diff options
Diffstat (limited to 'src/crypto/internal/nistec/generate.go')
| -rw-r--r-- | src/crypto/internal/nistec/generate.go | 639 |
1 files changed, 639 insertions, 0 deletions
diff --git a/src/crypto/internal/nistec/generate.go b/src/crypto/internal/nistec/generate.go new file mode 100644 index 0000000..0204bc1 --- /dev/null +++ b/src/crypto/internal/nistec/generate.go @@ -0,0 +1,639 @@ +// 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. + +//go:build ignore + +package main + +// Running this generator requires addchain v0.4.0, which can be installed with +// +// go install github.com/mmcloughlin/addchain/cmd/addchain@v0.4.0 +// + +import ( + "bytes" + "crypto/elliptic" + "fmt" + "go/format" + "io" + "log" + "math/big" + "os" + "os/exec" + "strings" + "text/template" +) + +var curves = []struct { + P string + Element string + Params *elliptic.CurveParams + BuildTags string +}{ + { + P: "P224", + Element: "fiat.P224Element", + Params: elliptic.P224().Params(), + }, + { + P: "P256", + Element: "fiat.P256Element", + Params: elliptic.P256().Params(), + BuildTags: "!amd64 && !arm64 && !ppc64le", + }, + { + P: "P384", + Element: "fiat.P384Element", + Params: elliptic.P384().Params(), + }, + { + P: "P521", + Element: "fiat.P521Element", + Params: elliptic.P521().Params(), + }, +} + +func main() { + t := template.Must(template.New("tmplNISTEC").Parse(tmplNISTEC)) + + tmplAddchainFile, err := os.CreateTemp("", "addchain-template") + if err != nil { + log.Fatal(err) + } + defer os.Remove(tmplAddchainFile.Name()) + if _, err := io.WriteString(tmplAddchainFile, tmplAddchain); err != nil { + log.Fatal(err) + } + if err := tmplAddchainFile.Close(); err != nil { + log.Fatal(err) + } + + for _, c := range curves { + p := strings.ToLower(c.P) + elementLen := (c.Params.BitSize + 7) / 8 + B := fmt.Sprintf("%#v", c.Params.B.FillBytes(make([]byte, elementLen))) + Gx := fmt.Sprintf("%#v", c.Params.Gx.FillBytes(make([]byte, elementLen))) + Gy := fmt.Sprintf("%#v", c.Params.Gy.FillBytes(make([]byte, elementLen))) + + log.Printf("Generating %s.go...", p) + f, err := os.Create(p + ".go") + if err != nil { + log.Fatal(err) + } + defer f.Close() + buf := &bytes.Buffer{} + if err := t.Execute(buf, map[string]interface{}{ + "P": c.P, "p": p, "B": B, "Gx": Gx, "Gy": Gy, + "Element": c.Element, "ElementLen": elementLen, + "BuildTags": c.BuildTags, + }); err != nil { + log.Fatal(err) + } + out, err := format.Source(buf.Bytes()) + if err != nil { + log.Fatal(err) + } + if _, err := f.Write(out); err != nil { + log.Fatal(err) + } + + // If p = 3 mod 4, implement modular square root by exponentiation. + mod4 := new(big.Int).Mod(c.Params.P, big.NewInt(4)) + if mod4.Cmp(big.NewInt(3)) != 0 { + continue + } + + exp := new(big.Int).Add(c.Params.P, big.NewInt(1)) + exp.Div(exp, big.NewInt(4)) + + tmp, err := os.CreateTemp("", "addchain-"+p) + if err != nil { + log.Fatal(err) + } + defer os.Remove(tmp.Name()) + cmd := exec.Command("addchain", "search", fmt.Sprintf("%d", exp)) + cmd.Stderr = os.Stderr + cmd.Stdout = tmp + if err := cmd.Run(); err != nil { + log.Fatal(err) + } + if err := tmp.Close(); err != nil { + log.Fatal(err) + } + cmd = exec.Command("addchain", "gen", "-tmpl", tmplAddchainFile.Name(), tmp.Name()) + cmd.Stderr = os.Stderr + out, err = cmd.Output() + if err != nil { + log.Fatal(err) + } + out = bytes.Replace(out, []byte("Element"), []byte(c.Element), -1) + out = bytes.Replace(out, []byte("sqrtCandidate"), []byte(p+"SqrtCandidate"), -1) + out, err = format.Source(out) + if err != nil { + log.Fatal(err) + } + if _, err := f.Write(out); err != nil { + log.Fatal(err) + } + } +} + +const tmplNISTEC = `// 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. + +{{ if .BuildTags }} +//go:build {{ .BuildTags }} +{{ end }} + +package nistec + +import ( + "crypto/internal/nistec/fiat" + "crypto/subtle" + "errors" + "sync" +) + +// {{.p}}ElementLength is the length of an element of the base or scalar field, +// which have the same bytes length for all NIST P curves. +const {{.p}}ElementLength = {{ .ElementLen }} + +// {{.P}}Point is a {{.P}} point. The zero value is NOT valid. +type {{.P}}Point struct { + // The point is represented in projective coordinates (X:Y:Z), + // where x = X/Z and y = Y/Z. + x, y, z *{{.Element}} +} + +// New{{.P}}Point returns a new {{.P}}Point representing the point at infinity point. +func New{{.P}}Point() *{{.P}}Point { + return &{{.P}}Point{ + x: new({{.Element}}), + y: new({{.Element}}).One(), + z: new({{.Element}}), + } +} + +// SetGenerator sets p to the canonical generator and returns p. +func (p *{{.P}}Point) SetGenerator() *{{.P}}Point { + p.x.SetBytes({{.Gx}}) + p.y.SetBytes({{.Gy}}) + p.z.One() + return p +} + +// Set sets p = q and returns p. +func (p *{{.P}}Point) Set(q *{{.P}}Point) *{{.P}}Point { + 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 *{{.P}}Point) SetBytes(b []byte) (*{{.P}}Point, error) { + switch { + // Point at infinity. + case len(b) == 1 && b[0] == 0: + return p.Set(New{{.P}}Point()), nil + + // Uncompressed form. + case len(b) == 1+2*{{.p}}ElementLength && b[0] == 4: + x, err := new({{.Element}}).SetBytes(b[1 : 1+{{.p}}ElementLength]) + if err != nil { + return nil, err + } + y, err := new({{.Element}}).SetBytes(b[1+{{.p}}ElementLength:]) + if err != nil { + return nil, err + } + if err := {{.p}}CheckOnCurve(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+{{.p}}ElementLength && (b[0] == 2 || b[0] == 3): + x, err := new({{.Element}}).SetBytes(b[1:]) + if err != nil { + return nil, err + } + + // y² = x³ - 3x + b + y := {{.p}}Polynomial(new({{.Element}}), x) + if !{{.p}}Sqrt(y, y) { + return nil, errors.New("invalid {{.P}} compressed point encoding") + } + + // Select the positive or negative root, as indicated by the least + // significant bit, based on the encoding type byte. + otherRoot := new({{.Element}}) + otherRoot.Sub(otherRoot, y) + cond := y.Bytes()[{{.p}}ElementLength-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 {{.P}} point encoding") + } +} + + +var _{{.p}}B *{{.Element}} +var _{{.p}}BOnce sync.Once + +func {{.p}}B() *{{.Element}} { + _{{.p}}BOnce.Do(func() { + _{{.p}}B, _ = new({{.Element}}).SetBytes({{.B}}) + }) + return _{{.p}}B +} + +// {{.p}}Polynomial sets y2 to x³ - 3x + b, and returns y2. +func {{.p}}Polynomial(y2, x *{{.Element}}) *{{.Element}} { + y2.Square(x) + y2.Mul(y2, x) + + threeX := new({{.Element}}).Add(x, x) + threeX.Add(threeX, x) + y2.Sub(y2, threeX) + + return y2.Add(y2, {{.p}}B()) +} + +func {{.p}}CheckOnCurve(x, y *{{.Element}}) error { + // y² = x³ - 3x + b + rhs := {{.p}}Polynomial(new({{.Element}}), x) + lhs := new({{.Element}}).Square(y) + if rhs.Equal(lhs) != 1 { + return errors.New("{{.P}} 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 *{{.P}}Point) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [1+2*{{.p}}ElementLength]byte + return p.bytes(&out) +} + +func (p *{{.P}}Point) bytes(out *[1+2*{{.p}}ElementLength]byte) []byte { + if p.z.IsZero() == 1 { + return append(out[:0], 0) + } + + zinv := new({{.Element}}).Invert(p.z) + x := new({{.Element}}).Mul(p.x, zinv) + y := new({{.Element}}).