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Add goff generated finite field arithmetic code for used field
feature/poseidon-opt-goff
3 changed files with 1120 additions and 0 deletions
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+122 -0ff/arith.go
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+764 -0ff/element.go
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+234 -0ff/element_test.go
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// Copyright 2020 ConsenSys AG
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// Code generated by goff DO NOT EDIT
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package ff |
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import ( |
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"math/bits" |
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) |
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func madd(a, b, t, u, v uint64) (uint64, uint64, uint64) { |
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var carry uint64 |
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hi, lo := bits.Mul64(a, b) |
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v, carry = bits.Add64(lo, v, 0) |
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u, carry = bits.Add64(hi, u, carry) |
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t, _ = bits.Add64(t, 0, carry) |
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return t, u, v |
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} |
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// madd0 hi = a*b + c (discards lo bits)
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func madd0(a, b, c uint64) (hi uint64) { |
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var carry, lo uint64 |
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hi, lo = bits.Mul64(a, b) |
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_, carry = bits.Add64(lo, c, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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return |
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} |
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// madd1 hi, lo = a*b + c
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func madd1(a, b, c uint64) (hi uint64, lo uint64) { |
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var carry uint64 |
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hi, lo = bits.Mul64(a, b) |
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lo, carry = bits.Add64(lo, c, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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return |
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} |
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// madd2 hi, lo = a*b + c + d
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func madd2(a, b, c, d uint64) (hi uint64, lo uint64) { |
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var carry uint64 |
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hi, lo = bits.Mul64(a, b) |
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c, carry = bits.Add64(c, d, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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lo, carry = bits.Add64(lo, c, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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return |
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} |
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// madd2s superhi, hi, lo = 2*a*b + c + d + e
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func madd2s(a, b, c, d, e uint64) (superhi, hi, lo uint64) { |
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var carry, sum uint64 |
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hi, lo = bits.Mul64(a, b) |
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lo, carry = bits.Add64(lo, lo, 0) |
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hi, superhi = bits.Add64(hi, hi, carry) |
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sum, carry = bits.Add64(c, e, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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lo, carry = bits.Add64(lo, sum, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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hi, _ = bits.Add64(hi, 0, d) |
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return |
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} |
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func madd1s(a, b, d, e uint64) (superhi, hi, lo uint64) { |
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var carry uint64 |
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hi, lo = bits.Mul64(a, b) |
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lo, carry = bits.Add64(lo, lo, 0) |
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hi, superhi = bits.Add64(hi, hi, carry) |
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lo, carry = bits.Add64(lo, e, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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hi, _ = bits.Add64(hi, 0, d) |
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return |
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} |
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func madd2sb(a, b, c, e uint64) (superhi, hi, lo uint64) { |
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var carry, sum uint64 |
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hi, lo = bits.Mul64(a, b) |
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lo, carry = bits.Add64(lo, lo, 0) |
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hi, superhi = bits.Add64(hi, hi, carry) |
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sum, carry = bits.Add64(c, e, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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lo, carry = bits.Add64(lo, sum, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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return |
