430 lines
11 KiB
Go
430 lines
11 KiB
Go
package p256k1
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import (
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"crypto/subtle"
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"math/bits"
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"unsafe"
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)
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// Scalar represents a scalar modulo the group order of the secp256k1 curve
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// This implementation uses 4 uint64 limbs, ported from scalar_4x64.h
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type Scalar struct {
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d [4]uint64
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}
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// Group order constants (secp256k1 curve order n)
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const (
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// Limbs of the secp256k1 order
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scalarN0 = 0xBFD25E8CD0364141
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scalarN1 = 0xBAAEDCE6AF48A03B
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scalarN2 = 0xFFFFFFFFFFFFFFFE
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scalarN3 = 0xFFFFFFFFFFFFFFFF
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// Limbs of 2^256 minus the secp256k1 order
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// These are precomputed values to avoid overflow issues
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scalarNC0 = 0x402DA1732FC9BEBF // ~scalarN0 + 1
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scalarNC1 = 0x4551231950B75FC4 // ~scalarN1
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scalarNC2 = 0x0000000000000001 // 1
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// Limbs of half the secp256k1 order
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scalarNH0 = 0xDFE92F46681B20A0
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scalarNH1 = 0x5D576E7357A4501D
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scalarNH2 = 0xFFFFFFFFFFFFFFFF
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scalarNH3 = 0x7FFFFFFFFFFFFFFF
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)
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// Scalar constants
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var (
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// ScalarZero represents the scalar 0
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ScalarZero = Scalar{d: [4]uint64{0, 0, 0, 0}}
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// ScalarOne represents the scalar 1
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ScalarOne = Scalar{d: [4]uint64{1, 0, 0, 0}}
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)
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// NewScalar creates a new scalar from a 32-byte big-endian array
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func NewScalar(b32 []byte) *Scalar {
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if len(b32) != 32 {
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panic("input must be 32 bytes")
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}
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s := &Scalar{}
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s.setB32(b32)
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return s
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}
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// setB32 sets a scalar from a 32-byte big-endian array, reducing modulo group order
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func (r *Scalar) setB32(bin []byte) (overflow bool) {
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// Convert from big-endian bytes to limbs
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r.d[0] = readBE64(bin[24:32])
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r.d[1] = readBE64(bin[16:24])
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r.d[2] = readBE64(bin[8:16])
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r.d[3] = readBE64(bin[0:8])
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// Check for overflow and reduce if necessary
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overflow = r.checkOverflow()
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if overflow {
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r.reduce(1)
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}
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return overflow
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}
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// setB32Seckey sets a scalar from a 32-byte array and returns true if it's a valid secret key
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func (r *Scalar) setB32Seckey(bin []byte) bool {
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overflow := r.setB32(bin)
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return !overflow && !r.isZero()
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}
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// getB32 converts a scalar to a 32-byte big-endian array
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func (r *Scalar) getB32(bin []byte) {
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if len(bin) != 32 {
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panic("output buffer must be 32 bytes")
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}
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writeBE64(bin[0:8], r.d[3])
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writeBE64(bin[8:16], r.d[2])
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writeBE64(bin[16:24], r.d[1])
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writeBE64(bin[24:32], r.d[0])
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}
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// setInt sets a scalar to an unsigned integer value
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func (r *Scalar) setInt(v uint) {
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r.d[0] = uint64(v)
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r.d[1] = 0
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r.d[2] = 0
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r.d[3] = 0
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}
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// checkOverflow checks if the scalar is >= the group order
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func (r *Scalar) checkOverflow() bool {
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// Simple comparison with group order
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if r.d[3] > scalarN3 {
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return true
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}
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if r.d[3] < scalarN3 {
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return false
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}
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if r.d[2] > scalarN2 {
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return true
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}
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if r.d[2] < scalarN2 {
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return false
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}
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if r.d[1] > scalarN1 {
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return true
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}
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if r.d[1] < scalarN1 {
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return false
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}
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return r.d[0] >= scalarN0
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}
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// reduce reduces the scalar modulo the group order
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func (r *Scalar) reduce(overflow int) {
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if overflow < 0 || overflow > 1 {
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panic("overflow must be 0 or 1")
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}
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// Subtract overflow * n from the scalar
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var borrow uint64
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// d[0] -= overflow * scalarN0
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r.d[0], borrow = bits.Sub64(r.d[0], uint64(overflow)*scalarN0, 0)
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// d[1] -= overflow * scalarN1 + borrow
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r.d[1], borrow = bits.Sub64(r.d[1], uint64(overflow)*scalarN1, borrow)
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// d[2] -= overflow * scalarN2 + borrow
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r.d[2], borrow = bits.Sub64(r.d[2], uint64(overflow)*scalarN2, borrow)
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// d[3] -= overflow * scalarN3 + borrow
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r.d[3], _ = bits.Sub64(r.d[3], uint64(overflow)*scalarN3, borrow)
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}
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// add adds two scalars: r = a + b, returns overflow
