From ac088de6322fc16ebe75c2e5554be73754bf1fe2 Mon Sep 17 00:00:00 2001 From: Wei-Ning Huang Date: Wed, 12 Jun 2019 17:31:08 +0800 Subject: Rebrand as tangerine-network/go-tangerine --- vendor/github.com/dexon-foundation/mcl/readme.md | 457 ----------------------- 1 file changed, 457 deletions(-) delete mode 100644 vendor/github.com/dexon-foundation/mcl/readme.md (limited to 'vendor/github.com/dexon-foundation/mcl/readme.md') diff --git a/vendor/github.com/dexon-foundation/mcl/readme.md b/vendor/github.com/dexon-foundation/mcl/readme.md deleted file mode 100644 index 39b3d4d42..000000000 --- a/vendor/github.com/dexon-foundation/mcl/readme.md +++ /dev/null @@ -1,457 +0,0 @@ -[![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. -The current version supports the optimal Ate pairing over BN curves and BLS12-381 curves. - -# News -* (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. - -# Support architecture - -* x86-64 Windows + Visual Studio -* x86, x86-64 Linux + gcc/clang -* ARM Linux -* ARM64 Linux -* (maybe any platform to be supported by LLVM) -* WebAssembly - -# Support curves - -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/) - -# 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" -``` - -# Installation Requirements - -* [GMP](https://gmplib.org/) and OpenSSL -``` -apt install libgmp-dev libssl-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_ext ; for only Windows -``` -* Cybozulib\_ext is a prerequisite for running OpenSSL and GMP on VC (Visual C++). - -# (Option) Without GMP -``` -make MCL_USE_GMP=0 -``` -Define `MCL_USE_VINT` before including `bn.hpp` - -# (Option) Without Openssl -``` -make MCL_USE_OPENSSL=0 -``` -Define `MCL_DONT_USE_OPENSSL` before including `bn.hpp` - -# Build and test on x86-64 Linux, macOS, ARM and ARM64 Linux -To make lib/libmcl.a and test it: -``` -cd work/mcl -make test -``` -To benchmark a pairing: -``` -bin/bn_test.exe -``` -To make sample programs: -``` -make sample -``` - -if you want to change compiler options for optimization, then set `CFLAGS_OPT_USER`. -``` -make CLFAGS_OPT_USER="-O2" -``` - -## Build for 32-bit Linux -Build openssl and gmp for 32-bit mode and install `` -``` -make ARCH=x86 CFLAGS_USER="-I /include" LDFLAGS_USER="-L /lib -Wl,-rpath,/lib" -``` - -## Build for 64-bit Windows -1) make static library and use it - -``` -mklib -mk -s test\bn_c256_test.cpp -bin\bn_c256_test.exe -``` -2) make dynamic library and use it - -``` -mklib dll -mk -d test\bn_c256_test.cpp -bin\bn_c256_test.exe -``` - -open mcl.sln and build or if you have msbuild.exe -``` -msbuild /p:Configuration=Release -``` - -## Build with cmake -For Linux, -``` -mkdir build -cd build -cmake .. -make -``` -For Visual Studio, -``` -mkdir build -cd build -cmake .. -A x64 -msbuild mcl.sln /p:Configuration=Release /m -``` -## 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 - -### 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 -``` - -# Libraries - -* G1 and G2 is defined over Fp -* The order of G1 and G2 is r. -* Use `bn256.hpp` if only BN254 is used. - -## C++ library - -* libmcl.a ; static C++ library of mcl -* libmcl.so ; shared C++ library of mcl -* the default parameter of curveType is BN254 - -header |support curveType |sizeof Fr|sizeof Fp| ---------------|-------------------------|---------|---------| -bn256.hpp |BN254 | 32 | 32 | -bls12_381.hpp |BLS12_381, BN254 | 32 | 48 | -bn384.hpp |BN381_1, BLS12_381, BN254| 48 | 48 | - -## C library - -* Define `MCLBN_FR_UNIT_SIZE` and `MCLBN_FP_UNIT_SIZE` and include bn.h -* set `MCLBN_FR_UNIT_SIZE = MCLBN_FP_UNIT_SIZE` unless `MCLBN_FR_UNIT_SIZE` is defined - - -library |MCLBN_FR_UNIT_SIZE|MCLBN_FP_UNIT_SIZE| -------------------|------------------|------------------| -sizeof | Fr | Fp | -libmclbn256.a | 4 | 4 | -libmclbn384_256.a | 4 | 6 | -libmclbn384.a | 6 | 6 | - - -* libmclbn*.a ; static C library -* libmclbn*.so ; shared C library - -### 2nd argument of `mclBn_init` -Specify `MCLBN_COMPILED_TIME_VAR` to 2nd argument of `mclBn_init`, which -is defined as `MCLBN_FR_UNIT_SIZE * 10 + MCLBN_FP_UNIT_SIZE`. -This parameter is used to make sure that the values are the same when the library is built and used. - -# How to initialize pairing library -Call `mcl::bn256::initPairing` before calling any operations. -``` -#include -mcl::bn::CurveParam cp = mcl::BN254; // or mcl::BN_SNARK1 -mcl::bn256::initPairing(cp); -mcl::bn256::G1 P(...); -mcl::bn256::G2 Q(...); -mcl::bn256::Fp12 e; -mcl::bn256::pairing(e, P, Q); -``` -1. (BN254) a