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} |
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func madd1sb(a, b, e uint64) (superhi, hi, lo uint64) { |
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var carry uint64 |
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hi, lo = bits.Mul64(a, b) |
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lo, carry = bits.Add64(lo, lo, 0) |
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hi, superhi = bits.Add64(hi, hi, carry) |
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lo, carry = bits.Add64(lo, e, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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return |
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} |
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func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) { |
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var carry uint64 |
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hi, lo = bits.Mul64(a, b) |
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c, carry = bits.Add64(c, d, 0) |
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hi, _ = bits.Add64(hi, 0, carry) |
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lo, carry = bits.Add64(lo, c, 0) |
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hi, _ = bits.Add64(hi, e, carry) |
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return |
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} |
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@ -0,0 +1,764 @@ |
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// Copyright 2020 ConsenSys AG
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// field modulus q =
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//
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// 21888242871839275222246405745257275088548364400416034343698204186575808495617
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// Code generated by goff DO NOT EDIT
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// goff version: - build:
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// Element are assumed to be in Montgomery form in all methods
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// Package ff (generated by goff) contains field arithmetics operations
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package ff |
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import ( |
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"crypto/rand" |
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"encoding/binary" |
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"io" |
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"math/big" |
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"math/bits" |
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"sync" |
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"unsafe" |
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) |
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// Element represents a field element stored on 4 words (uint64)
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// Element are assumed to be in Montgomery form in all methods
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type Element [4]uint64 |
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// ElementLimbs number of 64 bits words needed to represent Element
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const ElementLimbs = 4 |
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// ElementBits number bits needed to represent Element
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const ElementBits = 254 |
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// SetUint64 z = v, sets z LSB to v (non-Montgomery form) and convert z to Montgomery form
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func (z *Element) SetUint64(v uint64) *Element { |
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z[0] = v |
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z[1] = 0 |
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z[2] = 0 |
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z[3] = 0 |
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return z.ToMont() |
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} |
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// Set z = x
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func (z *Element) Set(x *Element) *Element { |
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z[0] = x[0] |
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z[1] = x[1] |
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z[2] = x[2] |
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z[3] = x[3] |
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return z |
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} |
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// SetZero z = 0
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func (z *Element) SetZero() *Element { |
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z[0] = 0 |
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z[1] = 0 |
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z[2] = 0 |
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z[3] = 0 |
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return z |
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} |
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// SetOne z = 1 (in Montgomery form)
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func (z *Element) SetOne() *Element { |
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z[0] = 12436184717236109307 |
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z[1] = 3962172157175319849 |
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z[2] = 7381016538464732718 |
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z[3] = 1011752739694698287 |
