// Copyright 2022 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Code generated by generate.go. DO NOT EDIT.
package nistec
import (
"crypto/internal/fips140/nistec/fiat"
"crypto/internal/fips140/subtle"
"errors"
"sync"
)
// p224ElementLength is the length of an element of the base or scalar field,
// which have the same bytes length for all NIST P curves.
const p224ElementLength = 28
// P224Point is a P224 point. The zero value is NOT valid.
type P224Point struct {
// The point is represented in projective coordinates (X:Y:Z),
// where x = X/Z and y = Y/Z.
x, y, z *fiat.P224Element
}
// NewP224Point returns a new P224Point representing the point at infinity point.
func NewP224Point() *P224Point {
return &P224Point{
x: new(fiat.P224Element),
y: new(fiat.P224Element).One(),
z: new(fiat.P224Element),
}
}
// SetGenerator sets p to the canonical generator and returns p.
func (p *P224Point) SetGenerator() *P224Point {
p.x.SetBytes([]byte{0xb7, 0xe, 0xc, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f, 0x32, 0x13, 0x90, 0xb9, 0x4a, 0x3, 0xc1, 0xd3, 0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6, 0x11, 0x5c, 0x1d, 0x21})
p.y.SetBytes([]byte{0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x7, 0x47, 0x64, 0x44, 0xd5, 0x81, 0x99, 0x85, 0x0, 0x7e, 0x34})
p.z.One()
return p
}
// Set sets p = q and returns p.
func (p *P224Point) Set(q *P224Point) *P224Point {
p.x.Set(q.x)
p.y.Set(q.y)
p.z.Set(q.z)
return p
}
// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in
// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on
// the curve, it returns nil and an error, and the receiver is unchanged.
// Otherwise, it returns p.
func (p *P224Point) SetBytes(b []byte) (*P224Point, error) {
switch {
// Point at infinity.
case len(b) == 1 && b[0] == 0:
return p.Set(NewP224Point()), nil
// Uncompressed form.
case len(b) == 1+2*p224ElementLength && b[0] == 4:
x, err := new(fiat.P224Element).SetBytes(b[1 : 1+p224ElementLength])
if err != nil {
return nil, err
}
y, err := new(fiat.P224Element).SetBytes(b[1+p224ElementLength:])
if err != nil {
return nil, err
}
if err := p224CheckOnCurve(x, y); err != nil {
return nil, err
}
p.x.Set(x)
p.y.Set(y)
p.z.One()
return p, nil
// Compressed form.
case len(b) == 1+p224ElementLength && (b[0] == 2 || b[0] == 3):
x, err := new(fiat.P224Element).SetBytes(b[1:])
if err != nil {
return nil, err
}
// y² = x³ - 3x + b
y := p224Polynomial(new(fiat.P224Element), x)
if !p224Sqrt(y, y) {
return nil, errors.New("invalid P224 compressed point encoding")
}
// Select the positive or negative root, as indicated by the least
// significant bit, based on the encoding type byte.
otherRoot := new(fiat.P224Element)
otherRoot.Sub(otherRoot, y)
cond := y.Bytes()[p224ElementLength-1]&1 ^ b[0]&1
y.Select(otherRoot, y, int(cond))
p.x.Set(x)
p.y.Set(y)
p.z.One()
return p, nil
default:
return nil, errors.New("invalid P224 point encoding")
}
}
var _p224B *fiat.P224Element
var _p224BOnce sync.Once
func p224B() *fiat.P224Element {
_p224BOnce.Do(func() {
_p224B, _ = new(fiat.P224Element).SetBytes([]byte{0xb4, 0x5, 0xa, 0x85, 0xc, 0x4, 0xb3, 0xab, 0xf5, 0x41, 0x32, 0x56, 0x50, 0x44, 0xb0, 0xb7, 0xd7, 0xbf, 0xd8, 0xba, 0x27, 0xb, 0x39, 0x43, 0x23, 0x55, 0xff, 0xb4})
})
return _p224B
}
// p224Polynomial sets y2 to x³ - 3x + b, and returns y2.
