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-rw-r--r--src/crypto/ed25519/internal/edwards25519/scalar.go1025
1 files changed, 1025 insertions, 0 deletions
diff --git a/src/crypto/ed25519/internal/edwards25519/scalar.go b/src/crypto/ed25519/internal/edwards25519/scalar.go
new file mode 100644
index 0000000..889acaa
--- /dev/null
+++ b/src/crypto/ed25519/internal/edwards25519/scalar.go
@@ -0,0 +1,1025 @@
+// Copyright (c) 2016 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 edwards25519
+
+import (
+ "crypto/subtle"
+ "encoding/binary"
+ "errors"
+)
+
+// A Scalar is an integer modulo
+//
+// l = 2^252 + 27742317777372353535851937790883648493
+//
+// which is the prime order of the edwards25519 group.
+//
+// This type works similarly to math/big.Int, and all arguments and
+// receivers are allowed to alias.
+//
+// The zero value is a valid zero element.
+type Scalar struct {
+ // s is the Scalar value in little-endian. The value is always reduced
+ // between operations.
+ s [32]byte
+}
+
+var (
+ scZero = Scalar{[32]byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
+
+ scOne = Scalar{[32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
+
+ scMinusOne = Scalar{[32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}}
+)
+
+// NewScalar returns a new zero Scalar.
+func NewScalar() *Scalar {
+ return &Scalar{}
+}
+
+// MultiplyAdd sets s = x * y + z mod l, and returns s.
+func (s *Scalar) MultiplyAdd(x, y, z *Scalar) *Scalar {
+ scMulAdd(&s.s, &x.s, &y.s, &z.s)
+ return s
+}
+
+// Add sets s = x + y mod l, and returns s.
+func (s *Scalar) Add(x, y *Scalar) *Scalar {
+ // s = 1 * x + y mod l
+ scMulAdd(&s.s, &scOne.s, &x.s, &y.s)
+ return s
+}
+
+// Subtract sets s = x - y mod l, and returns s.
+func (s *Scalar) Subtract(x, y *Scalar) *Scalar {
+ // s = -1 * y + x mod l
+ scMulAdd(&s.s, &scMinusOne.s, &y.s, &x.s)
+ return s
+}
+
+// Negate sets s = -x mod l, and returns s.
+func (s *Scalar) Negate(x *Scalar) *Scalar {
+ // s = -1 * x + 0 mod l
+ scMulAdd(&s.s, &scMinusOne.s, &x.s, &scZero.s)
+ return s
+}
+
+// Multiply sets s = x * y mod l, and returns s.
+func (s *Scalar) Multiply(x, y *Scalar) *Scalar {
+ // s = x * y + 0 mod l
+ scMulAdd(&s.s, &x.s, &y.s, &scZero.s)
+ return s
+}
+
+// Set sets s = x, and returns s.
+func (s *Scalar) Set(x *Scalar) *Scalar {
+ *s = *x
+ return s
+}
+
+// SetUniformBytes sets s to an uniformly distributed value given 64 uniformly
+// distributed random bytes.
+func (s *Scalar) SetUniformBytes(x []byte) *Scalar {
+ if len(x) != 64 {
+ panic("edwards25519: invalid SetUniformBytes input length")
+ }
+ var wideBytes [64]byte
+ copy(wideBytes[:], x[:])
+ scReduce(&s.s, &wideBytes)
+ return s
+}
+
+// SetCanonicalBytes sets s = x, where x is a 32-byte little-endian encoding of
+// s, and returns s. If x is not a canonical encoding of s, SetCanonicalBytes
+// returns nil and an error, and the receiver is unchanged.
+func (s *Scalar) SetCanonicalBytes(x []byte) (*Scalar, error) {
+ if len(x) != 32 {
+ return nil, errors.New("invalid scalar length")
+ }
+ ss := &Scalar{}
+ copy(ss.s[:], x)
+ if !isReduced(ss) {
+ return nil, errors.New("invalid scalar encoding")
+ }
+ s.s = ss.s
+ return s, nil
+}
+
+// isReduced returns whether the given scalar is reduced modulo l.