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return z |
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} |
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// Neg z = q - x
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func (z *Element) Neg(x *Element) *Element { |
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if x.IsZero() { |
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return z.SetZero() |
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} |
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var borrow uint64 |
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z[0], borrow = bits.Sub64(4891460686036598785, x[0], 0) |
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z[1], borrow = bits.Sub64(2896914383306846353, x[1], borrow) |
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z[2], borrow = bits.Sub64(13281191951274694749, x[2], borrow) |
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z[3], _ = bits.Sub64(3486998266802970665, x[3], borrow) |
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return z |
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} |
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// Div z = x*y^-1 mod q
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func (z *Element) Div(x, y *Element) *Element { |
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var yInv Element |
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yInv.Inverse(y) |
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z.Mul(x, &yInv) |
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return z |
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} |
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// Equal returns z == x
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func (z *Element) Equal(x *Element) bool { |
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return (z[3] == x[3]) && (z[2] == x[2]) && (z[1] == x[1]) && (z[0] == x[0]) |
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} |
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// IsZero returns z == 0
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func (z *Element) IsZero() bool { |
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return (z[3] | z[2] | z[1] | z[0]) == 0 |
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} |
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// field modulus stored as big.Int
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var _elementModulusBigInt big.Int |
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var onceelementModulus sync.Once |
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func elementModulusBigInt() *big.Int { |
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onceelementModulus.Do(func() { |
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_elementModulusBigInt.SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10) |
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}) |
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return &_elementModulusBigInt |
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} |
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// Inverse z = x^-1 mod q
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// Algorithm 16 in "Efficient Software-Implementation of Finite Fields with Applications to Cryptography"
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// if x == 0, sets and returns z = x
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func (z *Element) Inverse(x *Element) *Element { |
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if x.IsZero() { |
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return z.Set(x) |
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} |
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// initialize u = q
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var u = Element{ |
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4891460686036598785, |
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2896914383306846353, |
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13281191951274694749, |
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3486998266802970665, |
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} |
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// initialize s = r^2
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var s = Element{ |
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1997599621687373223, |
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6052339484930628067, |
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10108755138030829701, |
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150537098327114917, |
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} |
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// r = 0
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r := Element{} |
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v := *x |
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var carry, borrow, t, t2 uint64 |
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var bigger, uIsOne, vIsOne bool |
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for !uIsOne && !vIsOne { |
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for v[0]&1 == 0 { |
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// v = v >> 1
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t2 = v[3] << 63 |
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v[3] >>= 1 |
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t = t2 |
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t2 = v[2] << 63 |
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v[2] = (v[2] >> 1) | t |
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t = t2 |
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t2 = v[1] << 63 |
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v[1] = (v[1] >> 1) | t |
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t = t2 |