func p224Polynomial(y2, x *fiat.P224Element) *fiat.P224Element {
y2.Square(x)
y2.Mul(y2, x)
threeX := new(fiat.P224Element).Add(x, x)
threeX.Add(threeX, x)
y2.Sub(y2, threeX)
return y2.Add(y2, p224B())
}
func p224CheckOnCurve(x, y *fiat.P224Element) error {
// y² = x³ - 3x + b
rhs := p224Polynomial(new(fiat.P224Element), x)
lhs := new(fiat.P224Element).Square(y)
if rhs.Equal(lhs) != 1 {
return errors.New("P224 point not on curve")
}
return nil
}
// Bytes returns the uncompressed or infinity encoding of p, as specified in
// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at
// infinity is shorter than all other encodings.
func (p *P224Point) Bytes() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [1 + 2*p224ElementLength]byte
return p.bytes(&out)
}
func (p *P224Point) bytes(out *[1 + 2*p224ElementLength]byte) []byte {
if p.z.IsZero() == 1 {
return append(out[:0], 0)
}
zinv := new(fiat.P224Element).Invert(p.z)
x := new(fiat.P224Element).Mul(p.x, zinv)
y := new(fiat.P224Element).Mul(p.y, zinv)
buf := append(out[:0], 4)
buf = append(buf, x.Bytes()...)
buf = append(buf, y.Bytes()...)
return buf
}
// BytesX returns the encoding of the x-coordinate of p, as specified in SEC 1,
// Version 2.0, Section 2.3.5, or an error if p is the point at infinity.
func (p *P224Point) BytesX() ([]byte, error) {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [p224ElementLength]byte
return p.bytesX(&out)
}
func (p *P224Point) bytesX(out *[p224ElementLength]byte) ([]byte, error) {
if p.z.IsZero() == 1 {
return nil, errors.New("P224 point is the point at infinity")
}
zinv := new(fiat.P224Element).Invert(p.z)
x := new(fiat.P224Element).Mul(p.x, zinv)
return append(out[:0], x.Bytes()...), nil
}
// BytesCompressed returns the compressed or infinity encoding of p, as
// specified in SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the
// point at infinity is shorter than all other encodings.
func (p *P224Point) BytesCompressed() []byte {
// This function is outlined to make the allocations inline in the caller
// rather than happen on the heap.
var out [1 + p224ElementLength]byte
return p.bytesCompressed(&out)
}
func (p *P224Point) bytesCompressed(out *[1 + p224ElementLength]byte) []byte {
if p.z.IsZero() == 1 {
return append(out[:0], 0)
}
zinv := new(fiat.P224Element).Invert(p.z)
x := new(fiat.P224Element).Mul(p.x, zinv)
y := new(fiat.P224Element).Mul(p.y, zinv)
// Encode the sign of the y coordinate (indicated by the least significant
// bit) as the encoding type (2 or 3).
buf := append(out[:0], 2)
buf[0] |= y.Bytes()[p224ElementLength-1] & 1
buf = append(buf, x.Bytes()...)
return buf
}
// Add sets q = p1 + p2, and returns q. The points may overlap.
func (q *P224Point) Add(p1, p2 *P224Point) *P224Point {
// Complete addition formula for a = -3 from "Complete addition formulas for
// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2.
t0 := new(fiat.P224Element).Mul(p1.x, p2.x) // t0 := X1 * X2
t1 := new(fiat.P224Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2
t2 := new(fiat.P224Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2
