mirror of
https://github.com/autc04/Retro68.git
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515 lines
13 KiB
Go
515 lines
13 KiB
Go
// Copyright 2016 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// +build ignore
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// -build s390x
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package elliptic
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import (
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"math/big"
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)
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type p256CurveFast struct {
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*CurveParams
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}
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type p256Point struct {
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x [32]byte
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y [32]byte
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z [32]byte
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}
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var (
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p256 Curve
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p256PreFast *[37][64]p256Point
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)
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// hasVectorFacility reports whether the machine has the z/Architecture
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// vector facility installed and enabled.
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func hasVectorFacility() bool
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var hasVX = hasVectorFacility()
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func initP256Arch() {
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if hasVX {
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p256 = p256CurveFast{p256Params}
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initTable()
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return
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}
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// No vector support, use pure Go implementation.
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p256 = p256Curve{p256Params}
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return
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}
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func (curve p256CurveFast) Params() *CurveParams {
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return curve.CurveParams
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}
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// Functions implemented in p256_asm_s390x.s
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// Montgomery multiplication modulo P256
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func p256MulAsm(res, in1, in2 []byte)
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// Montgomery square modulo P256
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func p256Sqr(res, in []byte) {
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p256MulAsm(res, in, in)
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}
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// Montgomery multiplication by 1
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func p256FromMont(res, in []byte)
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// iff cond == 1 val <- -val
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func p256NegCond(val *p256Point, cond int)
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// if cond == 0 res <- b; else res <- a
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func p256MovCond(res, a, b *p256Point, cond int)
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// Constant time table access
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func p256Select(point *p256Point, table []p256Point, idx int)
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func p256SelectBase(point *p256Point, table []p256Point, idx int)
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// Montgomery multiplication modulo Ord(G)
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func p256OrdMul(res, in1, in2 []byte)
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// Montgomery square modulo Ord(G), repeated n times
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func p256OrdSqr(res, in []byte, n int) {
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copy(res, in)
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for i := 0; i < n; i += 1 {
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p256OrdMul(res, res, res)
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}
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}
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// Point add with P2 being affine point
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// If sign == 1 -> P2 = -P2
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// If sel == 0 -> P3 = P1
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// if zero == 0 -> P3 = P2
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func p256PointAddAffineAsm(P3, P1, P2 *p256Point, sign, sel, zero int)
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// Point add
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func p256PointAddAsm(P3, P1, P2 *p256Point)
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func p256PointDoubleAsm(P3, P1 *p256Point)
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func (curve p256CurveFast) Inverse(k *big.Int) *big.Int {
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if k.Cmp(p256Params.N) >= 0 {
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// This should never happen.
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reducedK := new(big.Int).Mod(k, p256Params.N)
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k = reducedK
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}
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// table will store precomputed powers of x. The 32 bytes at index
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// i store x^(i+1).
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var table [15][32]byte
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x := fromBig(k)
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// This code operates in the Montgomery domain where R = 2^256 mod n
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// and n is the order of the scalar field. (See initP256 for the
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// value.) Elements in the Montgomery domain take the form a×R and
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// multiplication of x and y in the calculates (x × y × R^-1) mod n. RR
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// is R×R mod n thus the Montgomery multiplication x and RR gives x×R,
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// i.e. converts x into the Montgomery domain. Stored in BigEndian form
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RR := []byte{0x66, 0xe1, 0x2d, 0x94, 0xf3, 0xd9, 0x56, 0x20, 0x28, 0x45, 0xb2, 0x39, 0x2b, 0x6b, 0xec, 0x59,
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0x46, 0x99, 0x79, 0x9c, 0x49, 0xbd, 0x6f, 0xa6, 0x83, 0x24, 0x4c, 0x95, 0xbe, 0x79, 0xee, 0xa2}
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p256OrdMul(table[0][:], x, RR)
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// Prepare the table, no need in constant time access, because the
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// power is not a secret. (Entry 0 is never used.)