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v[0] = (v[0] >> 1) | t |
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if s[0]&1 == 1 { |
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// s = s + q
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s[0], carry = bits.Add64(s[0], 4891460686036598785, 0) |
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s[1], carry = bits.Add64(s[1], 2896914383306846353, carry) |
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s[2], carry = bits.Add64(s[2], 13281191951274694749, carry) |
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s[3], _ = bits.Add64(s[3], 3486998266802970665, carry) |
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} |
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// s = s >> 1
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t2 = s[3] << 63 |
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s[3] >>= 1 |
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t = t2 |
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t2 = s[2] << 63 |
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s[2] = (s[2] >> 1) | t |
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t = t2 |
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t2 = s[1] << 63 |
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s[1] = (s[1] >> 1) | t |
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t = t2 |
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s[0] = (s[0] >> 1) | t |
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} |
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for u[0]&1 == 0 { |
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// u = u >> 1
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t2 = u[3] << 63 |
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u[3] >>= 1 |
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t = t2 |
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t2 = u[2] << 63 |
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u[2] = (u[2] >> 1) | t |
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t = t2 |
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t2 = u[1] << 63 |
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u[1] = (u[1] >> 1) | t |
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t = t2 |
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u[0] = (u[0] >> 1) | t |
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if r[0]&1 == 1 { |
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// r = r + q
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r[0], carry = bits.Add64(r[0], 4891460686036598785, 0) |
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r[1], carry = bits.Add64(r[1], 2896914383306846353, carry) |
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r[2], carry = bits.Add64(r[2], 13281191951274694749, carry) |
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r[3], _ = bits.Add64(r[3], 3486998266802970665, carry) |
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} |
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// r = r >> 1
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t2 = r[3] << 63 |
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r[3] >>= 1 |
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t = t2 |
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t2 = r[2] << 63 |
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r[2] = (r[2] >> 1) | t |
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t = t2 |
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t2 = r[1] << 63 |
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r[1] = (r[1] >> 1) | t |
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t = t2 |
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r[0] = (r[0] >> 1) | t |
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} |
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// v >= u
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bigger = !(v[3] < u[3] || (v[3] == u[3] && (v[2] < u[2] || (v[2] == u[2] && (v[1] < u[1] || (v[1] == u[1] && (v[0] < u[0]))))))) |
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if bigger { |
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// v = v - u
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v[0], borrow = bits.Sub64(v[0], u[0], 0) |
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v[1], borrow = bits.Sub64(v[1], u[1], borrow) |
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v[2], borrow = bits.Sub64(v[2], u[2], borrow) |
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v[3], _ = bits.Sub64(v[3], u[3], borrow) |
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// r >= s
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bigger = !(r[3] < s[3] || (r[3] == s[3] && (r[2] < s[2] || (r[2] == s[2] && (r[1] < s[1] || (r[1] == s[1] && (r[0] < s[0]))))))) |
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if bigger { |
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// s = s + q
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s[0], carry = bits.Add64(s[0], 4891460686036598785, 0) |
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s[1], carry = bits.Add64(s[1], 2896914383306846353, carry) |
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s[2], carry = bits.Add64(s[2], 13281191951274694749, carry) |
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s[3], _ = bits.Add64(s[3], 3486998266802970665, carry) |
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} |
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// s = s - r
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s[0], borrow = bits.Sub64(s[0], r[0], 0) |
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s[1], borrow = bits.Sub64(s[1], r[1], borrow) |
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s[2], borrow = bits.Sub64(s[2], r[2], borrow) |
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s[3], _ = bits.Sub64(s[3], r[3], borrow) |