t3 := new(fiat.P224Element).Add(p1.x, p1.y) // t3 := X1 + Y1
t4 := new(fiat.P224Element).Add(p2.x, p2.y) // t4 := X2 + Y2
t3.Mul(t3, t4) // t3 := t3 * t4
t4.Add(t0, t1) // t4 := t0 + t1
t3.Sub(t3, t4) // t3 := t3 - t4
t4.Add(p1.y, p1.z) // t4 := Y1 + Z1
x3 := new(fiat.P224Element).Add(p2.y, p2.z) // X3 := Y2 + Z2
t4.Mul(t4, x3) // t4 := t4 * X3
x3.Add(t1, t2) // X3 := t1 + t2
t4.Sub(t4, x3) // t4 := t4 - X3
x3.Add(p1.x, p1.z) // X3 := X1 + Z1
y3 := new(fiat.P224Element).Add(p2.x, p2.z) // Y3 := X2 + Z2
x3.Mul(x3, y3) // X3 := X3 * Y3
y3.Add(t0, t2) // Y3 := t0 + t2
y3.Sub(x3, y3) // Y3 := X3 - Y3
z3 := new(fiat.P224Element).Mul(p224B(), t2) // Z3 := b * t2
x3.Sub(y3, z3) // X3 := Y3 - Z3
z3.Add(x3, x3) // Z3 := X3 + X3
x3.Add(x3, z3) // X3 := X3 + Z3
z3.Sub(t1, x3) // Z3 := t1 - X3
x3.Add(t1, x3) // X3 := t1 + X3
y3.Mul(p224B(), y3) // Y3 := b * Y3
t1.Add(t2, t2) // t1 := t2 + t2
t2.Add(t1, t2) // t2 := t1 + t2
y3.Sub(y3, t2) // Y3 := Y3 - t2
y3.Sub(y3, t0) // Y3 := Y3 - t0
t1.Add(y3, y3) // t1 := Y3 + Y3
y3.Add(t1, y3) // Y3 := t1 + Y3
t1.Add(t0, t0) // t1 := t0 + t0
t0.Add(t1, t0) // t0 := t1 + t0
t0.Sub(t0, t2) // t0 := t0 - t2
t1.Mul(t4, y3) // t1 := t4 * Y3
t2.Mul(t0, y3) // t2 := t0 * Y3
y3.Mul(x3, z3) // Y3 := X3 * Z3
y3.Add(y3, t2) // Y3 := Y3 + t2
x3.Mul(t3, x3) // X3 := t3 * X3
x3.Sub(x3, t1) // X3 := X3 - t1
z3.Mul(t4, z3) // Z3 := t4 * Z3
t1.Mul(t3, t0) // t1 := t3 * t0
z3.Add(z3, t1) // Z3 := Z3 + t1
q.x.Set(x3)
q.y.Set(y3)
q.z.Set(z3)
return q
}
// Double sets q = p + p, and returns q. The points may overlap.
func (q *P224Point) Double(p *P224Point) *P224Point {
// Complete addition formula for a = -3 from "Complete addition formulas for
// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2.
t0 := new(fiat.P224Element).Square(p.x) // t0 := X ^ 2
t1 := new(fiat.P224Element).Square(p.y) // t1 := Y ^ 2
t2 := new(fiat.P224Element).Square(p.z) // t2 := Z ^ 2
t3 := new(fiat.P224Element).Mul(p.x, p.y) // t3 := X * Y
t3.Add(t3, t3) // t3 := t3 + t3
z3 := new(fiat.P224Element).Mul(p.x, p.z) // Z3 := X * Z
z3.Add(z3, z3) // Z3 := Z3 + Z3
y3 := new(fiat.P224Element).Mul(p224B(), t2) // Y3 := b * t2
y3.Sub(y3, z3) // Y3 := Y3 - Z3
x3 := new(fiat.P224Element).Add(y3, y3) // X3 := Y3 + Y3
y3.Add(x3, y3) // Y3 := X3 + Y3
x3.Sub(t1, y3) // X3 := t1 - Y3
y3.Add(t1, y3) // Y3 := t1 + Y3
y3.Mul(x3, y3) // Y3 := X3 * Y3
x3.Mul(x3, t3) // X3 := X3 * t3
t3.Add(t2, t2) // t3 := t2 + t2
t2.Add(t2, t3) // t2 := t2 + t3
z3.Mul(p224B(), z3) // Z3 := b * Z3
z3.Sub(z3, t2) // Z3 := Z3 - t2
z3.Sub(z3, t0) // Z3 := Z3 - t0
t3.Add(z3, z3) // t3 := Z3 + Z3
z3.Add(z3, t3) // Z3 := Z3 + t3
t3.Add(t0, t0) // t3 := t0 + t0
t0.Add(t3, t0) // t0 := t3 + t0
t0.Sub(t0, t2) // t0 := t0 - t2
t0.Mul(t0, z3) // t0 := t0 * Z3
y3.Add(y3, t0) // Y3 := Y3 + t0
t0.Mul(p.y, p.z) // t0 := Y * Z
t0.Add(t0, t0) // t0 := t0 + t0
z3.Mul(t0, z3) // Z3 := t0 * Z3
x3.Sub(x3, z3) // X3 := X3 - Z3
z3.Mul(t0, t1) // Z3 := t0 * t1
z3.Add(z3, z3) // Z3 := Z3 + Z3
z3.Add(z3, z3) // Z3 := Z3 + Z3
q.x.Set(x3)
q.y.Set(y3)
q.z.Set(z3)
return q
}
// Select sets q to p1 if cond == 1, and to p2 if cond == 0.
