Adding upstream version 1.18.10.upstream/1.18.10upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

4 files changed, 995 insertions, 0 deletions

diff --git a/src/crypto/elliptic/internal/nistec/nistec_test.go b/src/crypto/elliptic/internal/nistec/nistec_test.go
new file mode 100644
index 0000000..4eae998
--- /dev/null
+++ b/src/crypto/elliptic/internal/nistec/nistec_test.go
@@ -0,0 +1,94 @@
+// Copyright 2021 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.
+
+package nistec_test
+
+import (
+	"crypto/elliptic/internal/nistec"
+	"math/rand"
+	"os"
+	"strings"
+	"testing"
+)
+
+func TestAllocations(t *testing.T) {
+	if strings.HasSuffix(os.Getenv("GO_BUILDER_NAME"), "-noopt") {
+		t.Skip("skipping allocations test without relevant optimizations")
+	}
+	t.Run("P224", func(t *testing.T) {
+		if allocs := testing.AllocsPerRun(100, func() {
+			p := nistec.NewP224Generator()
+			scalar := make([]byte, 66)
+			rand.Read(scalar)
+			p.ScalarMult(p, scalar)
+			out := p.Bytes()
+			if _, err := p.SetBytes(out); err != nil {
+				t.Fatal(err)
+			}
+		}); allocs > 0 {
+			t.Errorf("expected zero allocations, got %0.1f", allocs)
+		}
+	})
+	t.Run("P384", func(t *testing.T) {
+		if allocs := testing.AllocsPerRun(100, func() {
+			p := nistec.NewP384Generator()
+			scalar := make([]byte, 66)
+			rand.Read(scalar)
+			p.ScalarMult(p, scalar)
+			out := p.Bytes()
+			if _, err := p.SetBytes(out); err != nil {
+				t.Fatal(err)
+			}
+		}); allocs > 0 {
+			t.Errorf("expected zero allocations, got %0.1f", allocs)
+		}
+	})
+	t.Run("P521", func(t *testing.T) {
+		if allocs := testing.AllocsPerRun(100, func() {
+			p := nistec.NewP521Generator()
+			scalar := make([]byte, 66)
+			rand.Read(scalar)
+			p.ScalarMult(p, scalar)
+			out := p.Bytes()
+			if _, err := p.SetBytes(out); err != nil {
+				t.Fatal(err)
+			}
+		}); allocs > 0 {
+			t.Errorf("expected zero allocations, got %0.1f", allocs)
+		}
+	})
+}
+
+func BenchmarkScalarMult(b *testing.B) {
+	b.Run("P224", func(b *testing.B) {
+		scalar := make([]byte, 66)
+		rand.Read(scalar)
+		p := nistec.NewP224Generator()
+		b.ReportAllocs()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			p.ScalarMult(p, scalar)
+		}
+	})
+	b.Run("P384", func(b *testing.B) {
+		scalar := make([]byte, 66)
+		rand.Read(scalar)
+		p := nistec.NewP384Generator()
+		b.ReportAllocs()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			p.ScalarMult(p, scalar)
+		}
+	})
+	b.Run("P521", func(b *testing.B) {
+		scalar := make([]byte, 66)
+		rand.Read(scalar)
+		p := nistec.NewP521Generator()
+		b.ReportAllocs()
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			p.ScalarMult(p, scalar)
+		}
+	})
+}
diff --git a/src/crypto/elliptic/internal/nistec/p224.go b/src/crypto/elliptic/internal/nistec/p224.go
new file mode 100644
index 0000000..74dbc18
--- /dev/null
+++ b/src/crypto/elliptic/internal/nistec/p224.go
@@ -0,0 +1,293 @@
+// Copyright 2021 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.