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} else { |
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// u = u - v
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u[0], borrow = bits.Sub64(u[0], v[0], 0) |
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u[1], borrow = bits.Sub64(u[1], v[1], borrow) |
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u[2], borrow = bits.Sub64(u[2], v[2], borrow) |
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u[3], _ = bits.Sub64(u[3], v[3], borrow) |
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// s >= r
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bigger = !(s[3] < r[3] || (s[3] == r[3] && (s[2] < r[2] || (s[2] == r[2] && (s[1] < r[1] || (s[1] == r[1] && (s[0] < r[0]))))))) |
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if bigger { |
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// r = r + q
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r[0], carry = bits.Add64(r[0], 4891460686036598785, 0) |
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r[1], carry = bits.Add64(r[1], 2896914383306846353, carry) |
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r[2], carry = bits.Add64(r[2], 13281191951274694749, carry) |
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r[3], _ = bits.Add64(r[3], 3486998266802970665, carry) |
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} |
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// r = r - s
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r[0], borrow = bits.Sub64(r[0], s[0], 0) |
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r[1], borrow = bits.Sub64(r[1], s[1], borrow) |
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r[2], borrow = bits.Sub64(r[2], s[2], borrow) |
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r[3], _ = bits.Sub64(r[3], s[3], borrow) |
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} |
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uIsOne = (u[0] == 1) && (u[3]|u[2]|u[1]) == 0 |
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vIsOne = (v[0] == 1) && (v[3]|v[2]|v[1]) == 0 |
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} |
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if uIsOne { |
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z.Set(&r) |
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} else { |
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z.Set(&s) |
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} |
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return z |
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} |
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// SetRandom sets z to a random element < q
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func (z *Element) SetRandom() *Element { |
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bytes := make([]byte, 32) |
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io.ReadFull(rand.Reader, bytes) |
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z[0] = binary.BigEndian.Uint64(bytes[0:8]) |
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z[1] = binary.BigEndian.Uint64(bytes[8:16]) |
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z[2] = binary.BigEndian.Uint64(bytes[16:24]) |
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z[3] = binary.BigEndian.Uint64(bytes[24:32]) |
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z[3] %= 3486998266802970665 |
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// if z > q --> z -= q
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if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
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var b uint64 |
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z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
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z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
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z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
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z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
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} |
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return z |
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} |
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// Add z = x + y mod q
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func (z *Element) Add(x, y *Element) *Element { |
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var carry uint64 |
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z[0], carry = bits.Add64(x[0], y[0], 0) |
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z[1], carry = bits.Add64(x[1], y[1], carry) |
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z[2], carry = bits.Add64(x[2], y[2], carry) |
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z[3], _ = bits.Add64(x[3], y[3], carry) |
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// if z > q --> z -= q
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if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
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var b uint64 |
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z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
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z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
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z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// AddAssign z = z + x mod q
|
|||
func (z *Element) AddAssign(x *Element) *Element { |
|||
var carry uint64 |
|||
|
|||
z[0], carry = bits.Add64(z[0], x[0], 0) |
|||
z[1], carry = bits.Add64(z[1], x[1], carry) |
|||
z[2], carry = bits.Add64(z[2], x[2], carry) |
|||
z[3], _ = bits.Add64(z[3], x[3], carry) |
|||
|
|||
// if z > q --> z -= q
|
|||
if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
|||
z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
