You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
81 lines
2.2 KiB
81 lines
2.2 KiB
// Copyright 2016 Google Inc. All Rights Reserved.
|
|
//
|
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
|
// you may not use this file except in compliance with the License.
|
|
// You may obtain a copy of the License at
|
|
//
|
|
// http://www.apache.org/licenses/LICENSE-2.0
|
|
//
|
|
// Unless required by applicable law or agreed to in writing, software
|
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
// See the License for the specific language governing permissions and
|
|
// limitations under the License.
|
|
|
|
package p256
|
|
|
|
// This file implements compressed point unmarshaling. Preferably this
|
|
// functionality would be in a standard library. Code borrowed from:
|
|
// https://go-review.googlesource.com/#/c/1883/2/src/crypto/elliptic/elliptic.go
|
|
|
|
import (
|
|
"crypto/elliptic"
|
|
"math/big"
|
|
)
|
|
|
|
// Unmarshal a compressed point in the form specified in section 4.3.6 of ANSI X9.62.
|
|
func Unmarshal(curve elliptic.Curve, data []byte) (x, y *big.Int) {
|
|
byteLen := (curve.Params().BitSize + 7) >> 3
|
|
if (data[0] &^ 1) != 2 {
|
|
return // unrecognized point encoding
|
|
}
|
|
if len(data) != 1+byteLen {
|
|
return
|
|
}
|
|
|
|
// Based on Routine 2.2.4 in NIST Mathematical routines paper
|
|
params := curve.Params()
|
|
tx := new(big.Int).SetBytes(data[1 : 1+byteLen])
|
|
y2 := y2(params, tx)
|
|
sqrt := defaultSqrt
|
|
ty := sqrt(y2, params.P)
|
|
if ty == nil {
|
|
return // "y^2" is not a square: invalid point
|
|
}
|
|
var y2c big.Int
|
|
y2c.Mul(ty, ty).Mod(&y2c, params.P)
|
|
if y2c.Cmp(y2) != 0 {
|
|
return // sqrt(y2)^2 != y2: invalid point
|
|
}
|
|
if ty.Bit(0) != uint(data[0]&1) {
|
|
ty.Sub(params.P, ty)
|
|
}
|
|
|
|
x, y = tx, ty // valid point: return it
|
|
return
|
|
}
|
|
|
|
// Use the curve equation to calculate y² given x.
|
|
// only applies to curves of the form y² = x³ - 3x + b.
|
|
func y2(curve *elliptic.CurveParams, x *big.Int) *big.Int {
|
|
|
|
// y² = x³ - 3x + b
|
|
x3 := new(big.Int).Mul(x, x)
|
|
x3.Mul(x3, x)
|
|
|
|
threeX := new(big.Int).Lsh(x, 1)
|
|
threeX.Add(threeX, x)
|
|
|
|
x3.Sub(x3, threeX)
|
|
x3.Add(x3, curve.B)
|
|
x3.Mod(x3, curve.P)
|
|
return x3
|
|
}
|
|
|
|
func defaultSqrt(x, p *big.Int) *big.Int {
|
|
var r big.Int
|
|
if nil == r.ModSqrt(x, p) {
|
|
return nil // x is not a square
|
|
}
|
|
return &r
|
|
}
|
|
|