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 *{{.P}}Point) BytesX() ([]byte, error) { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [{{.p}}ElementLength]byte + return p.bytesX(&out) +} + +func (p *{{.P}}Point) bytesX(out *[{{.p}}ElementLength]byte) ([]byte, error) { + if p.z.IsZero() == 1 { + return nil, errors.New("{{.P}} point is the point at infinity") + } + + zinv := new({{.Element}}).Invert(p.z) + x := new({{.Element}}).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 *{{.P}}Point) BytesCompressed() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [1 + {{.p}}ElementLength]byte + return p.bytesCompressed(&out) +} + +func (p *{{.P}}Point) bytesCompressed(out *[1 + {{.p}}ElementLength]byte) []byte { + if p.z.IsZero() == 1 { + return append(out[:0], 0) + } + + zinv := new({{.Element}}).Invert(p.z) + x := new({{.Element}}).Mul(p.x, zinv) + y := new({{.Element}}).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()[{{.p}}ElementLength-1] & 1 + buf = append(buf, x.Bytes()...) + return buf +} + +// Add sets q = p1 + p2, and returns q. The points may overlap. +func (q *{{.P}}Point) Add(p1, p2 *{{.P}}Point) *{{.P}}Point { + // 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({{.Element}}).Mul(p1.x, p2.x) // t0 := X1 * X2 + t1 := new({{.Element}}).Mul(p1.y, p2.y) // t1 := Y1 * Y2 + t2 := new({{.Element}}).Mul(p1.z, p2.z) // t2 := Z1 * Z2 + t3 := new({{.Element}}).Add(p1.x, p1.y) // t3 := X1 + Y1 + t4 := new({{.Element}}).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({{.Element}}).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({{.Element}}).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({{.Element}}).Mul({{.p}}B(), 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({{.p}}B(), 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 *{{.P}}Point) Double(p *{{.P}}Point) *{{.P}}Point { + // 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({{.Element}}).Square(p.x) // t0 := X ^ 2 + t1 := new({{.Element}}).Square(p.y) // t1 := Y ^ 2 + t2 := new({{.Element}}).Square(p.z) // t2 := Z ^ 2 + t3 := new({{.Element}}).Mul(p.x, p.y) // t3 := X * Y + t3.Add(t3, t3) // t3 := t3 + t3 + z3 := new({{.Element}}).Mul(p.x, p.z) // Z3 := X * Z + z3.Add(z3, z3) // Z3 := Z3 + Z3 + y3 := new({{.Element}}).Mul({{.p}}B(), t2) // Y3 := b * t2 + y3.Sub(y3, z3) // Y3 := Y3 - Z3 + x3 := new({{.Element}}).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({{.p}}B(), 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 *{{.P}}Point) Select(p1, p2 *{{.P}}Point, cond int) *{{.P}}Point { + 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 {{.p}}Table 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 {{.p}}Table [15]*{{.P}}Point + +// 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 *{{.p}}Table) Select(p *{{.P}}Point, n uint8) { + if n >= 16 { + panic("nistec: internal error: {{.p}}Table called with out-of-bounds value") + } + p.Set(New{{.P}}Point()) + 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 *{{.P}}Point) ScalarMult(q *{{.P}}Point, scalar []byte) (*{{.P}}Point, error) { + // Compute a {{.p}}Table for the base point q. The explicit New{{.P}}Point + // calls get inlined, letting the allocations live on the stack. + var table = {{.p}}Table{New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), + New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), + New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), + New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point(), New{{.P}}Point()} + 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 := New{{.P}}Point() + p.Set(New{{.P}}Point()) + 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 {{.p}}GeneratorTable *[{{.p}}ElementLength * 2]{{.p}}Table +var {{.p}}GeneratorTableOnce sync.Once + +// generatorTable returns a sequence of {{.p}}Tables. The first table contains +// multiples of G. Each successive table is the previous table doubled four +// times. +func (p *{{.P}}Point) generatorTable() *[{{.p}}ElementLength * 2]{{.p}}Table { + {{.p}}GeneratorTableOnce.Do(func() { + {{.p}}GeneratorTable = new([{{.p}}ElementLength * 2]{{.p}}Table) + base := New{{.P}}Point().SetGenerator() + for i := 0; i < {{.p}}ElementLength*2; i++ { + {{.p}}GeneratorTable[i][0] = New{{.P}}Point().Set(base) + for j := 1; j < 15; j++ { + {{.p}}GeneratorTable[i][j] = New{{.P}}Point().Add({{.p}}GeneratorTable[i][j-1], base) + } + base.Double(base) + base.Double(base) + base.Double(base) + base.Double(base) + } + }) + return {{.p}}GeneratorTable +} + +// ScalarBaseMult sets p = scalar * B, where B is the canonical generator, and +// returns p. +func (p *{{.P}}Point) ScalarBaseMult(scalar []byte) (*{{.P}}Point, error) { + if len(scalar) != {{.p}}ElementLength { + 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 := New{{.P}}Point() + p.Set(New{{.P}}Point()) + 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 +} + +// {{.p}}Sqrt sets e to a square root of x. If x is not a square, {{.p}}Sqrt returns +// false and e is unchanged. e and x can overlap. +func {{.p}}Sqrt(e, x *{{ .Element }}) (isSquare bool) { + candidate := new({{ .Element }}) + {{.p}}SqrtCandidate(candidate, x) + square := new({{ .Element }}).Square(candidate) + if square.Equal(x) != 1 { + return false + } + e.Set(candidate) + return true +} +` + +const tmplAddchain = ` +// sqrtCandidate sets z to a square root candidate for x. z and x must not overlap. +func sqrtCandidate(z, x *Element) { + // Since p = 3 mod 4, exponentiation by (p + 1) / 4 yields a square root candidate. + // + // The sequence of {{ .Ops.Adds }} multiplications and {{ .Ops.Doubles }} squarings is derived from the + // following addition chain generated with {{ .Meta.Module }} {{ .Meta.ReleaseTag }}. + // + {{- range lines (format .Script) }} + // {{ . }} + {{- end }} + // + + {{- range .Program.Temporaries }} + var {{ . }} = new(Element) + {{- end }} + {{ range $i := .Program.Instructions -}} + {{- with add $i.Op }} + {{ $i.Output }}.Mul({{ .X }}, {{ .Y }}) + {{- end -}} + + {{- with double $i.Op }} + {{ $i.Output }}.Square({{ .X }}) + {{- end -}} + + {{- with shift $i.Op -}} + {{- $first := 0 -}} + {{- if ne $i.Output.Identifier .X.Identifier }} + {{ $i.Output }}.Square({{ .X }}) + {{- $first = 1 -}} + {{- end }} + for s := {{ $first }}; s < {{ .S }}; s++ { + {{ $i.Output }}.Square({{ $i.Output }}) + } + {{- end -}} + {{- end }} +} +` |