func (q *P224Point) Select(p1, p2 *P224Point, cond int) *P224Point {
q.x.Select(p1.x, p2.x, cond)
q.y.Select(p1.y, p2.y, cond)
q.z.Select(p1.z, p2.z, cond)
return q
}
// A p224Table holds the first 15 multiples of a point at offset -1, so [1]P
// is at table[0], [15]P is at table[14], and [0]P is implicitly the identity
// point.
type p224Table [15]*P224Point
// Select selects the n-th multiple of the table base point into p. It works in
// constant time by iterating over every entry of the table. n must be in [0, 15].
func (table *p224Table) Select(p *P224Point, n uint8) {
if n >= 16 {
panic("nistec: internal error: p224Table called with out-of-bounds value")
}
p.Set(NewP224Point())
for i := uint8(1); i < 16; i++ {
cond := subtle.ConstantTimeByteEq(i, n)
p.Select(table[i-1], p, cond)
}
}
// ScalarMult sets p = scalar * q, and returns p.
func (p *P224Point) ScalarMult(q *P224Point, scalar []byte) (*P224Point, error) {
// Compute a p224Table for the base point q. The explicit NewP224Point
// calls get inlined, letting the allocations live on the stack.
var table = p224Table{NewP224Point(), NewP224Point(), NewP224Point(),
NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(),
NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(),
NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point()}
table[0].Set(q)
for i := 1; i < 15; i += 2 {
table[i].Double(table[i/2])
table[i+1].Add(table[i], q)
}
// Instead of doing the classic double-and-add chain, we do it with a
// four-bit window: we double four times, and then add [0-15]P.
t := NewP224Point()
p.Set(NewP224Point())
for i, byte := range scalar {
// No need to double on the first iteration, as p is the identity at
// this point, and [N]∞ = ∞.
if i != 0 {
p.Double(p)
p.Double(p)
p.Double(p)
p.Double(p)
}
windowValue := byte >> 4
table.Select(t, windowValue)
p.Add(p, t)
p.Double(p)
p.Double(p)
p.Double(p)
p.Double(p)
windowValue = byte & 0b1111
table.Select(t, windowValue)
p.Add(p, t)
}
return p, nil
}
var p224GeneratorTable *[p224ElementLength * 2]p224Table
var p224GeneratorTableOnce sync.Once
// generatorTable returns a sequence of p224Tables. The first table contains
// multiples of G. Each successive table is the previous table doubled four
// times.
func (p *P224Point) generatorTable() *[p224ElementLength * 2]p224Table {
p224GeneratorTableOnce.Do(func() {
p224GeneratorTable = new([p224ElementLength * 2]p224Table)
base := NewP224Point().SetGenerator()
for i := 0; i < p224ElementLength*2; i++ {
p224GeneratorTable[i][0] = NewP224Point().Set(base)
for j := 1; j < 15; j++ {
p224GeneratorTable[i][j] = NewP224Point().Add(p224GeneratorTable[i][j-1], base)
}
base.Double(base)
base.Double(base)
base.Double(base)
base.Double(base)
}
})
return p224GeneratorTable
}
// ScalarBaseMult sets p = scalar * B, where B is the canonical generator, and
// returns p.
func (p *P224Point) ScalarBaseMult(scalar []byte) (*P224Point, error) {
if len(scalar) != p224ElementLength {
return nil, errors.New("invalid scalar length")
}
tables := p.generatorTable()
// This is also a scalar multiplication with a four-bit window like in
// ScalarMult, but in this case the doublings are precomputed. The value
// [windowValue]G added at iteration k would normally get doubled
// (totIterations-k)×4 times, but with a larger precomputation we can
// instead add [2^((totIterations-k)×4)][windowValue]G and avoid the
// doublings between iterations.
t := NewP224Point()
p.Set(NewP224Point())
tableIndex := len(tables) - 1
for _, byte := range scalar {
windowValue := byte >> 4
tables[tableIndex].Select(t, windowValue)
p.Add(p, t)
tableIndex--
windowValue = byte & 0b1111
tables[tableIndex].Select(t, windowValue)
p.Add(p, t)
tableIndex--
}
return p, nil
}
// p224Sqrt sets e to a square root of x. If x is not a square, p224Sqrt returns
// false and e is unchanged. e and x can overlap.
func p224Sqrt(e, x *fiat.P224Element) (isSquare bool) {
candidate := new(fiat.P224Element)
p224SqrtCandidate(candidate, x)
square := new(fiat.P224Element).Square(candidate)
if square.Equal(x) != 1 {
return false
}
e.Set(candidate)
return true
}