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for i := 2; i < 16; i += 2 {
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p256OrdSqr(table[i-1][:], table[(i/2)-1][:], 1)
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p256OrdMul(table[i][:], table[i-1][:], table[0][:])
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}
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copy(x, table[14][:]) // f
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p256OrdSqr(x[0:32], x[0:32], 4)
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p256OrdMul(x[0:32], x[0:32], table[14][:]) // ff
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t := make([]byte, 32)
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copy(t, x)
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p256OrdSqr(x, x, 8)
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p256OrdMul(x, x, t) // ffff
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copy(t, x)
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p256OrdSqr(x, x, 16)
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p256OrdMul(x, x, t) // ffffffff
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copy(t, x)
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p256OrdSqr(x, x, 64) // ffffffff0000000000000000
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p256OrdMul(x, x, t) // ffffffff00000000ffffffff
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p256OrdSqr(x, x, 32) // ffffffff00000000ffffffff00000000
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p256OrdMul(x, x, t) // ffffffff00000000ffffffffffffffff
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// Remaining 32 windows
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expLo := [32]byte{0xb, 0xc, 0xe, 0x6, 0xf, 0xa, 0xa, 0xd, 0xa, 0x7, 0x1, 0x7, 0x9, 0xe, 0x8, 0x4,
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0xf, 0x3, 0xb, 0x9, 0xc, 0xa, 0xc, 0x2, 0xf, 0xc, 0x6, 0x3, 0x2, 0x5, 0x4, 0xf}
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for i := 0; i < 32; i++ {
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p256OrdSqr(x, x, 4)
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p256OrdMul(x, x, table[expLo[i]-1][:])
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}
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// Multiplying by one in the Montgomery domain converts a Montgomery
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// value out of the domain.
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one := []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}
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p256OrdMul(x, x, one)
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return new(big.Int).SetBytes(x)
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}
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// fromBig converts a *big.Int into a format used by this code.
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func fromBig(big *big.Int) []byte {
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// This could be done a lot more efficiently...
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res := big.Bytes()
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if 32 == len(res) {
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return res
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}
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t := make([]byte, 32)
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offset := 32 - len(res)
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for i := len(res) - 1; i >= 0; i-- {
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t[i+offset] = res[i]
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}
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return t
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}
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// p256GetMultiplier makes sure byte array will have 32 byte elements, If the scalar
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// is equal or greater than the order of the group, it's reduced modulo that order.
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func p256GetMultiplier(in []byte) []byte {
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n := new(big.Int).SetBytes(in)
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if n.Cmp(p256Params.N) >= 0 {
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n.Mod(n, p256Params.N)
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}
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return fromBig(n)
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}
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// p256MulAsm operates in a Montgomery domain with R = 2^256 mod p, where p is the
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// underlying field of the curve. (See initP256 for the value.) Thus rr here is
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// R×R mod p. See comment in Inverse about how this is used.
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var rr = []byte{0x00, 0x00, 0x00, 0x04, 0xff, 0xff, 0xff, 0xfd, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
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0xff, 0xff, 0xff, 0xfb, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03}
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// (This is one, in the Montgomery domain.)
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var one = []byte{0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}
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func maybeReduceModP(in *big.Int) *big.Int {
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if in.Cmp(p256Params.P) < 0 {
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return in
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}
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return new(big.Int).Mod(in, p256Params.P)
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}
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func (curve p256CurveFast) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
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var r1, r2 p256Point
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r1.p256BaseMult(p256GetMultiplier(baseScalar))
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copy(r2.x[:], fromBig(maybeReduceModP(bigX)))
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copy(r2.y[:], fromBig(maybeReduceModP(bigY)))
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copy(r2.z[:], one)
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p256MulAsm(r2.x[:], r2.x[:], rr[:])
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p256MulAsm(r2.y[:], r2.y[:], rr[:])
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r2.p256ScalarMult(p256GetMultiplier(scalar))
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p256PointAddAsm(&r1, &r1, &r2)
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return r1.p256PointToAffine()
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}
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func (curve p256CurveFast) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
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var r p256Point
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r.p256BaseMult(p256GetMultiplier(scalar))
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return r.p256PointToAffine()
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}
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func (curve p256CurveFast) ScalarMult(bigX, bigY *big.Int, scalar []byte) (x, y *big.Int) {
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var r p256Point
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copy(r.x[:], fromBig(maybeReduceModP(bigX)))
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copy(r.y[:], fromBig(maybeReduceModP(bigY)))
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copy(r.z[:], one)
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p256MulAsm(r.x[:], r.x[:], rr[:])
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p256MulAsm(r.y[:], r.y[:], rr[:])
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r.p256ScalarMult(p256GetMultiplier(scalar))
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return r.p256PointToAffine()
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}
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func (p *p256Point) p256PointToAffine() (x, y *big.Int) {
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zInv := make([]byte, 32)
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zInvSq := make([]byte, 32)
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p256Inverse(zInv, p.z[:])
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p256Sqr(zInvSq, zInv)
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p256MulAsm(zInv, zInv, zInvSq)
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p256MulAsm(zInvSq, p.x[:], zInvSq)
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p256MulAsm(zInv, p.y[:], zInv)
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p256FromMont(zInvSq, zInvSq)
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p256FromMont(zInv, zInv)
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return new(big.Int).SetBytes(zInvSq), new(big.Int).SetBytes(zInv)
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}
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// p256Inverse sets out to in^-1 mod p.
