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792 lines
22 KiB
792 lines
22 KiB
// 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)
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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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// AddAssign z = z + x mod q
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func (z *Element) AddAssign(x *Element) *Element {
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var carry uint64
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z[0], carry = bits.Add64(z[0], x[0], 0)
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z[1], carry = bits.Add64(z[1], x[1], carry)
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z[2], carry = bits.Add64(z[2], x[2], carry)
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z[3], _ = bits.Add64(z[3], x[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)
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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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// Double z = x + x mod q, aka Lsh 1
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func (z *Element) Double(x *Element) *Element {
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var carry uint64
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z[0], carry = bits.Add64(x[0], x[0], 0)
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z[1], carry = bits.Add64(x[1], x[1], carry)
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z[2], carry = bits.Add64(x[2], x[2], carry)
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z[3], _ = bits.Add64(x[3], x[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)
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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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// Sub z = x - y mod q
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func (z *Element) Sub(x, y *Element) *Element {
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var b uint64
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z[0], b = bits.Sub64(x[0], y[0], 0)
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z[1], b = bits.Sub64(x[1], y[1], b)
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z[2], b = bits.Sub64(x[2], y[2], b)
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z[3], b = bits.Sub64(x[3], y[3], b)
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if b != 0 {
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var c uint64
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z[0], c = bits.Add64(z[0], 4891460686036598785, 0)
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z[1], c = bits.Add64(z[1], 2896914383306846353, c)
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z[2], c = bits.Add64(z[2], 13281191951274694749, c)
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z[3], _ = bits.Add64(z[3], 3486998266802970665, c)
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}
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return z
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}
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// SubAssign z = z - x mod q
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func (z *Element) SubAssign(x *Element) *Element {
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var b uint64
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z[0], b = bits.Sub64(z[0], x[0], 0)
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z[1], b = bits.Sub64(z[1], x[1], b)
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z[2], b = bits.Sub64(z[2], x[2], b)
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z[3], b = bits.Sub64(z[3], x[3], b)
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if b != 0 {
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var c uint64
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z[0], c = bits.Add64(z[0], 4891460686036598785, 0)
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z[1], c = bits.Add64(z[1], 2896914383306846353, c)
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z[2], c = bits.Add64(z[2], 13281191951274694749, c)
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z[3], _ = bits.Add64(z[3], 3486998266802970665, c)
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}
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return z
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}
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// Exp z = x^e mod q
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func (z *Element) Exp(x Element, e uint64) *Element {
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if e == 0 {
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return z.SetOne()
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}
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z.Set(&x)
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l := bits.Len64(e) - 2
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for i := l; i >= 0; i-- {
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z.Square(z)
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if e&(1<<uint(i)) != 0 {
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z.MulAssign(&x)
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}
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}
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return z
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}
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// 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 {
|
|
if bits.UintSize == 64 {
|
|
bits := (*[4]big.Word)(unsafe.Pointer(z))
|
|
return res.SetBits(bits[:])
|
|
} else {
|
|
var bits [8]big.Word
|
|
for i := 0; i < len(z); i++ {
|
|
bits[i*2] = big.Word(z[i])
|
|
bits[i*2+1] = big.Word(z[i] >> 32)
|
|
}
|
|
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()
|
|
if bits.UintSize == 64 {
|
|
bits := (*[4]big.Word)(unsafe.Pointer(&z))
|
|
return res.SetBits(bits[:])
|
|
} else {
|
|
var bits [8]big.Word
|
|
for i := 0; i < len(z); i++ {
|
|
bits[i*2] = big.Word(z[i])
|
|
bits[i*2+1] = big.Word(z[i] >> 32)
|
|
}
|
|
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()
|
|
if bits.UintSize == 64 {
|
|
for i := 0; i < len(vBits); i++ {
|
|
z[i] = uint64(vBits[i])
|
|
}
|
|
} else {
|
|
for i := 0; i < len(vBits); i++ {
|
|
if i%2 == 0 {
|
|
z[i/2] = uint64(vBits[i])
|
|
} else {
|
|
z[i/2] |= uint64(vBits[i]) << 32
|
|
}
|
|
}
|
|
}
|
|
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
|
|
}
|