|||
z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// Double z = x + x mod q, aka Lsh 1
|
|||
func (z *Element) Double(x *Element) *Element { |
|||
var carry uint64 |
|||
|
|||
z[0], carry = bits.Add64(x[0], x[0], 0) |
|||
z[1], carry = bits.Add64(x[1], x[1], carry) |
|||
z[2], carry = bits.Add64(x[2], x[2], carry) |
|||
z[3], _ = bits.Add64(x[3], x[3], carry) |
|||
|
|||
// if z > q --> z -= q
|
|||
if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
|||
z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
|||
z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// Sub z = x - y mod q
|
|||
func (z *Element) Sub(x, y *Element) *Element { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(x[0], y[0], 0) |
|||
z[1], b = bits.Sub64(x[1], y[1], b) |
|||
z[2], b = bits.Sub64(x[2], y[2], b) |
|||
z[3], b = bits.Sub64(x[3], y[3], b) |
|||
if b != 0 { |
|||
var c uint64 |
|||
z[0], c = bits.Add64(z[0], 4891460686036598785, 0) |
|||
z[1], c = bits.Add64(z[1], 2896914383306846353, c) |
|||
z[2], c = bits.Add64(z[2], 13281191951274694749, c) |
|||
z[3], _ = bits.Add64(z[3], 3486998266802970665, c) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// SubAssign z = z - x mod q
|
|||
func (z *Element) SubAssign(x *Element) *Element { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], x[0], 0) |
|||
z[1], b = bits.Sub64(z[1], x[1], b) |
|||
z[2], b = bits.Sub64(z[2], x[2], b) |
|||
z[3], b = bits.Sub64(z[3], x[3], b) |
|||
if b != 0 { |
|||
var c uint64 |
|||
z[0], c = bits.Add64(z[0], 4891460686036598785, 0) |
|||
z[1], c = bits.Add64(z[1], 2896914383306846353, c) |
|||
z[2], c = bits.Add64(z[2], 13281191951274694749, c) |
|||
z[3], _ = bits.Add64(z[3], 3486998266802970665, c) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// Exp z = x^e mod q
|
|||
func (z *Element) Exp(x Element, e uint64) *Element { |
|||
if e == 0 { |
|||
return z.SetOne() |
|||
} |
|||
|
|||
z.Set(&x) |
|||
|
|||
l := bits.Len64(e) - 2 |
|||
for i := l; i >= 0; i-- { |
|||
z.Square(z) |
|||
if e&(1<<uint(i)) != 0 { |
|||
z.MulAssign(&x) |
|||
} |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// FromMont converts z in place (i.e. mutates) from Montgomery to regular representation
|
|||
// sets and returns z = z * 1
|
|||
func (z *Element) FromMont() *Element { |
|||
|
|||
// the following lines implement z = z * 1
|
|||
// with a modified CIOS montgomery multiplication
|
|||
{ |
|||
// m = z[0]n'[0] mod W
|
|||
m := z[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, z[0]) |
|||
C, z[0] = madd2(m, 2896914383306846353, z[1], C) |
|||
C, z[1] = madd2(m, 13281191951274694749, z[2], C) |
|||
C, z[2] = madd2(m, 3486998266802970665, z[3], C) |
|||
z[3] = C |
|||
} |
|||
{ |
|||
// m = z[0]n'[0] mod W
|
|||
m := z[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, z[0]) |
|||
C, z[0] = madd2(m, 2896914383306846353, z[1], C) |
|||
C, z[1] = madd2(m, 13281191951274694749, z[2], C) |
|||
C, z[2] = madd2(m, 3486998266802970665, z[3], C) |
|||
z[3] = C |
|||
} |
|||
{ |
|||
// m = z[0]n'[0] mod W
|
|||
m := z[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, z[0]) |
|||
C, z[0] = madd2(m, 2896914383306846353, z[1], C) |
|||
C, z[1] = madd2(m, 13281191951274694749, z[2], C) |
|||
C, z[2] = madd2(m, 3486998266802970665, z[3], C) |
|||
z[3] = C |
|||
} |
|||
{ |
|||
// m = z[0]n'[0] mod W
|
|||
m := z[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, z[0]) |
|||
C, z[0] = madd2(m, 2896914383306846353, z[1], C) |
|||
C, z[1] = madd2(m, 13281191951274694749, z[2], C) |
|||
C, z[2] = madd2(m, 3486998266802970665, z[3], C) |
|||
z[3] = C |
|||
} |
|||
|
|||
// if z > q --> z -= q
|
|||
if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
|||
z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
|||
z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// ToMont converts z to Montgomery form
|
|||
// sets and returns z = z * r^2
|
|||
func (z *Element) ToMont() *Element { |
|||
var rSquare = Element{ |
|||
1997599621687373223, |
|||
6052339484930628067, |
|||
10108755138030829701, |
|||
150537098327114917, |
|||
} |
|||
return z.MulAssign(&rSquare) |
|||
} |
|||
|
|||
// ToRegular returns z in regular form (doesn't mutate z)
|
|||
func (z Element) ToRegular() Element { |
|||
return *z.FromMont() |
|||
} |
|||
|
|||
// String returns the string form of an Element in Montgomery form
|
|||
func (z *Element) String() string { |
|||
var _z big.Int |
|||
return z.ToBigIntRegular(&_z).String() |
|||
} |
|||
|
|||
// ToBigInt returns z as a big.Int in Montgomery form
|
|||
func (z *Element) ToBigInt(res *big.Int) *big.Int { |
|||
bits := (*[4]big.Word)(unsafe.Pointer(z)) |
|||
return res.SetBits(bits[:]) |
|||
} |
|||
|
|||
// ToBigIntRegular returns z as a big.Int in regular form
|
|||
func (z Element) ToBigIntRegular(res *big.Int) *big.Int { |
|||
z.FromMont() |
|||
bits := (*[4]big.Word)(unsafe.Pointer(&z)) |
|||
return res.SetBits(bits[:]) |
|||
} |
|||
|
|||
// SetBigInt sets z to v (regular form) and returns z in Montgomery form
|
|||
func (z *Element) SetBigInt(v *big.Int) *Element { |
|||
z.SetZero() |
|||
|
|||
zero := big.NewInt(0) |
|||
q := elementModulusBigInt() |
|||
|
|||
// copy input
|
|||
vv := new(big.Int).Set(v) |
|||
|
|||
// while v < 0, v+=q
|
|||
for vv.Cmp(zero) == -1 { |
|||
vv.Add(vv, q) |
|||
} |
|||
// while v > q, v-=q
|
|||
for vv.Cmp(q) == 1 { |
|||
vv.Sub(vv, q) |
|||
} |
|||
// if v == q, return 0
|
|||
if vv.Cmp(q) == 0 { |
|||
return z |
|||
} |
|||
// v should
|
|||
vBits := vv.Bits() |
|||
for i := 0; i < len(vBits); i++ { |
|||
z[i] = uint64(vBits[i]) |
|||
} |
|||
return z.ToMont() |
|||
} |
|||
|
|||
// SetString creates a big.Int with s (in base 10) and calls SetBigInt on z
|
|||
func (z *Element) SetString(s string) *Element { |
|||
x, ok := new(big.Int).SetString(s, 10) |
|||
if !ok { |
|||
panic("Element.SetString failed -> can't parse number in base10 into a big.Int") |
|||
} |
|||
return z.SetBigInt(x) |
|||
} |
|||
|
|||