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func p256Inverse(out, in []byte) {
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var stack [6 * 32]byte
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p2 := stack[32*0 : 32*0+32]
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p4 := stack[32*1 : 32*1+32]
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p8 := stack[32*2 : 32*2+32]
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p16 := stack[32*3 : 32*3+32]
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p32 := stack[32*4 : 32*4+32]
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p256Sqr(out, in)
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p256MulAsm(p2, out, in) // 3*p
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p256Sqr(out, p2)
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p256Sqr(out, out)
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p256MulAsm(p4, out, p2) // f*p
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p256Sqr(out, p4)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256MulAsm(p8, out, p4) // ff*p
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p256Sqr(out, p8)
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for i := 0; i < 7; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(p16, out, p8) // ffff*p
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p256Sqr(out, p16)
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for i := 0; i < 15; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(p32, out, p16) // ffffffff*p
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p256Sqr(out, p32)
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for i := 0; i < 31; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(out, out, in)
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for i := 0; i < 32*4; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(out, out, p32)
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for i := 0; i < 32; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(out, out, p32)
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for i := 0; i < 16; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(out, out, p16)
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for i := 0; i < 8; i++ {
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p256Sqr(out, out)
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}
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p256MulAsm(out, out, p8)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256MulAsm(out, out, p4)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256MulAsm(out, out, p2)
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p256Sqr(out, out)
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p256Sqr(out, out)
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p256MulAsm(out, out, in)
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}
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func boothW5(in uint) (int, int) {
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var s uint = ^((in >> 5) - 1)
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var d uint = (1 << 6) - in - 1
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d = (d & s) | (in & (^s))
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d = (d >> 1) + (d & 1)
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return int(d), int(s & 1)
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}
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func boothW7(in uint) (int, int) {
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var s uint = ^((in >> 7) - 1)
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var d uint = (1 << 8) - in - 1
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d = (d & s) | (in & (^s))
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d = (d >> 1) + (d & 1)
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return int(d), int(s & 1)
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}
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func initTable() {
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p256PreFast = new([37][64]p256Point) //z coordinate not used
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basePoint := p256Point{
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x: [32]byte{0x18, 0x90, 0x5f, 0x76, 0xa5, 0x37, 0x55, 0xc6, 0x79, 0xfb, 0x73, 0x2b, 0x77, 0x62, 0x25, 0x10,
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0x75, 0xba, 0x95, 0xfc, 0x5f, 0xed, 0xb6, 0x01, 0x79, 0xe7, 0x30, 0xd4, 0x18, 0xa9, 0x14, 0x3c}, //(p256.x*2^256)%p
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y: [32]byte{0x85, 0x71, 0xff, 0x18, 0x25, 0x88, 0x5d, 0x85, 0xd2, 0xe8, 0x86, 0x88, 0xdd, 0x21, 0xf3, 0x25,
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0x8b, 0x4a, 0xb8, 0xe4, 0xba, 0x19, 0xe4, 0x5c, 0xdd, 0xf2, 0x53, 0x57, 0xce, 0x95, 0x56, 0x0a}, //(p256.y*2^256)%p
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z: [32]byte{0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, //(p256.z*2^256)%p
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}
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t1 := new(p256Point)
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t2 := new(p256Point)
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*t2 = basePoint
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zInv := make([]byte, 32)
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zInvSq := make([]byte, 32)
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for j := 0; j < 64; j++ {
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*t1 = *t2
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for i := 0; i < 37; i++ {
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// The window size is 7 so we need to double 7 times.
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if i != 0 {
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for k := 0; k < 7; k++ {
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p256PointDoubleAsm(t1, t1)
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}
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}
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// Convert the point to affine form. (Its values are
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// still in Montgomery form however.)