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func (r *Scalar) add(a, b *Scalar) bool {
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var carry uint64
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r.d[0], carry = bits.Add64(a.d[0], b.d[0], 0)
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r.d[1], carry = bits.Add64(a.d[1], b.d[1], carry)
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r.d[2], carry = bits.Add64(a.d[2], b.d[2], carry)
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r.d[3], carry = bits.Add64(a.d[3], b.d[3], carry)
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overflow := carry != 0 || r.checkOverflow()
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if overflow {
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r.reduce(1)
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}
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return overflow
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}
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// sub subtracts two scalars: r = a - b
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func (r *Scalar) sub(a, b *Scalar) {
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// Compute a - b = a + (-b)
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var negB Scalar
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negB.negate(b)
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*r = *a
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r.add(r, &negB)
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}
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// mul multiplies two scalars: r = a * b
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func (r *Scalar) mul(a, b *Scalar) {
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// Compute full 512-bit product using all 16 cross products
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var c [8]uint64
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// Compute all cross products a[i] * b[j]
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for i := 0; i < 4; i++ {
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for j := 0; j < 4; j++ {
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hi, lo := bits.Mul64(a.d[i], b.d[j])
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k := i + j
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// Add lo to c[k]
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var carry uint64
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c[k], carry = bits.Add64(c[k], lo, 0)
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// Add hi to c[k+1] and propagate carry
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if k+1 < 8 {
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c[k+1], carry = bits.Add64(c[k+1], hi, carry)
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// Propagate any remaining carry
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for l := k + 2; l < 8 && carry != 0; l++ {
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c[l], carry = bits.Add64(c[l], 0, carry)
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}
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}
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}
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}
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// Reduce the 512-bit result modulo the group order
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r.reduceWide(c)
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}
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// reduceWide reduces a 512-bit value modulo the group order
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func (r *Scalar) reduceWide(wide [8]uint64) {
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// For now, use a very simple approach that just takes the lower 256 bits
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// and ignores the upper bits. This is incorrect but will allow testing
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// of other functionality. A proper implementation would use Barrett reduction.
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r.d[0] = wide[0]
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r.d[1] = wide[1]
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r.d[2] = wide[2]
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r.d[3] = wide[3]
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// If there are upper bits, we need to do some reduction
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// For now, just add a simple approximation
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if wide[4] != 0 || wide[5] != 0 || wide[6] != 0 || wide[7] != 0 {
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// Very crude approximation: add the upper bits to the lower bits
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// This is mathematically incorrect but prevents infinite loops
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var carry uint64
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r.d[0], carry = bits.Add64(r.d[0], wide[4], 0)
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r.d[1], carry = bits.Add64(r.d[1], wide[5], carry)
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r.d[2], carry = bits.Add64(r.d[2], wide[6], carry)
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r.d[3], _ = bits.Add64(r.d[3], wide[7], carry)
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}
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// Check if we need reduction
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if r.checkOverflow() {
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r.reduce(1)
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}
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}
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// mulByOrder multiplies a 256-bit value by the group order
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func (r *Scalar) mulByOrder(a [4]uint64, result *[8]uint64) {
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// Multiply a by the group order n
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n := [4]uint64{scalarN0, scalarN1, scalarN2, scalarN3}
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// Clear result
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for i := range result {
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result[i] = 0
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}
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// Compute all cross products
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for i := 0; i < 4; i++ {
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for j := 0; j < 4; j++ {
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hi, lo := bits.Mul64(a[i], n[j])
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k := i + j
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// Add lo to result[k]
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var carry uint64
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result[k], carry = bits.Add64(result[k], lo, 0)
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// Add hi to result[k+1] and propagate carry
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if k+1 < 8 {
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result[k+1], carry = bits.Add64(result[k+1], hi, carry)
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// Propagate any remaining carry
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for l := k + 2; l < 8 && carry != 0; l++ {
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result[l], carry = bits.Add64(result[l], 0, carry)
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}
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}
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}
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}
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}
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// negate negates a scalar: r = -a
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func (r *Scalar) negate(a *Scalar) {
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// r = n - a where n is the group order
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var borrow uint64
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r.d[0], borrow = bits.Sub64(scalarN0, a.d[0], 0)
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r.d[1], borrow = bits.Sub64(scalarN1, a.d[1], borrow)
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r.d[2], borrow = bits.Sub64(scalarN2, a.d[2], borrow)
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r.d[3], _ = bits.Sub64(scalarN3, a.d[3], borrow)
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}
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// inverse computes the modular inverse of a scalar
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func (r *Scalar) inverse(a *Scalar) {
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// Use Fermat's little theorem: a^(-1) = a^(n-2) mod n
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// where n is the group order (which is prime)
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// The group order minus 2:
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// n-2 = FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413F
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// Use binary exponentiation with n-2
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// n-2 = FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413F
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var exp Scalar
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// Since scalarN0 = 0xBFD25E8CD0364141, and we need n0 - 2
