE_OPENSSL=OFF ; without OpenSSL ``` 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](https://herumi.github.io/mcl-wasm/ibe-demo.html) * [SHE on browser](https://herumi.github.io/she-wasm/she-demo.html) * [BLS signature on brower](https://herumi.github.io/bls-wasm/bls-demo.html) The timing of a pairing on `BN254` is 2.8msec on 64-bit Firefox with Skylake 3.4GHz. # Node.js * [mcl-wasm](https://www.npmjs.com/package/mcl-wasm) pairing library * [bls-wasm](https://www.npmjs.com/package/bls-wasm) BLS signature library * [she-wasm](https://www.npmjs.com/package/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](https://herumi.github.io/mcl-wasm/ibe-demo.html). 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](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](http://www.96boards.org/product/hikey/) software | x64| x86| arm|arm64(msec) ---------------------------------------------------------|------|-----|----|----- [ate-pairing](https://github.com/herumi/ate-pairing) | 0.21 | - | - | - mcl | 0.31 | 1.6 |22.6| 3.9 [TEPLA](http://www.cipher.risk.tsukuba.ac.jp/tepla/) | 1.76 | 3.7 | 37 | 17.9 [RELIC](https://github.com/relic-toolkit/relic) PRIME=254| 0.30 | 3.5 | 36 | - [MIRACL](https://github.com/miracl/MIRACL) ake12bnx | 4.2 | - | 78 | - [NEONabe](http://sandia.cs.cinvestav.mx/Site/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](http://llvm.org/). ``` make MCL_USE_LLVM=1 LLVM_VER= UPDATE_ASM=1 ``` For example, specify `-3.8` for `` 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= 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_](https://dl.acm.org/citation.cfm?doid=3196494.3196552), N. Attrapadung, G. Hanaoka, S. Mitsunari, Y. Sakai, K. Shimizu, and T. Teruya. ASIACCS 2018 * [she-api](https://github.com/herumi/mcl/blob/master/misc/she/she-api.md) * [she-api(Japanese)](https://github.com/herumi/mcl/blob/master/misc/she/she-api-ja.md) # Java API See [java.md](https://github.com/herumi/mcl/blob/master/ffi/java/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](https://github.com/heurmi/xbyak) * [cybozulib](https://github.com/heurmi/cybozulib) * [Lifted-ElGamal](https://github.com/aistcrypt/Lifted-ElGamal) # References * [ate-pairing](https://github.com/herumi/ate-pairing/) * [_Faster Explicit Formulas for Computing Pairings over Ordinary Curves_](http://dx.doi.org/10.1007/978-3-642-20465-4_5), D.F. Aranha, K. Karabina, P. Longa, C.H. Gebotys, J. Lopez, EUROCRYPTO 2011, ([preprint](http://eprint.iacr.org/2010/526)) * [_High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves_](http://dx.doi.org/10.1007/978-3-642-17455-1_2), Jean-Luc Beuchat, Jorge Enrique González Díaz, Shigeo Mitsunari, Eiji Okamoto, Francisco Rodríguez-Henríquez, Tadanori Teruya, Pairing 2010, ([preprint](http://eprint.iacr.org/2010/354)) * [_Faster hashing to G2_](https://link.springer.com/chapter/10.1007/978-3-642-28496-0_25),Laura Fuentes-Castañeda, Edward Knapp, Francisco Rodríguez-Henríquez, SAC 2011, ([PDF](http://cacr.uwaterloo.ca/techreports/2011/cacr2011-26.pdf)) * [_Skew Frobenius Map and Efficient Scalar Multiplication for Pairing–Based Cryptography_](https://www.researchgate.net/publication/221282560_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](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/bls_signature.md#point-representations) 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 - 2019/Sep/30 v1.00 add some functions to bn.h ; [api.md](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](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/bls_signature.md#point-representations) - 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)