Remove deprecated files and update README to reflect current implementation status and features. This commit deletes unused context, ecmult, and test files, streamlining the codebase. The README has been revised to include architectural details, performance benchmarks, and security considerations for the secp256k1 implementation.
This commit is contained in:
429
scalar.go
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429
scalar.go
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@@ -0,0 +1,429 @@
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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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