// Copyright 2020 The go-ethereum Authors // This file is part of the go-ethereum library. // // The go-ethereum library is free software: you can redistribute it and/or modify // it under the terms of the GNU Lesser General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // The go-ethereum library is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU Lesser General Public License for more details. // // You should have received a copy of the GNU Lesser General Public License // along with the go-ethereum library. If not, see . package bls12381 import ( "crypto/rand" "encoding/hex" "fmt" "io" "math/big" ) // fe is base field element representation type fe [6]uint64 // fe2 is element representation of 'fp2' which is quadratic extension of base field 'fp' // Representation follows c[0] + c[1] * u encoding order. type fe2 [2]fe // fe6 is element representation of 'fp6' field which is cubic extension of 'fp2' // Representation follows c[0] + c[1] * v + c[2] * v^2 encoding order. type fe6 [3]fe2 // fe12 is element representation of 'fp12' field which is quadratic extension of 'fp6' // Representation follows c[0] + c[1] * w encoding order. type fe12 [2]fe6 func (fe *fe) setBytes(in []byte) *fe { size := 48 l := len(in) if l >= size { l = size } padded := make([]byte, size) copy(padded[size-l:], in[:]) var a int for i := 0; i < 6; i++ { a = size - i*8 fe[i] = uint64(padded[a-1]) | uint64(padded[a-2])<<8 | uint64(padded[a-3])<<16 | uint64(padded[a-4])<<24 | uint64(padded[a-5])<<32 | uint64(padded[a-6])<<40 | uint64(padded[a-7])<<48 | uint64(padded[a-8])<<56 } return fe } func (fe *fe) setBig(a *big.Int) *fe { return fe.setBytes(a.Bytes()) } func (fe *fe) setString(s string) (*fe, error) { if s[:2] == "0x" { s = s[2:] } bytes, err := hex.DecodeString(s) if err != nil { return nil, err } return fe.setBytes(bytes), nil } func (fe *fe) set(fe2 *fe) *fe { fe[0] = fe2[0] fe[1] = fe2[1] fe[2] = fe2[2] fe[3] = fe2[3] fe[4] = fe2[4] fe[5] = fe2[5] return fe } func (fe *fe) bytes() []byte { out := make([]byte, 48) var a int for i := 0; i < 6; i++ { a = 48 - i*8 out[a-1] = byte(fe[i]) out[a-2] = byte(fe[i] >> 8) out[a-3] = byte(fe[i] >> 16) out[a-4] = byte(fe[i] >> 24) out[a-5] = byte(fe[i] >> 32) out[a-6] = byte(fe[i] >> 40) out[a-7] = byte(fe[i] >> 48) out[a-8] = byte(fe[i] >> 56) } return out } func (fe *fe) big() *big.Int { return new(big.Int).SetBytes(fe.bytes()) } func (fe *fe) string() (s string) { for i := 5; i >= 0; i-- { s = fmt.Sprintf("%s%16.16x", s, fe[i]) } return "0x" + s } func (fe *fe) zero() *fe { fe[0] = 0 fe[1] = 0 fe[2] = 0 fe[3] = 0 fe[4] = 0 fe[5] = 0 return fe } func (fe *fe) one() *fe { return fe.set(r1) } func (fe *fe) rand(r io.Reader) (*fe, error) { bi, err := rand.Int(r, modulus.big()) if err != nil { return nil, err } return fe.setBig(bi), nil } func (fe *fe) isValid() bool { return fe.cmp(&modulus) < 0 } func (fe *fe) isOdd() bool { var mask uint64 = 1 return fe[0]&mask != 0 } func (fe *fe) isEven() bool { var mask uint64 = 1 return fe[0]&mask == 0 } func (fe *fe) isZero() bool { return (fe[5] | fe[4] | fe[3] | fe[2] | fe[1] | fe[0]) == 0 } func (fe *fe) isOne() bool { return fe.equal(r1) } func (fe *fe) cmp(fe2 *fe) int { for i := 5; i >= 0; i-- { if fe[i] > fe2[i] { return 1 } else if fe[i] < fe2[i] { return -1 } } return 0 } func (fe *fe) equal(fe2 *fe) bool { return fe2[0] == fe[0] && fe2[1] == fe[1] && fe2[2] == fe[2] && fe2[3] == fe[3] && fe2[4] == fe[4] && fe2[5] == fe[5] } func (e *fe) sign() bool { r := new(fe) fromMont(r, e) return r[0]&1 == 0 } func (fe *fe) div2(e uint64) { fe[0] = fe[0]>>1 | fe[1]<<63 fe[1] = fe[1]>>1 | fe[2]<<63 fe[2] = fe[2]>>1 | fe[3]<<63 fe[3] = fe[3]>>1 | fe[4]<<63 fe[4] = fe[4]>>1 | fe[5]<<63 fe[5] = fe[5]>>1 | e<<63 } func (fe *fe) mul2() uint64 { e := fe[5] >> 63 fe[5] = fe[5]<<1 | fe[4]>>63 fe[4] = fe[4]<<1 | fe[3]>>63 fe[3] = fe[3]<<1 | fe[2]>>63 fe[2] = fe[2]<<1 | fe[1]>>63 fe[1] = fe[1]<<1 | fe[0]>>63 fe[0] = fe[0] << 1 return e } func (e *fe2) zero() *fe2 { e[0].zero() e[1].zero() return e } func (e *fe2) one() *fe2 { e[0].one() e[1].zero() return e } func (e *fe2) set(e2 *fe2) *fe2 { e[0].set(&e2[0]) e[1].set(&e2[1]) return e } func (e *fe2) rand(r io.Reader) (*fe2, error) { a0, err := new(fe).rand(r) if err != nil { return nil, err } a1, err := new(fe).rand(r) if err != nil { return nil, err } return &fe2{*a0, *a1}, nil } func (e *fe2) isOne() bool { return e[0].isOne() && e[1].isZero() } func (e *fe2) isZero() bool { return e[0].isZero() && e[1].isZero() } func (e *fe2) equal(e2 *fe2) bool { return e[0].equal(&e2[0]) && e[1].equal(&e2[1]) } func (e *fe2) sign() bool { r := new(fe) if !e[0].isZero() { fromMont(r, &e[0]) return r[0]&1 == 0 } fromMont(r, &e[1]) return r[0]&1 == 0 } func (e *fe6) zero() *fe6 { e[0].zero() e[1].zero() e[2].zero() return e } func (e *fe6) one() *fe6 { e[0].one() e[1].zero() e[2].zero() return e } func (e *fe6) set(e2 *fe6) *fe6 { e[0].set(&e2[0]) e[1].set(&e2[1]) e[2].set(&e2[2]) return e } func (e *fe6) rand(r io.Reader) (*fe6, error) { a0, err := new(fe2).rand(r) if err != nil { return nil, err } a1, err := new(fe2).rand(r) if err != nil { return nil, err } a2, err := new(fe2).rand(r) if err != nil { return nil, err } return &fe6{*a0, *a1, *a2}, nil } func (e *fe6) isOne() bool { return e[0].isOne() && e[1].isZero() && e[2].isZero() } func (e *fe6) isZero() bool { return e[0].isZero() && e[1].isZero() && e[2].isZero() } func (e *fe6) equal(e2 *fe6) bool { return e[0].equal(&e2[0]) && e[1].equal(&e2[1]) && e[2].equal(&e2[2]) } func (e *fe12) zero() *fe12 { e[0].zero() e[1].zero() return e } func (e *fe12) one() *fe12 { e[0].one() e[1].zero() return e } func (e *fe12) set(e2 *fe12) *fe12 { e[0].set(&e2[0]) e[1].set(&e2[1]) return e } func (e *fe12) rand(r io.Reader) (*fe12, error) { a0, err := new(fe6).rand(r) if err != nil { return nil, err } a1, err := new(fe6).rand(r) if err != nil { return nil, err } return &fe12{*a0, *a1}, nil } func (e *fe12) isOne() bool { return e[0].isOne() && e[1].isZero() } func (e *fe12) isZero() bool { return e[0].isZero() && e[1].isZero() } func (e *fe12) equal(e2 *fe12) bool { return e[0].equal(&e2[0]) && e[1].equal(&e2[1]) }