1 files changed, 453 insertions, 0 deletions
diff --git a/src/crypto/internal/nistec/p224.go b/src/crypto/internal/nistec/p224.go
new file mode 100644
index 0000000..faa971d
--- /dev/null
+++ b/src/crypto/internal/nistec/p224.go
@@ -0,0 +1,453 @@
+// 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/nistec/fiat"
+	"crypto/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
+}