+func isReduced(s *Scalar) bool {
+ for i := len(s.s) - 1; i >= 0; i-- {
+ switch {
+ case s.s[i] > scMinusOne.s[i]:
+ return false
+ case s.s[i] < scMinusOne.s[i]:
+ return true
+ }
+ }
+ return true
+}
+
+// SetBytesWithClamping applies the buffer pruning described in RFC 8032,
+// Section 5.1.5 (also known as clamping) and sets s to the result. The input
+// must be 32 bytes, and it is not modified.
+//
+// Note that since Scalar values are always reduced modulo the prime order of
+// the curve, the resulting value will not preserve any of the cofactor-clearing
+// properties that clamping is meant to provide. It will however work as
+// expected as long as it is applied to points on the prime order subgroup, like
+// in Ed25519. In fact, it is lost to history why RFC 8032 adopted the
+// irrelevant RFC 7748 clamping, but it is now required for compatibility.
+func (s *Scalar) SetBytesWithClamping(x []byte) *Scalar {
+ // The description above omits the purpose of the high bits of the clamping
+ // for brevity, but those are also lost to reductions, and are also
+ // irrelevant to edwards25519 as they protect against a specific
+ // implementation bug that was once observed in a generic Montgomery ladder.
+ if len(x) != 32 {
+ panic("edwards25519: invalid SetBytesWithClamping input length")
+ }
+ var wideBytes [64]byte
+ copy(wideBytes[:], x[:])
+ wideBytes[0] &= 248
+ wideBytes[31] &= 63
+ wideBytes[31] |= 64
+ scReduce(&s.s, &wideBytes)
+ return s
+}
+
+// Bytes returns the canonical 32-byte little-endian encoding of s.
+func (s *Scalar) Bytes() []byte {
+ buf := make([]byte, 32)
+ copy(buf, s.s[:])
+ return buf
+}
+
+// Equal returns 1 if s and t are equal, and 0 otherwise.
+func (s *Scalar) Equal(t *Scalar) int {
+ return subtle.ConstantTimeCompare(s.s[:], t.s[:])
+}
+
+// scMulAdd and scReduce are ported from the public domain, “ref10”
+// implementation of ed25519 from SUPERCOP.
+
+func load3(in []byte) int64 {
+ r := int64(in[0])
+ r |= int64(in[1]) << 8
+ r |= int64(in[2]) << 16
+ return r
+}
+
+func load4(in []byte) int64 {
+ r := int64(in[0])
+ r |= int64(in[1]) << 8
+ r |= int64(in[2]) << 16
+ r |= int64(in[3]) << 24
+ return r
+}
+
+// Input:
+// a[0]+256*a[1]+...+256^31*a[31] = a
+// b[0]+256*b[1]+...+256^31*b[31] = b
+// c[0]+256*c[1]+...+256^31*c[31] = c
+//
+// Output:
+// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+// where l = 2^252 + 27742317777372353535851937790883648493.
+func scMulAdd(s, a, b, c *[32]byte) {
+ a0 := 2097151 & load3(a[:])
+ a1 := 2097151 & (load4(a[2:]) >> 5)
+ a2 := 2097151 & (load3(a[5:]) >> 2)
+ a3 := 2097151 & (load4(a[7:]) >> 7)
+ a4 := 2097151 & (load4(a[10:]) >> 4)
+ a5 := 2097151 & (load3(a[13:]) >> 1)
+ a6 := 2097151 & (load4(a[15:]) >> 6)
+ a7 := 2097151 & (load3(a[18:]) >> 3)
+ a8 := 2097151 & load3(a[21:])
+ a9 := 2097151 & (load4(a[23:]) >> 5)
+ a10 := 2097151 & (load3(a[26:]) >> 2)
+ a11 := (load4(a[28:]) >> 7)
+ b0 := 2097151 & load3(b[:])
+ b1 := 2097151 & (load4(b[2:]) >> 5)
+ b2 := 2097151 & (load3(b[5:]) >> 2)
+ b3 := 2097151 & (load4(b[7:]) >> 7)
+ b4 := 2097151 & (load4(b[10:]) >> 4)
+ b5 := 2097151 & (load3(b[13:]) >> 1)
+ b6 := 2097151 & (load4(b[15:]) >> 6)
+ b7 := 2097151 & (load3(b[18:]) >> 3)
+ b8 := 2097151 & load3(b[21:])
+ b9 := 2097151 & (load4(b[23:]) >> 5)
+ b10 := 2097151 & (load3(b[26:]) >> 2)
+ b11 := (load4(b[28:]) >> 7)