BN curve over the 254-bit prime p = p(z) where z = -(2^62 + 2^55 + 1). -2. (BN_SNARK1) a BN curve over a 254-bit prime p such that n := p + 1 - t has high 2-adicity. -3. BN381_1 with `mcl/bn384.hpp`. -4. BN462 with `mcl/bn512.hpp`. - -See [test/bn_test.cpp](https://github.com/herumi/mcl/blob/master/test/bn_test.cpp). - -## Default constructor of Fp, Ec, etc. -A default constructor does not initialize the instance. -Set a valid value before reffering it. - -## Definition of groups - -The curve equation for a BN curve is: - - E/Fp: y^2 = x^3 + b . - -* the cyclic group G1 is instantiated as E(Fp)[n] where n := p + 1 - t; -* the cyclic group G2 is instantiated as the inverse image of E'(Fp^2)[n] under a twisting isomorphism phi from E' to E; and -* the pairing e: G1 x G2 -> Fp12 is the optimal ate pairing. - -The field Fp12 is constructed via the following tower: - -* Fp2 = Fp[u] / (u^2 + 1) -* Fp6 = Fp2[v] / (v^3 - Xi) where Xi = u + 1 -* Fp12 = Fp6[w] / (w^2 - v) -* GT = { x in Fp12 | x^r = 1 } - - -## Arithmetic operations - -G1 and G2 is additive group and has the following operations: - -* T::add(T& z, const T& x, const T& y); // z = x + y -* T::sub(T& z, const T& x, const T& y); // z = x - y -* T::neg(T& y, const T& x); // y = -x -* T::mul(T& z, const T& x, const INT& y); // z = y times scalar multiplication of x - -Remark: &z == &x or &y are allowed. INT means integer type such as Fr, int and mpz_class. - -`T::mul` uses GLV method then `G2::mul` returns wrong value if x is not in G2. -Use `T::mulGeneric(T& z, const T& x, const INT& y)` for x in phi^-1(E'(Fp^2)) - G2. - -Fp, Fp2, Fp6 and Fp12 have the following operations: - -* T::add(T& z, const T& x, const T& y); // z = x + y -* T::sub(T& z, const T& x, const T& y); // z = x - y -* T::mul(T& z, const T& x, const T& y); // z = x * y -* T::div(T& z, const T& x, const T& y); // z = x / y -* T::neg(T& y, const T& x); // y = -x -* T::inv(T& y, const T& x); // y = 1/x -* T::pow(T& z, const T& x, const INT& y); // z = x^y -* Fp12::unitaryInv(T& y, const T& x); // y = conjugate of x - -Remark: `Fp12::mul` uses GLV method then returns wrong value if x is not in GT. -Use `Fp12::mulGeneric` for x in Fp12 - GT. - -## Map To points - -Use these functions to make a point of G1 and G2. - -* mapToG1(G1& P, const Fp& x); // assume x != 0 -* mapToG2(G2& P, const Fp2& x); -* hashAndMapToG1(G1& P, const void *buf, size_t bufSize); // set P by the hash value of [buf, bufSize) -* hashAndMapToG2(G2& P, const void *buf, size_t bufSize); - -These functions maps x into Gi according to [\[_Faster hashing to G2_\]]. - -## String format of G1 and G2 -G1 and G2 have three elements of Fp (x, y, z) for Jacobi coordinate. -normalize() method normalizes it to affine coordinate (x, y, 1) or (0, 0, 0). - -getStr() method gets - -* `0` ; infinity -* `1 ` ; not compressed format -* `2 ` ; compressed format for even y -* `3 ` ; compressed format for odd y - -## Generator of G1 and G2 - -If you want to use the same generators of BLS12-381 with [zkcrypto](https://github.com/zkcrypto/pairing/tree/master/src/bls12_381#g2) then, - -``` -// G1 P -P.setStr('1 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569') - -// G2 Q -Q.setStr('1 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582') -``` - -## Serialization format of G1 and G2 - -pseudo-code to serialize of p -``` -if bit-length(p) % 8 != 0: - size = Fp::getByteSize() - if p is zero: - return [0] * size - else: - s = x.serialize() - # x in Fp2 is odd <=> x.a is odd - if y is odd: - s[byte-length(s) - 1] |= 0x80 - return s -else: - size = Fp::getByteSize() + 1 - if p is zero: - return [0] * size - else: - s = x.serialize() - if y is odd: - return 2:s - else: - return 3:s -``` - -## Verify an element in G2 -`G2::isValid()` checks that the element is in the curve of G2 and the order of it is r for subgroup attack. -`G2::set()`, `G2::setStr` and `operator<<` also check the order. -If you check it out of the library, then you can stop the verification by calling `G2::verifyOrderG2(false)`. - -# 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/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_](http://dx.doi.org/10.1007/978-3-642-28496-0_25),Laura Fuentes-Castañeda, Edward Knapp, Francisco Rodríguez-Henríquez, - SAC 2011, ([preprint](https://eprint.iacr.org/2008/530)) -* [_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. - -# History - -* 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) -- cgit