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* Add Secp256k1 Signed-off-by: bytemare <[email protected]>
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,217 @@ | ||
| // SPDX-License-Identifier: MIT | ||
| // | ||
| // Copyright (C) 2020-2023 Daniel Bourdrez. All Rights Reserved. | ||
| // | ||
| // This source code is licensed under the MIT license found in the | ||
| // LICENSE file in the root directory of this source tree or at | ||
| // https://spdx.org/licenses/MIT.html | ||
|
|
||
| // Package field provides modular operations over very high integers. | ||
| package field | ||
|
|
||
| import ( | ||
| "crypto/rand" | ||
| "fmt" | ||
| "math/big" | ||
| ) | ||
|
|
||
| var ( | ||
| zero = big.NewInt(0) | ||
| one = big.NewInt(1) | ||
| ) | ||
|
|
||
| // String2Int returns a big.Int representation of the integer s. | ||
| func String2Int(s string) big.Int { | ||
| if p, _ := new(big.Int).SetString(s, 0); p != nil { | ||
| return *p | ||
| } | ||
|
|
||
| panic("invalid string to convert") | ||
| } | ||
|
|
||
| // Field represents a Gaulois Field. | ||
| type Field struct { | ||
| order big.Int | ||
| pMinus1div2 big.Int // used in IsSquare | ||
| pMinus2 big.Int // used for Field big.Int inversion | ||
| exp big.Int | ||
| } | ||
|
|
||
| // NewField returns a newly instantiated field for the given prime order. | ||
| func NewField(prime *big.Int) Field { | ||
| // pMinus1div2 is used to determine whether a big Int is a quadratic square. | ||
| pMinus1div2 := big.NewInt(1) | ||
| pMinus1div2.Sub(prime, pMinus1div2) | ||
| pMinus1div2.Rsh(pMinus1div2, 1) | ||
|
|
||
| // pMinus2 is used for modular inversion. | ||
| pMinus2 := big.NewInt(2) | ||
| pMinus2.Sub(prime, pMinus2) | ||
|
|
||
| // precompute e = (p + 1) / 4 | ||
| exp := big.NewInt(1) | ||
| exp.Add(prime, exp) | ||
| exp.Rsh(exp, 2) | ||
|
|
||
| return Field{ | ||
| order: *prime, | ||
| pMinus1div2: *pMinus1div2, | ||
| pMinus2: *pMinus2, | ||
| exp: *exp, | ||
| } | ||
| } | ||
|
|
||
| // Zero returns the zero big.Int of the finite Field. | ||
| func (f Field) Zero() *big.Int { | ||
| return zero | ||
| } | ||
|
|
||
| // One returns one big.Int of the finite Field. | ||
| func (f Field) One() *big.Int { | ||
| return one | ||
| } | ||
|
|
||
| // Random sets res to a random big.Int in the Field. | ||
| func (f Field) Random(res *big.Int) *big.Int { | ||
| tmp, err := rand.Int(rand.Reader, &f.order) | ||
| if err != nil { | ||
| // We can as well not panic and try again in a loop | ||
| panic(fmt.Errorf("unexpected error in generating random bytes : %w", err)) | ||
| } | ||
|
|
||
| res.Set(tmp) | ||
|
|
||
| return res | ||
| } | ||
|
|
||
| // Order returns the size of the Field. | ||
| func (f Field) Order() *big.Int { | ||
| return &f.order | ||
| } | ||
|
|
||
| // BitLen of the order. | ||
| func (f Field) BitLen() int { | ||
| return f.order.BitLen() | ||
| } | ||
|
|
||
| // AreEqual returns whether both elements are equal. | ||
| func (f Field) AreEqual(f1, f2 *big.Int) bool { | ||
| return f.IsZero(f.Sub(&big.Int{}, f1, f2)) | ||