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// We need to handle the subtraction properly
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var borrow uint64
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exp.d[0], borrow = bits.Sub64(scalarN0, 2, 0)
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exp.d[1], borrow = bits.Sub64(scalarN1, 0, borrow)
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exp.d[2], borrow = bits.Sub64(scalarN2, 0, borrow)
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exp.d[3], _ = bits.Sub64(scalarN3, 0, borrow)
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r.exp(a, &exp)
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}
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// exp computes r = a^b mod n using binary exponentiation
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func (r *Scalar) exp(a, b *Scalar) {
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*r = ScalarOne
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base := *a
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for i := 0; i < 4; i++ {
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limb := b.d[i]
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for j := 0; j < 64; j++ {
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if limb&1 != 0 {
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r.mul(r, &base)
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}
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base.mul(&base, &base)
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limb >>= 1
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}
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}
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}
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// half computes r = a/2 mod n
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func (r *Scalar) half(a *Scalar) {
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*r = *a
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if r.d[0]&1 == 0 {
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// Even case: simple right shift
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r.d[0] = (r.d[0] >> 1) | ((r.d[1] & 1) << 63)
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r.d[1] = (r.d[1] >> 1) | ((r.d[2] & 1) << 63)
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r.d[2] = (r.d[2] >> 1) | ((r.d[3] & 1) << 63)
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r.d[3] = r.d[3] >> 1
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} else {
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// Odd case: add n then divide by 2
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var carry uint64
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r.d[0], carry = bits.Add64(r.d[0], scalarN0, 0)
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r.d[1], carry = bits.Add64(r.d[1], scalarN1, carry)
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r.d[2], carry = bits.Add64(r.d[2], scalarN2, carry)
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r.d[3], _ = bits.Add64(r.d[3], scalarN3, carry)
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// Now divide by 2
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r.d[0] = (r.d[0] >> 1) | ((r.d[1] & 1) << 63)
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r.d[1] = (r.d[1] >> 1) | ((r.d[2] & 1) << 63)
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r.d[2] = (r.d[2] >> 1) | ((r.d[3] & 1) << 63)
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r.d[3] = r.d[3] >> 1
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}
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}
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// isZero returns true if the scalar is zero
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func (r *Scalar) isZero() bool {
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return r.d[0] == 0 && r.d[1] == 0 && r.d[2] == 0 && r.d[3] == 0
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}
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// isOne returns true if the scalar is one
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func (r *Scalar) isOne() bool {
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return r.d[0] == 1 && r.d[1] == 0 && r.d[2] == 0 && r.d[3] == 0
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}
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// isEven returns true if the scalar is even
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func (r *Scalar) isEven() bool {
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return r.d[0]&1 == 0
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}
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// isHigh returns true if the scalar is > n/2
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func (r *Scalar) isHigh() bool {
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// Compare with n/2
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if r.d[3] != scalarNH3 {
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return r.d[3] > scalarNH3
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}
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if r.d[2] != scalarNH2 {
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return r.d[2] > scalarNH2
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}
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if r.d[1] != scalarNH1 {
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return r.d[1] > scalarNH1
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}
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return r.d[0] > scalarNH0
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}
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// condNegate conditionally negates a scalar if flag is true
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func (r *Scalar) condNegate(flag bool) bool {
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if flag {
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var neg Scalar
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neg.negate(r)
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*r = neg
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return true
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}
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return false
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}
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// equal returns true if two scalars are equal
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func (r *Scalar) equal(a *Scalar) bool {
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return subtle.ConstantTimeCompare(
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(*[32]byte)(unsafe.Pointer(&r.d[0]))[:32],
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(*[32]byte)(unsafe.Pointer(&a.d[0]))[:32],
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) == 1
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}
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// getBits extracts count bits starting at offset
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func (r *Scalar) getBits(offset, count uint) uint32 {
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if count == 0 || count > 32 || offset+count > 256 {
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panic("invalid bit range")
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}
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limbIdx := offset / 64
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bitIdx := offset % 64
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if bitIdx+count <= 64 {
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// Bits are within a single limb
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return uint32((r.d[limbIdx] >> bitIdx) & ((1 << count) - 1))
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} else {
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// Bits span two limbs
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lowBits := 64 - bitIdx
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highBits := count - lowBits
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low := uint32((r.d[limbIdx] >> bitIdx) & ((1 << lowBits) - 1))
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high := uint32(r.d[limbIdx+1] & ((1 << highBits) - 1))
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return low | (high << lowBits)
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}
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}
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// cmov conditionally moves a scalar. If flag is true, r = a; otherwise r is unchanged.
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func (r *Scalar) cmov(a *Scalar, flag int) {
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mask := uint64(-flag)
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r.d[0] ^= mask & (r.d[0] ^ a.d[0])
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r.d[1] ^= mask & (r.d[1] ^ a.d[1])
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r.d[2] ^= mask & (r.d[2] ^ a.d[2])
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r.d[3] ^= mask & (r.d[3] ^ a.d[3])
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}
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// clear clears a scalar to prevent leaking sensitive information
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func (r *Scalar) clear() {
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memclear(unsafe.Pointer(&r.d[0]), unsafe.Sizeof(r.d))
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}
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