+
+package nistec
+
+import (
+	"crypto/elliptic/internal/fiat"
+	"crypto/subtle"
+	"errors"
+)
+
+var p224B, _ = new(fiat.P224Element).SetBytes([]byte{0xb4, 0x05, 0x0a, 0x85,
+	0x0c, 0x04, 0xb3, 0xab, 0xf5, 0x41, 0x32, 0x56, 0x50, 0x44, 0xb0, 0xb7,
+	0xd7, 0xbf, 0xd8, 0xba, 0x27, 0x0b, 0x39, 0x43, 0x23, 0x55, 0xff, 0xb4})
+
+var p224G, _ = NewP224Point().SetBytes([]byte{0x04,
+	0xb7, 0x0e, 0x0c, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f, 0x32, 0x13, 0x90, 0xb9,
+	0x4a, 0x03, 0xc1, 0xd3, 0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6,
+	0x11, 0x5c, 0x1d, 0x21, 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb,
+	0x4c, 0x22, 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64,
+	0x44, 0xd5, 0x81, 0x99, 0x85, 0x0, 0x7e, 0x34})
+
+const p224ElementLength = 28
+
+// P224Point is a P-224 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),
+	}
+}
+
+// NewP224Generator returns a new P224Point set to the canonical generator.
+func NewP224Generator() *P224Point {
+	return (&P224Point{
+		x: new(fiat.P224Element),
+		y: new(fiat.P224Element),
+		z: new(fiat.P224Element),
+	}).Set(p224G)
+}
+
+// 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] == 0:
+		return nil, errors.New("unimplemented") // TODO(filippo)
+
+	default:
+		return nil, errors.New("invalid P224 point encoding")
+	}
+}
+
+func p224CheckOnCurve(x, y *fiat.P224Element) error {
+	// x³ - 3x + b.
+	x3 := new(fiat.P224Element).Square(x)
+	x3.Mul(x3, x)
+
+	threeX := new(fiat.P224Element).Add(x, x)
+	threeX.Add(threeX, x)
+
+	x3.Sub(x3, threeX)
+	x3.Add(x3, p224B)
+
+	// y² = x³ - 3x + b
+	y2 := new(fiat.P224Element).Square(y)
+
+	if x3.Equal(y2) != 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 [133]byte
+	return p.bytes(&out)
+}
+
+func (p *P224Point) bytes(out *[133]byte) []byte {
+	if p.z.IsZero() == 1 {
+		return append(out[:0], 0)
+	}
+
+	zinv := new(fiat.P224Element).Invert(p.z)
+	xx := new(fiat.P224Element).Mul(p.x, zinv)
+	yy := new(fiat.P224Element).Mul(p.y, zinv)
+
+	buf := append(out[:0], 4)
+	buf = append(buf, xx.Bytes()...)
+	buf = append(buf, yy.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
+}
+
+// ScalarMult sets p = scalar * q, and returns p.
+func (p *P224Point) ScalarMult(q *P224Point, scalar []byte) *P224Point {
+	// table holds the first 16 multiples of q. The explicit newP224Point calls
+	// get inlined, letting the allocations live on the stack.
+	var table = [16]*P224Point{
+		NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(),
+		NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(),
+		NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(),
+		NewP224Point(), NewP224Point(), NewP224Point(), NewP224Point(),
+	}
+	for i := 1; i < 16; i++ {
+		table[i].Add(table[i-1], 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 _, byte := range scalar {
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+
+		for i := uint8(0); i < 16; i++ {
+			cond := subtle.ConstantTimeByteEq(byte>>4, i)
+			t.Select(table[i], t, cond)
+		}
+		p.Add(p, t)
+
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+
+		for i := uint8(0); i < 16; i++ {
+			cond := subtle.ConstantTimeByteEq(byte&0b1111, i)
+			t.Select(table[i], t, cond)
+		}
+		p.Add(p, t)
+	}
+
+	return p
+}
diff --git a/src/crypto/elliptic/internal/nistec/p384.go b/src/crypto/elliptic/internal/nistec/p384.go
new file mode 100644
index 0000000..24a166d
--- /dev/null
+++ b/src/crypto/elliptic/internal/nistec/p384.go
@@ -0,0 +1,298 @@
+// Copyright 2021 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.
