summaryrefslogtreecommitdiffstats
path: root/src/crypto/internal/nistec/p521.go
diff options
context:
space:
mode:
Diffstat (limited to 'src/crypto/internal/nistec/p521.go')
-rw-r--r--src/crypto/internal/nistec/p521.go469
1 files changed, 469 insertions, 0 deletions
diff --git a/src/crypto/internal/nistec/p521.go b/src/crypto/internal/nistec/p521.go
new file mode 100644
index 0000000..a57ad24
--- /dev/null
+++ b/src/crypto/internal/nistec/p521.go
@@ -0,0 +1,469 @@
+// 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"
+)
+
+// p521ElementLength is the length of an element of the base or scalar field,
+// which have the same bytes length for all NIST P curves.
+const p521ElementLength = 66
+
+// P521Point is a P521 point. The zero value is NOT valid.
+type P521Point struct {
+ // The point is represented in projective coordinates (X:Y:Z),
+ // where x = X/Z and y = Y/Z.
+ x, y, z *fiat.P521Element
+}
+
+// NewP521Point returns a new P521Point representing the point at infinity point.
+func NewP521Point() *P521Point {
+ return &P521Point{
+ x: new(fiat.P521Element),
+ y: new(fiat.P521Element).One(),
+ z: new(fiat.P521Element),
+ }
+}
+
+// SetGenerator sets p to the canonical generator and returns p.
+func (p *P521Point) SetGenerator() *P521Point {
+ p.x.SetBytes([]byte{0x0, 0xc6, 0x85, 0x8e, 0x6, 0xb7, 0x4, 0x4, 0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x5, 0x3f, 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, 0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7, 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, 0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5, 0xbd, 0x66})
+ p.y.SetBytes([]byte{0x1, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, 0xc0, 0x4, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x1, 0x3f, 0xad, 0x7, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50})
+ p.z.One()
+ return p
+}
+
+// Set sets p = q and returns p.
+func (p *P521Point) Set(q *P521Point) *P521Point {
+ 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 *P521Point) SetBytes(b []byte) (*P521Point, error) {
+ switch {
+ // Point at infinity.
+ case len(b) == 1 && b[0] == 0:
+ return p.Set(NewP521Point()), nil
+
+ // Uncompressed form.
+ case len(b) == 1+2*p521ElementLength && b[0] == 4:
+ x, err := new(fiat.P521Element).SetBytes(b[1 : 1+p521ElementLength])
+ if err != nil {
+ return nil, err
+ }
+ y, err := new(fiat.P521Element).SetBytes(b[1+p521ElementLength:])
+ if err != nil {
+ return nil, err
+ }
+ if err := p521CheckOnCurve(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+p521ElementLength && (b[0] == 2 || b[0] == 3):
+ x, err := new(fiat.P521Element).SetBytes(b[1:])
+ if err != nil {
+ return nil, err
+ }
+
+ // y² = x³ - 3x + b
+ y := p521Polynomial(new(fiat.P521Element), x)
+ if !p521Sqrt(y, y) {
+ return nil, errors.New("invalid P521 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.P521Element)
+ otherRoot.Sub(otherRoot, y)
+ cond := y.Bytes()[p521ElementLength-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 P521 point encoding")
+ }
+}
+
+var _p521B *fiat.P521Element
+var _p521BOnce sync.Once
+
+func p521B() *fiat.P521Element {
+ _p521BOnce.Do(func() {
+ _p521B, _ = new(fiat.P521Element).SetBytes([]byte{0x0, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x9, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, 0xbf, 0x7, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x0})
+ })
+ return _p521B
+}
+
+// p521Polynomial sets y2 to x³ - 3x + b, and returns y2.
+func p521Polynomial(y2, x *fiat.P521Element) *fiat.P521Element {
+ y2.Square(x)
+ y2.Mul(y2, x)
+
+ threeX := new(fiat.P521Element).Add(x, x)
+ threeX.Add(threeX, x)
+ y2.Sub(y2, threeX)
+
+ return y2.Add(y2, p521B())
+}
+
+func p521CheckOnCurve(x, y *fiat.P521Element) error {
+ // y² = x³ - 3x + b
+ rhs := p521Polynomial(new(fiat.P521Element), x)
+ lhs := new(fiat.P521Element).Square(y)
+ if rhs.Equal(lhs) != 1 {
+ return errors.New("P521 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 *P521Point) Bytes() []byte {
+ // This function is outlined to make the allocations inline in the caller
+ // rather than happen on the heap.
+ var out [1 + 2*p521ElementLength]byte
+ return p.bytes(&out)
+}
+
+func (p *P521Point) bytes(out *[1 + 2*p521ElementLength]byte) []byte {
+ if p.z.IsZero() == 1 {
+ return append(out[:0], 0)
+ }
+
+ zinv := new(fiat.P521Element).Invert(p.z)
+ x := new(fiat.P521Element).Mul(p.x, zinv)
+ y := new(fiat.P521Element).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 *P521Point) BytesX() ([]byte, error) {
+ // This function is outlined to make the allocations inline in the caller
+ // rather than happen on the heap.
+ var out [p521ElementLength]byte
+ return p.bytesX(&out)
+}
+
+func (p *P521Point) bytesX(out *[p521ElementLength]byte) ([]byte, error) {
+ if p.z.IsZero() == 1 {
+ return nil, errors.New("P521 point is the point at infinity")
+ }
+
+ zinv := new(fiat.P521Element).Invert(p.z)
+ x := new(fiat.P521Element).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 *P521Point) BytesCompressed() []byte {
+ // This function is outlined to make the allocations inline in the caller
+ // rather than happen on the heap.