| } | ||
|
|
||
| // IsZero returns whether the big.Int is equivalent to zero. | ||
| func (f Field) IsZero(e *big.Int) bool { | ||
| return e.Sign() == 0 | ||
| } | ||
|
|
||
| // Inv sets res to the modular inverse of x mod field order. | ||
| func (f Field) Inv(res, x *big.Int) { | ||
| f.Exponent(res, x, &f.pMinus2) | ||
| } | ||
|
|
||
| // LegendreSymbol applies the Legendre symbole on (a/p) and returns either {-1, 0, 1} mod field order. | ||
| func (f Field) LegendreSymbol(a *big.Int) *big.Int { | ||
| var res big.Int | ||
| return f.Exponent(&res, a, &f.pMinus1div2) | ||
| } | ||
|
|
||
| // Exponent returns x^n mod field order. | ||
| func (f Field) Exponent(res, x, n *big.Int) *big.Int { | ||
| return res.Exp(x, n, &f.order) | ||
| } | ||
|
|
||
| // IsSquare returns whether e is a quadratic square. | ||
| func (f Field) IsSquare(e *big.Int) bool { | ||
| return f.AreEqual(f.LegendreSymbol(e), f.One()) | ||
| } | ||
|
|
||
| // IsEqual returns whether the two fields have the same order. | ||
| func (f Field) IsEqual(f2 *Field) bool { | ||
| return f.order.Cmp(&f2.order) == 0 | ||
| } | ||
|
|
||
| // Mod reduces x modulo the field order. | ||
| func (f Field) Mod(x *big.Int) *big.Int { | ||
| return x.Mod(x, &f.order) | ||
| } | ||
|
|
||
| // Neg sets res to the -x modulo the field order. | ||
| func (f Field) Neg(res, x *big.Int) *big.Int { | ||
| return f.Mod(res.Neg(x)) | ||
| } | ||
|
|
||
| // CondNeg sets res to -x if cond == 1. | ||
| func (f Field) CondNeg(res, x *big.Int, cond int) { | ||
| var neg, cpy big.Int | ||
| cpy.Set(x) | ||
| f.Neg(&neg, x) | ||
|
|
||
| if cond == 1 { | ||
| res.Set(&neg) | ||
| } else { | ||
| res.Set(&cpy) | ||
| } | ||
| } | ||
|
|
||
| // Add sets res to x + y modulo the field order. | ||
| func (f Field) Add(res, x, y *big.Int) { | ||
| f.Mod(res.Add(x, y)) | ||
| } | ||
|
|
||
| // Sub sets res to x - y modulo the field order. | ||
| func (f Field) Sub(res, x, y *big.Int) *big.Int { | ||
| return f.Mod(res.Sub(x, y)) | ||
| } | ||
|
|
||
| // Lsh sets res to the left shift of n bits on x modulo the field order. | ||
| func (f Field) Lsh(res, x *big.Int, n uint) { | ||
| f.Mod(res.Lsh(x, n)) | ||
| } | ||
|
|
||
| // Mul sets res to the multiplication of x and y modulo the field order. | ||
| func (f Field) Mul(res, x, y *big.Int) { | ||
| f.Mod(res.Mul(x, y)) | ||
| } | ||
|
|
||
| // Square sets res to the square of x modulo the field order. | ||
| func (f Field) Square(res, x *big.Int) { | ||
| f.Mod(res.Mul(x, x)) | ||
| } | ||
|
|
||
| // CondMov sets res to y if b true, and to x otherwise. | ||
| func (f Field) CondMov(res, x, y *big.Int, b bool) { | ||
| if b { | ||
| res.Set(y) | ||
| } else { | ||
| res.Set(x) | ||
| } | ||
| } | ||
|
|
||
| // Sgn0 returns the first bit in the big-endian representation. | ||
| func (f Field) Sgn0(x *big.Int) int { | ||
| return int(x.Bit(0)) | ||
| } | ||
|
|
||
| func (f Field) sqrt3mod4(res, e *big.Int) *big.Int { | ||
| return f.Exponent(res, e, &f.exp) | ||
| } | ||
|
|
||