+
+package nistec
+
+import (
+	"crypto/elliptic/internal/fiat"
+	"crypto/subtle"
+	"errors"
+)
+
+var p384B, _ = new(fiat.P384Element).SetBytes([]byte{
+	0xb3, 0x31, 0x2f, 0xa7, 0xe2, 0x3e, 0xe7, 0xe4, 0x98, 0x8e, 0x05, 0x6b,
+	0xe3, 0xf8, 0x2d, 0x19, 0x18, 0x1d, 0x9c, 0x6e, 0xfe, 0x81, 0x41, 0x12,
+	0x03, 0x14, 0x08, 0x8f, 0x50, 0x13, 0x87, 0x5a, 0xc6, 0x56, 0x39, 0x8d,
+	0x8a, 0x2e, 0xd1, 0x9d, 0x2a, 0x85, 0xc8, 0xed, 0xd3, 0xec, 0x2a, 0xef})
+
+var p384G, _ = NewP384Point().SetBytes([]byte{0x4,
+	0xaa, 0x87, 0xca, 0x22, 0xbe, 0x8b, 0x05, 0x37, 0x8e, 0xb1, 0xc7, 0x1e,
+	0xf3, 0x20, 0xad, 0x74, 0x6e, 0x1d, 0x3b, 0x62, 0x8b, 0xa7, 0x9b, 0x98,
+	0x59, 0xf7, 0x41, 0xe0, 0x82, 0x54, 0x2a, 0x38, 0x55, 0x02, 0xf2, 0x5d,
+	0xbf, 0x55, 0x29, 0x6c, 0x3a, 0x54, 0x5e, 0x38, 0x72, 0x76, 0x0a, 0xb7,
+	0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, 0x98, 0xbf,
+	0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, 0x28, 0x9a, 0x14, 0x7c,
+	0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, 0xb8, 0xc0, 0x0a, 0x60, 0xb1, 0xce,
+	0x1d, 0x7e, 0x81, 0x9d, 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f})
+
+const p384ElementLength = 48
+
+// P384Point is a P-384 point. The zero value is NOT valid.
+type P384Point struct {
+	// The point is represented in projective coordinates (X:Y:Z),
+	// where x = X/Z and y = Y/Z.
+	x, y, z *fiat.P384Element
+}
+
+// NewP384Point returns a new P384Point representing the point at infinity point.
+func NewP384Point() *P384Point {
+	return &P384Point{
+		x: new(fiat.P384Element),
+		y: new(fiat.P384Element).One(),
+		z: new(fiat.P384Element),
+	}
+}
+
+// NewP384Generator returns a new P384Point set to the canonical generator.
+func NewP384Generator() *P384Point {
+	return (&P384Point{
+		x: new(fiat.P384Element),
+		y: new(fiat.P384Element),
+		z: new(fiat.P384Element),
+	}).Set(p384G)
+}
+
+// Set sets p = q and returns p.
+func (p *P384Point) Set(q *P384Point) *P384Point {
+	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 *P384Point) SetBytes(b []byte) (*P384Point, error) {
+	switch {
+	// Point at infinity.
+	case len(b) == 1 && b[0] == 0:
+		return p.Set(NewP384Point()), nil
+
+	// Uncompressed form.
+	case len(b) == 1+2*p384ElementLength && b[0] == 4:
+		x, err := new(fiat.P384Element).SetBytes(b[1 : 1+p384ElementLength])
+		if err != nil {
+			return nil, err
+		}
+		y, err := new(fiat.P384Element).SetBytes(b[1+p384ElementLength:])
+		if err != nil {
+			return nil, err
+		}
+		if err := p384CheckOnCurve(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+p384ElementLength && b[0] == 0:
+		return nil, errors.New("unimplemented") // TODO(filippo)
+
+	default:
+		return nil, errors.New("invalid P384 point encoding")
+	}
+}
+
+func p384CheckOnCurve(x, y *fiat.P384Element) error {
+	// x³ - 3x + b.
