mirror of https://github.com/status-im/op-geth.git
83 lines
1.8 KiB
Go
83 lines
1.8 KiB
Go
// Copyright 2020 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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import (
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"math/big"
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"math/bits"
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"github.com/ethereum/go-ethereum/common"
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)
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// FastExp is semantically equivalent to x.Exp(x,y, m), but is faster for even
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// modulus.
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func FastExp(x, y, m *big.Int) *big.Int {
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// Split m = m1 × m2 where m1 = 2ⁿ
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n := m.TrailingZeroBits()
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m1 := new(big.Int).Lsh(common.Big1, n)
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mask := new(big.Int).Sub(m1, common.Big1)
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m2 := new(big.Int).Rsh(m, n)
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// We want z = x**y mod m.
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// z1 = x**y mod m1 = (x**y mod m) mod m1 = z mod m1
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// z2 = x**y mod m2 = (x**y mod m) mod m2 = z mod m2
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z1 := fastExpPow2(x, y, mask)
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z2 := new(big.Int).Exp(x, y, m2)
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// Reconstruct z from z1, z2 using CRT, using algorithm from paper,
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// which uses only a single modInverse.
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// p = (z1 - z2) * m2⁻¹ (mod m1)
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// z = z2 + p * m2
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z := new(big.Int).Set(z2)
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// Compute (z1 - z2) mod m1 [m1 == 2**n] into z1.
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z1 = z1.And(z1, mask)
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z2 = z2.And(z2, mask)
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z1 = z1.Sub(z1, z2)
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if z1.Sign() < 0 {
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z1 = z1.Add(z1, m1)
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}
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// Reuse z2 for p = z1 * m2inv.
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m2inv := new(big.Int).ModInverse(m2, m1)
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z2 = z2.Mul(z1, m2inv)
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z2 = z2.And(z2, mask)
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// Reuse z1 for m2 * p.
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z = z.Add(z, z1.Mul(z2, m2))
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z = z.Rem(z, m)
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return z
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}
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func fastExpPow2(x, y *big.Int, mask *big.Int) *big.Int {
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z := big.NewInt(1)
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if y.Sign() == 0 {
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return z
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}
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p := new(big.Int).Set(x)
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p = p.And(p, mask)
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if p.Cmp(z) <= 0 { // p <= 1
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return p
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}
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if y.Cmp(mask) > 0 {
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y = new(big.Int).And(y, mask)
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}
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t := new(big.Int)
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for _, b := range y.Bits() {
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for i := 0; i < bits.UintSize; i++ {
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if b&1 != 0 {
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z, t = t.Mul(z, p), z
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z = z.And(z, mask)
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}
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p, t = t.Mul(p, p), p
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p = p.And(p, mask)
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b >>= 1
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}
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}
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return z
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}
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