// Mul z = x * y mod q
|
|||
func (z *Element) Mul(x, y *Element) *Element { |
|||
|
|||
var t [4]uint64 |
|||
var c [3]uint64 |
|||
{ |
|||
// round 0
|
|||
v := x[0] |
|||
c[1], c[0] = bits.Mul64(v, y[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd1(v, y[1], c[1]) |
|||
c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd1(v, y[2], c[1]) |
|||
c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd1(v, y[3], c[1]) |
|||
t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
{ |
|||
// round 1
|
|||
v := x[1] |
|||
c[1], c[0] = madd1(v, y[0], t[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd2(v, y[1], c[1], t[1]) |
|||
c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, y[2], c[1], t[2]) |
|||
c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, y[3], c[1], t[3]) |
|||
t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
{ |
|||
// round 2
|
|||
v := x[2] |
|||
c[1], c[0] = madd1(v, y[0], t[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd2(v, y[1], c[1], t[1]) |
|||
c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, y[2], c[1], t[2]) |
|||
c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, y[3], c[1], t[3]) |
|||
t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
{ |
|||
// round 3
|
|||
v := x[3] |
|||
c[1], c[0] = madd1(v, y[0], t[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd2(v, y[1], c[1], t[1]) |
|||
c[2], z[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, y[2], c[1], t[2]) |
|||
c[2], z[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, y[3], c[1], t[3]) |
|||
z[3], z[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
|
|||
// if z > q --> z -= q
|
|||
if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
|||
z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
|||
z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// MulAssign z = z * x mod q
|
|||
func (z *Element) MulAssign(x *Element) *Element { |
|||
|
|||
var t [4]uint64 |
|||
var c [3]uint64 |
|||
{ |
|||
// round 0
|
|||
v := z[0] |
|||
c[1], c[0] = bits.Mul64(v, x[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd1(v, x[1], c[1]) |
|||
c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd1(v, x[2], c[1]) |
|||
c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd1(v, x[3], c[1]) |
|||
t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
{ |
|||
// round 1
|
|||
v := z[1] |
|||
c[1], c[0] = madd1(v, x[0], t[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd2(v, x[1], c[1], t[1]) |
|||
c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, x[2], c[1], t[2]) |
|||
c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, x[3], c[1], t[3]) |
|||
t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
{ |
|||
// round 2
|
|||
v := z[2] |
|||
c[1], c[0] = madd1(v, x[0], t[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd2(v, x[1], c[1], t[1]) |
|||
c[2], t[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, x[2], c[1], t[2]) |
|||
c[2], t[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, x[3], c[1], t[3]) |
|||
t[3], t[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
{ |
|||
// round 3
|
|||
v := z[3] |
|||
c[1], c[0] = madd1(v, x[0], t[0]) |
|||
m := c[0] * 14042775128853446655 |
|||
c[2] = madd0(m, 4891460686036598785, c[0]) |
|||
c[1], c[0] = madd2(v, x[1], c[1], t[1]) |
|||
c[2], z[0] = madd2(m, 2896914383306846353, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, x[2], c[1], t[2]) |
|||
c[2], z[1] = madd2(m, 13281191951274694749, c[2], c[0]) |
|||
c[1], c[0] = madd2(v, x[3], c[1], t[3]) |
|||
z[3], z[2] = madd3(m, 3486998266802970665, c[0], c[2], c[1]) |
|||
} |
|||
|
|||
// if z > q --> z -= q
|
|||
if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
|||
z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
|||
z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
|
|||
// Square z = x * x mod q
|
|||
func (z *Element) Square(x *Element) *Element { |
|||
|
|||
var p [4]uint64 |
|||
|
|||
var u, v uint64 |
|||
{ |
|||
// round 0
|
|||
u, p[0] = bits.Mul64(x[0], x[0]) |
|||
m := p[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, p[0]) |
|||
var t uint64 |
|||
t, u, v = madd1sb(x[0], x[1], u) |
|||
C, p[0] = madd2(m, 2896914383306846353, v, C) |
|||
t, u, v = madd1s(x[0], x[2], t, u) |
|||
C, p[1] = madd2(m, 13281191951274694749, v, C) |
|||
_, u, v = madd1s(x[0], x[3], t, u) |
|||
p[3], p[2] = madd3(m, 3486998266802970665, v, C, u) |
|||
} |
|||
{ |
|||
// round 1
|
|||
m := p[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, p[0]) |
|||
u, v = madd1(x[1], x[1], p[1]) |
|||
C, p[0] = madd2(m, 2896914383306846353, v, C) |
|||
var t uint64 |
|||
t, u, v = madd2sb(x[1], x[2], p[2], u) |
|||
C, p[1] = madd2(m, 13281191951274694749, v, C) |
|||
_, u, v = madd2s(x[1], x[3], p[3], t, u) |
|||
p[3], p[2] = madd3(m, 3486998266802970665, v, C, u) |
|||
} |
|||
{ |
|||
// round 2
|
|||
m := p[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, p[0]) |
|||
C, p[0] = madd2(m, 2896914383306846353, p[1], C) |
|||
u, v = madd1(x[2], x[2], p[2]) |
|||
C, p[1] = madd2(m, 13281191951274694749, v, C) |
|||
_, u, v = madd2sb(x[2], x[3], p[3], u) |
|||
p[3], p[2] = madd3(m, 3486998266802970665, v, C, u) |
|||
} |
|||
{ |
|||
// round 3
|
|||
m := p[0] * 14042775128853446655 |
|||
C := madd0(m, 4891460686036598785, p[0]) |
|||
C, z[0] = madd2(m, 2896914383306846353, p[1], C) |
|||
C, z[1] = madd2(m, 13281191951274694749, p[2], C) |
|||
u, v = madd1(x[3], x[3], p[3]) |
|||
z[3], z[2] = madd3(m, 3486998266802970665, v, C, u) |
|||
} |
|||
|
|||
// if z > q --> z -= q
|
|||
if !(z[3] < 3486998266802970665 || (z[3] == 3486998266802970665 && (z[2] < 13281191951274694749 || (z[2] == 13281191951274694749 && (z[1] < 2896914383306846353 || (z[1] == 2896914383306846353 && (z[0] < 4891460686036598785))))))) { |
|||
var b uint64 |
|||
z[0], b = bits.Sub64(z[0], 4891460686036598785, 0) |
|||
z[1], b = bits.Sub64(z[1], 2896914383306846353, b) |
|||
z[2], b = bits.Sub64(z[2], 13281191951274694749, b) |
|||