| // SquareRoot sets res to a square root of e mod the field's order, if such a square root exists. | ||
| func (f Field) SquareRoot(res, e *big.Int) *big.Int { | ||
| return f.sqrt3mod4(res, e) | ||
| } | ||
|
|
||
| // SqrtRatio res result to the square root of (e/v), and indicates whether (e/v) is a square. | ||
| func (f Field) SqrtRatio(res, zMapConstant, e, v *big.Int) bool { | ||
| f.Inv(res, v) | ||
| f.Mul(res, res, e) | ||
|
|
||
| square := f.IsSquare(res) | ||
| if !square { | ||
| f.Mul(res, res, zMapConstant) | ||
| } | ||
|
|
||
| f.SquareRoot(res, res) | ||
|
|
||
| return square | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,52 @@ | ||
| // SPDX-License-Identifier: MIT | ||
| // | ||
| // Copyright (C)2020-2023 Daniel Bourdrez. All Rights Reserved. | ||
| // | ||
| // This source code is licensed under the MIT license found in the | ||
| // LICENSE file in the root directory of this source tree or at | ||
| // https://spdx.org/licenses/MIT.html | ||
|
|
||
| // Package h2c provides hash-to-curve primitives and mapping. | ||
| package h2c | ||
|
|
||
| import ( | ||
| "math/big" | ||
|
|
||
| "github.com/bytemare/crypto/internal/field" | ||
| ) | ||
|
|
||
| // MapToCurveSSWU implements the Simplified SWU method for Weierstrass curves for any base field. | ||
| func MapToCurveSSWU(f *field.Field, a, b, z, fe *big.Int) (x, y *big.Int) { | ||
| var tv1, tv2, tv3, tv4, tv5, tv6, _y1, _px, _py big.Int | ||
|
|
||
| f.Square(&tv1, fe) // 1. tv1 = u^2 | ||
| f.Mul(&tv1, z, &tv1) // 2. tv1 = Z * tv1 | ||
| f.Square(&tv2, &tv1) // 3. tv2 = tv1^2 | ||
| f.Add(&tv2, &tv2, &tv1) // 4. tv2 = tv2 + tv1 | ||
| f.Add(&tv3, &tv2, f.One()) // 5. tv3 = tv2 + 1 | ||
| f.Mul(&tv3, b, &tv3) // 6. tv3 = B * tv3 | ||
| f.CondMov(&tv4, z, | ||
| f.Neg(&big.Int{}, &tv2), | ||
| !f.IsZero(&tv2)) // 7. tv4 = CMOV(Z, -tv2, tv2 != 0) | ||
| f.Mul(&tv4, a, &tv4) // 8. tv4 = A * tv4 | ||
| f.Square(&tv2, &tv3) // 9. tv2 = tv3^2 | ||
| f.Square(&tv6, &tv4) // 10. tv6 = tv4^2 | ||
| f.Mul(&tv5, a, &tv6) // 11. tv5 = A * tv6 | ||
| f.Add(&tv2, &tv2, &tv5) // 12. tv2 = tv2 + tv5 | ||
| f.Mul(&tv2, &tv2, &tv3) // 13. tv2 = tv2 * tv3 | ||
| f.Mul(&tv6, &tv6, &tv4) // 14. tv6 = tv6 * tv4 | ||
| f.Mul(&tv5, b, &tv6) // 15. tv5 = B * tv6 | ||
| f.Add(&tv2, &tv2, &tv5) // 16. tv2 = tv2 + tv5 | ||
| f.Mul(&_px, &tv1, &tv3) // 17. x = tv1 * tv3 | ||
| isGx1Square := f.SqrtRatio(&_y1, z, &tv2, &tv6) // 18. isGx1Square, y1 = sqrt_ratio(tv2, tv6) | ||
| f.Mul(&_py, &tv1, fe) // 19. y = tv1 * u | ||
| f.Mul(&_py, &_py, &_y1) // 20. y = y * y1 | ||
| f.CondMov(&_px, &_px, &tv3, isGx1Square) // 21. x = CMOV(x, tv3, isGx1Square) | ||
| f.CondMov(&_py, &_py, &_y1, isGx1Square) // 22. y = CMOV(y, y1, isGx1Square) | ||
| e1 := f.Sgn0(fe) == f.Sgn0(&_py) // 23. e1 = sgn0(u) == sgn0(y) | ||
| f.CondMov(&_py, f.Neg(&big.Int{}, &_py), &_py, e1) // 24. y = CMOV(-y, y, e1) | ||
| f.Inv(&tv4, &tv4) // 25. 1 / tv4 | ||
| f.Mul(&_px, &_px, &tv4) // 26. x = x / tv4 | ||
|
|
||
| return &_px, &_py | ||
| } |
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