+ var out [1 + p521ElementLength]byte
+ return p.bytesCompressed(&out)
+}
+
+func (p *P521Point) bytesCompressed(out *[1 + p521ElementLength]byte) []byte {
+ if p.z.IsZero() == 1 {
+ return append(out[:0], 0)
+ }
+
+ zinv := new(fiat.P521Element).Invert(p.z)
+ x := new(fiat.P521Element).Mul(p.x, zinv)
+ y := new(fiat.P521Element).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()[p521ElementLength-1] & 1
+ buf = append(buf, x.Bytes()...)
+ return buf
+}
+
+// Add sets q = p1 + p2, and returns q. The points may overlap.
+func (q *P521Point) Add(p1, p2 *P521Point) *P521Point {
+ // 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.P521Element).Mul(p1.x, p2.x) // t0 := X1 * X2
+ t1 := new(fiat.P521Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2
+ t2 := new(fiat.P521Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2
+ t3 := new(fiat.P521Element).Add(p1.x, p1.y) // t3 := X1 + Y1
+ t4 := new(fiat.P521Element).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.P521Element).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.P521Element).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.P521Element).Mul(p521B(), 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(p521B(), 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 *P521Point) Double(p *P521Point) *P521Point {
+ // 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.P521Element).Square(p.x) // t0 := X ^ 2
+ t1 := new(fiat.P521Element).Square(p.y) // t1 := Y ^ 2
+ t2 := new(fiat.P521Element).Square(p.z) // t2 := Z ^ 2
+ t3 := new(fiat.P521Element).Mul(p.x, p.y) // t3 := X * Y
+ t3.Add(t3, t3) // t3 := t3 + t3
+ z3 := new(fiat.P521Element).Mul(p.x, p.z) // Z3 := X * Z
+ z3.Add(z3, z3) // Z3 := Z3 + Z3
+ y3 := new(fiat.P521Element).Mul(p521B(), t2) // Y3 := b * t2
+ y3.Sub(y3, z3) // Y3 := Y3 - Z3
+ x3 := new(fiat.P521Element).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(p521B(), 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 *P521Point) Select(p1, p2 *P521Point, cond int) *P521Point {
+ 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 p521Table 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 p521Table [15]*P521Point
+
+// 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 *p521Table) Select(p *P521Point, n uint8) {
+ if n >= 16 {
+ panic("nistec: internal error: p521Table called with out-of-bounds value")
+ }
+ p.Set(NewP521Point())
+ 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 *P521Point) ScalarMult(q *P521Point, scalar []byte) (*P521Point, error) {
+ // Compute a p521Table for the base point q. The explicit NewP521Point
+ // calls get inlined, letting the allocations live on the stack.
+ var table = p521Table{NewP521Point(), NewP521Point(), NewP521Point(),
+ NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(),
+ NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(),
+ NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point()}
+ 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 := NewP521Point()
+ p.Set(NewP521Point())
+ 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 p521GeneratorTable *[p521ElementLength * 2]p521Table
+var p521GeneratorTableOnce sync.Once
+
+// generatorTable returns a sequence of p521Tables. The first table contains
+// multiples of G. Each successive table is the previous table doubled four
+// times.
+func (p *P521Point) generatorTable() *[p521ElementLength * 2]p521Table {
+ p521GeneratorTableOnce.Do(func() {
+ p521GeneratorTable = new([p521ElementLength * 2]p521Table)
+ base := NewP521Point().SetGenerator()
+ for i := 0; i < p521ElementLength*2; i++ {
+ p521GeneratorTable[i][0] = NewP521Point().Set(base)
+ for j := 1; j < 15; j++ {
+ p521GeneratorTable[i][j] = NewP521Point().Add(p521GeneratorTable[i][j-1], base)
+ }
+ base.Double(base)
+ base.Double(base)
+ base.Double(base)
+ base.Double(base)
+ }
+ })
+ return p521GeneratorTable
+}
+
+// ScalarBaseMult sets p = scalar * B, where B is the canonical generator, and
+// returns p.
+func (p *P521Point) ScalarBaseMult(scalar []byte) (*P521Point, error) {
+ if len(scalar) != p521ElementLength {
+ 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 := NewP521Point()
+ p.Set(NewP521Point())
+ 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
+}
+
+// p521Sqrt sets e to a square root of x. If x is not a square, p521Sqrt returns
+// false and e is unchanged. e and x can overlap.
+func p521Sqrt(e, x *fiat.P521Element) (isSquare bool) {
+ candidate := new(fiat.P521Element)
+ p521SqrtCandidate(candidate, x)
+ square := new(fiat.P521Element).Square(candidate)
+ if square.Equal(x) != 1 {
+ return false
+ }
+ e.Set(candidate)
+ return true
+}
+
+// p521SqrtCandidate sets z to a square root candidate for x. z and x must not overlap.
+func p521SqrtCandidate(z, x *fiat.P521Element) {
+ // Since p = 3 mod 4, exponentiation by (p + 1) / 4 yields a square root candidate.
+ //
+ // The sequence of 0 multiplications and 519 squarings is derived from the
+ // following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
+ //
+ // return 1 << 519
+ //
+
+ z.Square(x)
+ for s := 1; s < 519; s++ {
+ z.Square(z)
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-10-30 09:18:10 +0000