z[3], _ = bits.Sub64(z[3], 3486998266802970665, b) |
|||
} |
|||
return z |
|||
} |
|||
@ -0,0 +1,234 @@ |
|||
// Code generated by goff DO NOT EDIT
|
|||
package ff |
|||
|
|||
import ( |
|||
"crypto/rand" |
|||
"math/big" |
|||
mrand "math/rand" |
|||
"testing" |
|||
) |
|||
|
|||
func TestELEMENTCorrectnessAgainstBigInt(t *testing.T) { |
|||
modulus, _ := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10) |
|||
cmpEandB := func(e *Element, b *big.Int, name string) { |
|||
var _e big.Int |
|||
if e.FromMont().ToBigInt(&_e).Cmp(b) != 0 { |
|||
t.Fatal(name, "failed") |
|||
} |
|||
} |
|||
var modulusMinusOne, one big.Int |
|||
one.SetUint64(1) |
|||
|
|||
modulusMinusOne.Sub(modulus, &one) |
|||
|
|||
for i := 0; i < 1000; i++ { |
|||
|
|||
// sample 2 random big int
|
|||
b1, _ := rand.Int(rand.Reader, modulus) |
|||
b2, _ := rand.Int(rand.Reader, modulus) |
|||
rExp := mrand.Uint64() |
|||
|
|||
// adding edge cases
|
|||
// TODO need more edge cases
|
|||
switch i { |
|||
case 0: |
|||
rExp = 0 |
|||
b1.SetUint64(0) |
|||
case 1: |
|||
b2.SetUint64(0) |
|||
case 2: |
|||
b1.SetUint64(0) |
|||
b2.SetUint64(0) |
|||
case 3: |
|||
rExp = 0 |
|||
case 4: |
|||
rExp = 1 |
|||
case 5: |
|||
rExp = ^uint64(0) // max uint
|
|||
case 6: |
|||
rExp = 2 |
|||
b1.Set(&modulusMinusOne) |
|||
case 7: |
|||
b2.Set(&modulusMinusOne) |
|||
case 8: |
|||
b1.Set(&modulusMinusOne) |
|||
b2.Set(&modulusMinusOne) |
|||
} |
|||
|
|||
rbExp := new(big.Int).SetUint64(rExp) |
|||
|
|||
var bMul, bAdd, bSub, bDiv, bNeg, bLsh, bInv, bExp, bSquare big.Int |
|||
|
|||
// e1 = mont(b1), e2 = mont(b2)
|
|||
var e1, e2, eMul, eAdd, eSub, eDiv, eNeg, eLsh, eInv, eExp, eSquare, eMulAssign, eSubAssign, eAddAssign Element |
|||
e1.SetBigInt(b1) |
|||
e2.SetBigInt(b2) |
|||
|
|||
// (e1*e2).FromMont() === b1*b2 mod q ... etc
|
|||
eSquare.Square(&e1) |
|||
eMul.Mul(&e1, &e2) |
|||
eMulAssign.Set(&e1) |
|||
eMulAssign.MulAssign(&e2) |
|||
eAdd.Add(&e1, &e2) |
|||
eAddAssign.Set(&e1) |
|||
eAddAssign.AddAssign(&e2) |
|||
eSub.Sub(&e1, &e2) |
|||
eSubAssign.Set(&e1) |
|||
eSubAssign.SubAssign(&e2) |
|||
eDiv.Div(&e1, &e2) |
|||
eNeg.Neg(&e1) |
|||
eInv.Inverse(&e1) |
|||
eExp.Exp(e1, rExp) |
|||
eLsh.Double(&e1) |
|||
|
|||
// same operations with big int
|
|||
bAdd.Add(b1, b2).Mod(&bAdd, modulus) |
|||
bMul.Mul(b1, b2).Mod(&bMul, modulus) |
|||
bSquare.Mul(b1, b1).Mod(&bSquare, modulus) |
|||
bSub.Sub(b1, b2).Mod(&bSub, modulus) |
|||
bDiv.ModInverse(b2, modulus) |
|||
bDiv.Mul(&bDiv, b1). |
|||
Mod(&bDiv, modulus) |
|||
bNeg.Neg(b1).Mod(&bNeg, modulus) |
|||
|
|||
bInv.ModInverse(b1, modulus) |
|||
bExp.Exp(b1, rbExp, modulus) |
|||
bLsh.Lsh(b1, 1).Mod(&bLsh, modulus) |
|||
|
|||
cmpEandB(&eSquare, &bSquare, "Square") |
|||
cmpEandB(&eMul, &bMul, "Mul") |
|||
cmpEandB(&eMulAssign, &bMul, "MulAssign") |
|||
cmpEandB(&eAdd, &bAdd, "Add") |
|||
cmpEandB(&eAddAssign, &bAdd, "AddAssign") |
|||
cmpEandB(&eSub, &bSub, "Sub") |
|||
cmpEandB(&eSubAssign, &bSub, "SubAssign") |
|||
cmpEandB(&eDiv, &bDiv, "Div") |
|||
cmpEandB(&eNeg, &bNeg, "Neg") |
|||
cmpEandB(&eInv, &bInv, "Inv") |
|||
cmpEandB(&eExp, &bExp, "Exp") |
|||
cmpEandB(&eLsh, &bLsh, "Lsh") |
|||
} |
|||
} |
|||
|
|||
func TestELEMENTIsRandom(t *testing.T) { |
|||
for i := 0; i < 1000; i++ { |
|||
var x, y Element |
|||
x.SetRandom() |
|||
y.SetRandom() |
|||
if x.Equal(&y) { |
|||
t.Fatal("2 random numbers are unlikely to be equal") |
|||
} |
|||
} |
|||
} |
|||
|
|||
// -------------------------------------------------------------------------------------------------
|
|||
// benchmarks
|
|||
// most benchmarks are rudimentary and should sample a large number of random inputs
|
|||
// or be run multiple times to ensure it didn't measure the fastest path of the function
|
|||
// TODO: clean up and push benchmarking branch
|
|||
|
|||
var benchResElement Element |
|||
|
|||
func BenchmarkInverseELEMENT(b *testing.B) { |
|||
var x Element |
|||
x.SetRandom() |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
|
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Inverse(&x) |
|||
} |
|||
|
|||
} |
|||
func BenchmarkExpELEMENT(b *testing.B) { |
|||
var x Element |
|||
x.SetRandom() |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Exp(x, mrand.Uint64()) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkDoubleELEMENT(b *testing.B) { |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Double(&benchResElement) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkAddELEMENT(b *testing.B) { |
|||
var x Element |
|||
x.SetRandom() |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Add(&x, &benchResElement) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkSubELEMENT(b *testing.B) { |
|||
var x Element |
|||
x.SetRandom() |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Sub(&x, &benchResElement) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkNegELEMENT(b *testing.B) { |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Neg(&benchResElement) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkDivELEMENT(b *testing.B) { |
|||
var x Element |
|||
x.SetRandom() |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Div(&x, &benchResElement) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkFromMontELEMENT(b *testing.B) { |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.FromMont() |
|||
} |
|||
} |
|||
|
|||
func BenchmarkToMontELEMENT(b *testing.B) { |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.ToMont() |
|||
} |
|||
} |
|||
func BenchmarkSquareELEMENT(b *testing.B) { |
|||
benchResElement.SetRandom() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.Square(&benchResElement) |
|||
} |
|||
} |
|||
|
|||
func BenchmarkMulAssignELEMENT(b *testing.B) { |
|||
x := Element{ |
|||
1997599621687373223, |
|||
6052339484930628067, |
|||
10108755138030829701, |
|||
150537098327114917, |
|||
} |
|||
benchResElement.SetOne() |
|||
b.ResetTimer() |
|||
for i := 0; i < b.N; i++ { |
|||
benchResElement.MulAssign(&x) |
|||
} |
|||
} |
|||