+	x3 := new(fiat.P384Element).Square(x)
+	x3.Mul(x3, x)
+
+	threeX := new(fiat.P384Element).Add(x, x)
+	threeX.Add(threeX, x)
+
+	x3.Sub(x3, threeX)
+	x3.Add(x3, p384B)
+
+	// y² = x³ - 3x + b
+	y2 := new(fiat.P384Element).Square(y)
+
+	if x3.Equal(y2) != 1 {
+		return errors.New("P384 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 *P384Point) Bytes() []byte {
+	// This function is outlined to make the allocations inline in the caller
+	// rather than happen on the heap.
+	var out [133]byte
+	return p.bytes(&out)
+}
+
+func (p *P384Point) bytes(out *[133]byte) []byte {
+	if p.z.IsZero() == 1 {
+		return append(out[:0], 0)
+	}
+
+	zinv := new(fiat.P384Element).Invert(p.z)
+	xx := new(fiat.P384Element).Mul(p.x, zinv)
+	yy := new(fiat.P384Element).Mul(p.y, zinv)
+
+	buf := append(out[:0], 4)
+	buf = append(buf, xx.Bytes()...)
+	buf = append(buf, yy.Bytes()...)
+	return buf
+}
+
+// Add sets q = p1 + p2, and returns q. The points may overlap.
+func (q *P384Point) Add(p1, p2 *P384Point) *P384Point {
+	// 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.P384Element).Mul(p1.x, p2.x) // t0 := X1 * X2
+	t1 := new(fiat.P384Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2
+	t2 := new(fiat.P384Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2
+	t3 := new(fiat.P384Element).Add(p1.x, p1.y) // t3 := X1 + Y1
+	t4 := new(fiat.P384Element).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.P384Element).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.P384Element).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.P384Element).Mul(p384B, 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(p384B, 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 *P384Point) Double(p *P384Point) *P384Point {
+	// 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.P384Element).Square(p.x)    // t0 := X ^ 2
+	t1 := new(fiat.P384Element).Square(p.y)    // t1 := Y ^ 2
+	t2 := new(fiat.P384Element).Square(p.z)    // t2 := Z ^ 2
+	t3 := new(fiat.P384Element).Mul(p.x, p.y)  // t3 := X * Y
+	t3.Add(t3, t3)                             // t3 := t3 + t3
+	z3 := new(fiat.P384Element).Mul(p.x, p.z)  // Z3 := X * Z
+	z3.Add(z3, z3)                             // Z3 := Z3 + Z3
+	y3 := new(fiat.P384Element).Mul(p384B, t2) // Y3 := b * t2
+	y3.Sub(y3, z3)                             // Y3 := Y3 - Z3
+	x3 := new(fiat.P384Element).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(p384B, 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 *P384Point) Select(p1, p2 *P384Point, cond int) *P384Point {
+	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
+}
+
+// ScalarMult sets p = scalar * q, and returns p.
+func (p *P384Point) ScalarMult(q *P384Point, scalar []byte) *P384Point {
+	// table holds the first 16 multiples of q. The explicit newP384Point calls
+	// get inlined, letting the allocations live on the stack.
+	var table = [16]*P384Point{
+		NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(),
+		NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(),
+		NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(),
+		NewP384Point(), NewP384Point(), NewP384Point(), NewP384Point(),
+	}
+	for i := 1; i < 16; i++ {
+		table[i].Add(table[i-1], 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 := NewP384Point()
+	p.Set(NewP384Point())
+	for _, byte := range scalar {
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+
+		for i := uint8(0); i < 16; i++ {
+			cond := subtle.ConstantTimeByteEq(byte>>4, i)
+			t.Select(table[i], t, cond)
+		}
+		p.Add(p, t)
+
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+
+		for i := uint8(0); i < 16; i++ {
+			cond := subtle.ConstantTimeByteEq(byte&0b1111, i)
+			t.Select(table[i], t, cond)
+		}
+		p.Add(p, t)
+	}
+
+	return p
+}
diff --git a/src/crypto/elliptic/internal/nistec/p521.go b/src/crypto/elliptic/internal/nistec/p521.go
new file mode 100644
index 0000000..cdbd195
--- /dev/null
+++ b/src/crypto/elliptic/internal/nistec/p521.go
@@ -0,0 +1,310 @@
+// Copyright 2021 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.
