// 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 }