+ c0 := 2097151 & load3(c[:])
+ c1 := 2097151 & (load4(c[2:]) >> 5)
+ c2 := 2097151 & (load3(c[5:]) >> 2)
+ c3 := 2097151 & (load4(c[7:]) >> 7)
+ c4 := 2097151 & (load4(c[10:]) >> 4)
+ c5 := 2097151 & (load3(c[13:]) >> 1)
+ c6 := 2097151 & (load4(c[15:]) >> 6)
+ c7 := 2097151 & (load3(c[18:]) >> 3)
+ c8 := 2097151 & load3(c[21:])
+ c9 := 2097151 & (load4(c[23:]) >> 5)
+ c10 := 2097151 & (load3(c[26:]) >> 2)
+ c11 := (load4(c[28:]) >> 7)
+ var carry [23]int64
+
+ s0 := c0 + a0*b0
+ s1 := c1 + a0*b1 + a1*b0
+ s2 := c2 + a0*b2 + a1*b1 + a2*b0
+ s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0
+ s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0
+ s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0
+ s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0
+ s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0
+ s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0
+ s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0
+ s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0
+ s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0
+ s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1
+ s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2
+ s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3
+ s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4
+ s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5
+ s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6
+ s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7
+ s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8
+ s20 := a9*b11 + a10*b10 + a11*b9
+ s21 := a10*b11 + a11*b10
+ s22 := a11 * b11
+ s23 := int64(0)
+
+ carry[0] = (s0 + (1 << 20)) >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[2] = (s2 + (1 << 20)) >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[4] = (s4 + (1 << 20)) >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[6] = (s6 + (1 << 20)) >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[8] = (s8 + (1 << 20)) >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[10] = (s10 + (1 << 20)) >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+ carry[12] = (s12 + (1 << 20)) >> 21
+ s13 += carry[12]
+ s12 -= carry[12] << 21
+ carry[14] = (s14 + (1 << 20)) >> 21
+ s15 += carry[14]
+ s14 -= carry[14] << 21
+ carry[16] = (s16 + (1 << 20)) >> 21
+ s17 += carry[16]
+ s16 -= carry[16] << 21
+ carry[18] = (s18 + (1 << 20)) >> 21
+ s19 += carry[18]
+ s18 -= carry[18] << 21
+ carry[20] = (s20 + (1 << 20)) >> 21
+ s21 += carry[20]
+ s20 -= carry[20] << 21
+ carry[22] = (s22 + (1 << 20)) >> 21
+ s23 += carry[22]
+ s22 -= carry[22] << 21
+
+ carry[1] = (s1 + (1 << 20)) >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[3] = (s3 + (1 << 20)) >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[5] = (s5 + (1 << 20)) >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[7] = (s7 + (1 << 20)) >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[9] = (s9 + (1 << 20)) >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[11] = (s11 + (1 << 20)) >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+ carry[13] = (s13 + (1 << 20)) >> 21
+ s14 += carry[13]
+ s13 -= carry[13] << 21
+ carry[15] = (s15 + (1 << 20)) >> 21
+ s16 += carry[15]
+ s15 -= carry[15] << 21
+ carry[17] = (s17 + (1 << 20)) >> 21
+ s18 += carry[17]
+ s17 -= carry[17] << 21
+ carry[19] = (s19 + (1 << 20)) >> 21