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p256Inverse(zInv, t1.z[:])
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p256Sqr(zInvSq, zInv)
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p256MulAsm(zInv, zInv, zInvSq)
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p256MulAsm(t1.x[:], t1.x[:], zInvSq)
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p256MulAsm(t1.y[:], t1.y[:], zInv)
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copy(t1.z[:], basePoint.z[:])
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// Update the table entry
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copy(p256PreFast[i][j].x[:], t1.x[:])
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copy(p256PreFast[i][j].y[:], t1.y[:])
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}
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if j == 0 {
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p256PointDoubleAsm(t2, &basePoint)
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} else {
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p256PointAddAsm(t2, t2, &basePoint)
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}
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}
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}
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func (p *p256Point) p256BaseMult(scalar []byte) {
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wvalue := (uint(scalar[31]) << 1) & 0xff
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sel, sign := boothW7(uint(wvalue))
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p256SelectBase(p, p256PreFast[0][:], sel)
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p256NegCond(p, sign)
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copy(p.z[:], one[:])
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var t0 p256Point
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copy(t0.z[:], one[:])
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index := uint(6)
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zero := sel
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for i := 1; i < 37; i++ {
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if index < 247 {
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wvalue = ((uint(scalar[31-index/8]) >> (index % 8)) + (uint(scalar[31-index/8-1]) << (8 - (index % 8)))) & 0xff
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} else {
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wvalue = (uint(scalar[31-index/8]) >> (index % 8)) & 0xff
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}
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index += 7
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sel, sign = boothW7(uint(wvalue))
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p256SelectBase(&t0, p256PreFast[i][:], sel)
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p256PointAddAffineAsm(p, p, &t0, sign, sel, zero)
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zero |= sel
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}
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}
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func (p *p256Point) p256ScalarMult(scalar []byte) {
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// precomp is a table of precomputed points that stores powers of p
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// from p^1 to p^16.
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var precomp [16]p256Point
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var t0, t1, t2, t3 p256Point
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// Prepare the table
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*&precomp[0] = *p
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p256PointDoubleAsm(&t0, p)
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p256PointDoubleAsm(&t1, &t0)
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p256PointDoubleAsm(&t2, &t1)
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p256PointDoubleAsm(&t3, &t2)
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*&precomp[1] = t0 // 2
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*&precomp[3] = t1 // 4
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||
*&precomp[7] = t2 // 8
|
||
*&precomp[15] = t3 // 16
|
||
|
||
p256PointAddAsm(&t0, &t0, p)
|
||
p256PointAddAsm(&t1, &t1, p)
|
||
p256PointAddAsm(&t2, &t2, p)
|
||
*&precomp[2] = t0 // 3
|
||
*&precomp[4] = t1 // 5
|
||
*&precomp[8] = t2 // 9
|
||
|
||
p256PointDoubleAsm(&t0, &t0)
|
||
p256PointDoubleAsm(&t1, &t1)
|
||
*&precomp[5] = t0 // 6
|
||
*&precomp[9] = t1 // 10
|
||
|
||
p256PointAddAsm(&t2, &t0, p)
|
||
p256PointAddAsm(&t1, &t1, p)
|
||
*&precomp[6] = t2 // 7
|
||
*&precomp[10] = t1 // 11
|
||
|
||
p256PointDoubleAsm(&t0, &t0)
|
||
p256PointDoubleAsm(&t2, &t2)
|
||
*&precomp[11] = t0 // 12
|
||
*&precomp[13] = t2 // 14
|
||
|
||
p256PointAddAsm(&t0, &t0, p)
|
||
p256PointAddAsm(&t2, &t2, p)
|
||
*&precomp[12] = t0 // 13
|
||
*&precomp[14] = t2 // 15
|
||
|
||
// Start scanning the window from top bit
|
||
index := uint(254)
|
||
var sel, sign int
|
||
|
||
wvalue := (uint(scalar[31-index/8]) >> (index % 8)) & 0x3f
|
||
sel, _ = boothW5(uint(wvalue))
|
||
p256Select(p, precomp[:], sel)
|
||
zero := sel
|
||
|
||
for index > 4 {
|
||
index -= 5
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
|
||
if index < 247 {
|
||
wvalue = ((uint(scalar[31-index/8]) >> (index % 8)) + (uint(scalar[31-index/8-1]) << (8 - (index % 8)))) & 0x3f
|
||
} else {
|
||
wvalue = (uint(scalar[31-index/8]) >> (index % 8)) & 0x3f
|
||
}
|
||
|
||
sel, sign = boothW5(uint(wvalue))
|
||
|
||
p256Select(&t0, precomp[:], sel)
|
||
p256NegCond(&t0, sign)
|
||
p256PointAddAsm(&t1, p, &t0)
|
||
p256MovCond(&t1, &t1, p, sel)
|
||
p256MovCond(p, &t1, &t0, zero)
|
||
zero |= sel
|
||
}
|
||
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
p256PointDoubleAsm(p, p)
|
||
|
||
wvalue = (uint(scalar[31]) << 1) & 0x3f
|
||
sel, sign = boothW5(uint(wvalue))
|
||
|
||
p256Select(&t0, precomp[:], sel)
|
||
p256NegCond(&t0, sign)
|
||
p256PointAddAsm(&t1, p, &t0)
|
||
p256MovCond(&t1, &t1, p, sel)
|
||
p256MovCond(p, &t1, &t0, zero)
|
||
}
|