+
+// Package nistec implements the NIST P elliptic curves from FIPS 186-4.
+//
+// This package uses fiat-crypto for its backend field arithmetic (not math/big)
+// and exposes constant-time, heap allocation-free, byte slice-based safe APIs.
+// Group operations use modern and safe complete addition formulas. The point at
+// infinity is handled and encoded according to SEC 1, Version 2.0, and invalid
+// curve points can't be represented.
+package nistec
+
+import (
+	"crypto/elliptic/internal/fiat"
+	"crypto/subtle"
+	"errors"
+)
+
+var p521B, _ = new(fiat.P521Element).SetBytes([]byte{
+	0x00, 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, 0x09, 0xe1, 0x56, 0x19,
+	0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1,
+	0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34, 0xf1, 0xef, 0x45,
+	0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x00})
+
+var p521G, _ = NewP521Point().SetBytes([]byte{0x04,
+	0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, 0xe9, 0xcd, 0x9e, 0x3e,
+	0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 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, 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78,
+	0x9a, 0x3b, 0xc0, 0x04, 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, 0x01, 0x3f, 0xad, 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86,
+	0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50})
+
+const p521ElementLength = 66
+
+// P521Point is a P-521 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),
+	}
+}
+
+// NewP521Generator returns a new P521Point set to the canonical generator.
+func NewP521Generator() *P521Point {
+	return (&P521Point{
+		x: new(fiat.P521Element),
+		y: new(fiat.P521Element),
+		z: new(fiat.P521Element),
+	}).Set(p521G)
+}
+
+// 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] == 0:
+		return nil, errors.New("unimplemented") // TODO(filippo)
+
+	default:
+		return nil, errors.New("invalid P521 point encoding")
+	}
+}
+
+func p521CheckOnCurve(x, y *fiat.P521Element) error {
+	// x³ - 3x + b.
+	x3 := new(fiat.P521Element).Square(x)
+	x3.Mul(x3, x)
+
+	threeX := new(fiat.P521Element).Add(x, x)
+	threeX.Add(threeX, x)
+
+	x3.Sub(x3, threeX)
+	x3.Add(x3, p521B)
+
+	// y² = x³ - 3x + b
+	y2 := new(fiat.P521Element).Square(y)
+
+	if x3.Equal(y2) != 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 [133]byte
+	return p.bytes(&out)
+}
+
+func (p *P521Point) bytes(out *[133]byte) []byte {
+	if p.z.IsZero() == 1 {
+		return append(out[:0], 0)
+	}
+
+	zinv := new(fiat.P521Element).Invert(p.z)
+	xx := new(fiat.P521Element).Mul(p.x, zinv)
+	yy := new(fiat.P521Element).Mul(p.y, zinv)
+
+	buf := append(out[:0], 4)
+	buf = append(buf, xx.Bytes()...)
+	buf = append(buf, yy.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
+}
+
+// ScalarMult sets p = scalar * q, and returns p.
+func (p *P521Point) ScalarMult(q *P521Point, scalar []byte) *P521Point {
+	// table holds the first 16 multiples of q. The explicit newP521Point calls
+	// get inlined, letting the allocations live on the stack.
+	var table = [16]*P521Point{
+		NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(),
+		NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(),
+		NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(),
+		NewP521Point(), NewP521Point(), NewP521Point(), NewP521Point(),
+	}
+	for i := 1; i < 16; i++ {
+		table[i].Add(table[i-1], 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 _, byte := range scalar {
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+
+		for i := uint8(0); i < 16; i++ {
+			cond := subtle.ConstantTimeByteEq(byte>>4, i)
+			t.Select(table[i], t, cond)
+		}
+		p.Add(p, t)
+
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+		p.Double(p)
+
+		for i := uint8(0); i < 16; i++ {
+			cond := subtle.ConstantTimeByteEq(byte&0b1111, i)
+			t.Select(table[i], t, cond)
+		}
+		p.Add(p, t)
+	}
+
+	return p
+}