+ s20 += carry[19]
+ s19 -= carry[19] << 21
+ carry[21] = (s21 + (1 << 20)) >> 21
+ s22 += carry[21]
+ s21 -= carry[21] << 21
+
+ s11 += s23 * 666643
+ s12 += s23 * 470296
+ s13 += s23 * 654183
+ s14 -= s23 * 997805
+ s15 += s23 * 136657
+ s16 -= s23 * 683901
+ s23 = 0
+
+ s10 += s22 * 666643
+ s11 += s22 * 470296
+ s12 += s22 * 654183
+ s13 -= s22 * 997805
+ s14 += s22 * 136657
+ s15 -= s22 * 683901
+ s22 = 0
+
+ s9 += s21 * 666643
+ s10 += s21 * 470296
+ s11 += s21 * 654183
+ s12 -= s21 * 997805
+ s13 += s21 * 136657
+ s14 -= s21 * 683901
+ s21 = 0
+
+ s8 += s20 * 666643
+ s9 += s20 * 470296
+ s10 += s20 * 654183
+ s11 -= s20 * 997805
+ s12 += s20 * 136657
+ s13 -= s20 * 683901
+ s20 = 0
+
+ s7 += s19 * 666643
+ s8 += s19 * 470296
+ s9 += s19 * 654183
+ s10 -= s19 * 997805
+ s11 += s19 * 136657
+ s12 -= s19 * 683901
+ s19 = 0
+
+ s6 += s18 * 666643
+ s7 += s18 * 470296
+ s8 += s18 * 654183
+ s9 -= s18 * 997805
+ s10 += s18 * 136657
+ s11 -= s18 * 683901
+ s18 = 0
+
+ carry[6] = (s6 + (1 << 20)) >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[8] = (s8 + (1 << 20)) >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[10] = (s10 + (1 << 20)) >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+ carry[12] = (s12 + (1 << 20)) >> 21
+ s13 += carry[12]
+ s12 -= carry[12] << 21
+ carry[14] = (s14 + (1 << 20)) >> 21
+ s15 += carry[14]
+ s14 -= carry[14] << 21
+ carry[16] = (s16 + (1 << 20)) >> 21
+ s17 += carry[16]
+ s16 -= carry[16] << 21
+
+ carry[7] = (s7 + (1 << 20)) >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[9] = (s9 + (1 << 20)) >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[11] = (s11 + (1 << 20)) >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+ carry[13] = (s13 + (1 << 20)) >> 21
+ s14 += carry[13]
+ s13 -= carry[13] << 21
+ carry[15] = (s15 + (1 << 20)) >> 21
+ s16 += carry[15]
+ s15 -= carry[15] << 21
+
+ s5 += s17 * 666643
+ s6 += s17 * 470296
+ s7 += s17 * 654183
+ s8 -= s17 * 997805
+ s9 += s17 * 136657
+ s10 -= s17 * 683901
+ s17 = 0
+
+ s4 += s16 * 666643
+ s5 += s16 * 470296
+ s6 += s16 * 654183
+ s7 -= s16 * 997805
+ s8 += s16 * 136657
+ s9 -= s16 * 683901
+ s16 = 0
+
+ s3 += s15 * 666643
+ s4 += s15 * 470296
+ s5 += s15 * 654183
+ s6 -= s15 * 997805
+ s7 += s15 * 136657
+ s8 -= s15 * 683901
+ s15 = 0
+
+ s2 += s14 * 666643
+ s3 += s14 * 470296
+ s4 += s14 * 654183
+ s5 -= s14 * 997805
+ s6 += s14 * 136657
+ s7 -= s14 * 683901
+ s14 = 0
+
+ s1 += s13 * 666643
+ s2 += s13 * 470296
+ s3 += s13 * 654183
+ s4 -= s13 * 997805
+ s5 += s13 * 136657
+ s6 -= s13 * 683901
+ s13 = 0
+
+ s0 += s12 * 666643
+ s1 += s12 * 470296
+ s2 += s12 * 654183
+ s3 -= s12 * 997805
+ s4 += s12 * 136657
+ s5 -= s12 * 683901
+ s12 = 0
+
+ carry[0] = (s0 + (1 << 20)) >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[2] = (s2 + (1 << 20)) >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[4] = (s4 + (1 << 20)) >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[6] = (s6 + (1 << 20)) >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[8] = (s8 + (1 << 20)) >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[10] = (s10 + (1 << 20)) >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+
+ carry[1] = (s1 + (1 << 20)) >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[3] = (s3 + (1 << 20)) >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[5] = (s5 + (1 << 20)) >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[7] = (s7 + (1 << 20)) >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[9] = (s9 + (1 << 20)) >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[11] = (s11 + (1 << 20)) >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+
+ s0 += s12 * 666643
+ s1 += s12 * 470296
+ s2 += s12 * 654183
+ s3 -= s12 * 997805
+ s4 += s12 * 136657
+ s5 -= s12 * 683901
+ s12 = 0
+
+ carry[0] = s0 >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[1] = s1 >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[2] = s2 >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[3] = s3 >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[4] = s4 >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[5] = s5 >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[6] = s6 >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[7] = s7 >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[8] = s8 >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[9] = s9 >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[10] = s10 >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+ carry[11] = s11 >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+
+ s0 += s12 * 666643
+ s1 += s12 * 470296
+ s2 += s12 * 654183
+ s3 -= s12 * 997805
+ s4 += s12 * 136657
+ s5 -= s12 * 683901
+ s12 = 0
+
+ carry[0] = s0 >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[1] = s1 >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[2] = s2 >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[3] = s3 >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[4] = s4 >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[5] = s5 >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[6] = s6 >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[7] = s7 >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[8] = s8 >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[9] = s9 >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[10] = s10 >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+
+ s[0] = byte(s0 >> 0)
+ s[1] = byte(s0 >> 8)
+ s[2] = byte((s0 >> 16) | (s1 << 5))
+ s[3] = byte(s1 >> 3)
+ s[4] = byte(s1 >> 11)
+ s[5] = byte((s1 >> 19) | (s2 << 2))
+ s[6] = byte(s2 >> 6)
+ s[7] = byte((s2 >> 14) | (s3 << 7))
+ s[8] = byte(s3 >> 1)
+ s[9] = byte(s3 >> 9)
+ s[10] = byte((s3 >> 17) | (s4 << 4))
+ s[11] = byte(s4 >> 4)
+ s[12] = byte(s4 >> 12)
+ s[13] = byte((s4 >> 20) | (s5 << 1))
+ s[14] = byte(s5 >> 7)
+ s[15] = byte((s5 >> 15) | (s6 << 6))
+ s[16] = byte(s6 >> 2)
+ s[17] = byte(s6 >> 10)
+ s[18] = byte((s6 >> 18) | (s7 << 3))
+ s[19] = byte(s7 >> 5)
+ s[20] = byte(s7 >> 13)
+ s[21] = byte(s8 >> 0)
+ s[22] = byte(s8 >> 8)
+ s[23] = byte((s8 >> 16) | (s9 << 5))
+ s[24] = byte(s9 >> 3)
+ s[25] = byte(s9 >> 11)
+ s[26] = byte((s9 >> 19) | (s10 << 2))
+ s[27] = byte(s10 >> 6)
+ s[28] = byte((s10 >> 14) | (s11 << 7))
+ s[29] = byte(s11 >> 1)
+ s[30] = byte(s11 >> 9)
+ s[31] = byte(s11 >> 17)
+}
+
+// Input:
+// s[0]+256*s[1]+...+256^63*s[63] = s
+//
+// Output:
+// s[0]+256*s[1]+...+256^31*s[31] = s mod l
+// where l = 2^252 + 27742317777372353535851937790883648493.
+func scReduce(out *[32]byte, s *[64]byte) {
+ s0 := 2097151 & load3(s[:])
+ s1 := 2097151 & (load4(s[2:]) >> 5)
+ s2 := 2097151 & (load3(s[5:]) >> 2)
+ s3 := 2097151 & (load4(s[7:]) >> 7)
+ s4 := 2097151 & (load4(s[10:]) >> 4)
+ s5 := 2097151 & (load3(s[13:]) >> 1)
+ s6 := 2097151 & (load4(s[15:]) >> 6)
+ s7 := 2097151 & (load3(s[18:]) >> 3)
+ s8 := 2097151 & load3(s[21:])
+ s9 := 2097151 & (load4(s[23:]) >> 5)
+ s10 := 2097151 & (load3(s[26:]) >> 2)
+ s11 := 2097151 & (load4(s[28:]) >> 7)
+ s12 := 2097151 & (load4(s[31:]) >> 4)
+ s13 := 2097151 & (load3(s[34:]) >> 1)
+ s14 := 2097151 & (load4(s[36:]) >> 6)
+ s15 := 2097151 & (load3(s[39:]) >> 3)
+ s16 := 2097151 & load3(s[42:])
+ s17 := 2097151 & (load4(s[44:]) >> 5)
+ s18 := 2097151 & (load3(s[47:]) >> 2)
+ s19 := 2097151 & (load4(s[49:]) >> 7)
+ s20 := 2097151 & (load4(s[52:]) >> 4)
+ s21 := 2097151 & (load3(s[55:]) >> 1)
+ s22 := 2097151 & (load4(s[57:]) >> 6)
+ s23 := (load4(s[60:]) >> 3)
+
+ s11 += s23 * 666643
+ s12 += s23 * 470296
+ s13 += s23 * 654183
+ s14 -= s23 * 997805
+ s15 += s23 * 136657
+ s16 -= s23 * 683901
+ s23 = 0
+
+ s10 += s22 * 666643
+ s11 += s22 * 470296
+ s12 += s22 * 654183
+ s13 -= s22 * 997805
+ s14 += s22 * 136657
+ s15 -= s22 * 683901
+ s22 = 0
+
+ s9 += s21 * 666643
+ s10 += s21 * 470296
+ s11 += s21 * 654183
+ s12 -= s21 * 997805
+ s13 += s21 * 136657
+ s14 -= s21 * 683901
+ s21 = 0
+
+ s8 += s20 * 666643
+ s9 += s20 * 470296
+ s10 += s20 * 654183
+ s11 -= s20 * 997805
+ s12 += s20 * 136657
+ s13 -= s20 * 683901
+ s20 = 0
+
+ s7 += s19 * 666643
+ s8 += s19 * 470296
+ s9 += s19 * 654183
+ s10 -= s19 * 997805
+ s11 += s19 * 136657
+ s12 -= s19 * 683901
+ s19 = 0
+
+ s6 += s18 * 666643
+ s7 += s18 * 470296
+ s8 += s18 * 654183
+ s9 -= s18 * 997805
+ s10 += s18 * 136657
+ s11 -= s18 * 683901
+ s18 = 0
+
+ var carry [17]int64
+
+ carry[6] = (s6 + (1 << 20)) >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[8] = (s8 + (1 << 20)) >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[10] = (s10 + (1 << 20)) >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+ carry[12] = (s12 + (1 << 20)) >> 21
+ s13 += carry[12]
+ s12 -= carry[12] << 21
+ carry[14] = (s14 + (1 << 20)) >> 21
+ s15 += carry[14]
+ s14 -= carry[14] << 21
+ carry[16] = (s16 + (1 << 20)) >> 21
+ s17 += carry[16]
+ s16 -= carry[16] << 21
+
+ carry[7] = (s7 + (1 << 20)) >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[9] = (s9 + (1 << 20)) >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[11] = (s11 + (1 << 20)) >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+ carry[13] = (s13 + (1 << 20)) >> 21
+ s14 += carry[13]
+ s13 -= carry[13] << 21
+ carry[15] = (s15 + (1 << 20)) >> 21
+ s16 += carry[15]
+ s15 -= carry[15] << 21
+
+ s5 += s17 * 666643
+ s6 += s17 * 470296
+ s7 += s17 * 654183
+ s8 -= s17 * 997805
+ s9 += s17 * 136657
+ s10 -= s17 * 683901
+ s17 = 0
+
+ s4 += s16 * 666643
+ s5 += s16 * 470296
+ s6 += s16 * 654183
+ s7 -= s16 * 997805
+ s8 += s16 * 136657
+ s9 -= s16 * 683901
+ s16 = 0
+
+ s3 += s15 * 666643
+ s4 += s15 * 470296
+ s5 += s15 * 654183
+ s6 -= s15 * 997805
+ s7 += s15 * 136657
+ s8 -= s15 * 683901
+ s15 = 0
+
+ s2 += s14 * 666643
+ s3 += s14 * 470296
+ s4 += s14 * 654183
+ s5 -= s14 * 997805
+ s6 += s14 * 136657
+ s7 -= s14 * 683901
+ s14 = 0
+
+ s1 += s13 * 666643
+ s2 += s13 * 470296
+ s3 += s13 * 654183
+ s4 -= s13 * 997805
+ s5 += s13 * 136657
+ s6 -= s13 * 683901
+ s13 = 0
+
+ s0 += s12 * 666643
+ s1 += s12 * 470296
+ s2 += s12 * 654183
+ s3 -= s12 * 997805
+ s4 += s12 * 136657
+ s5 -= s12 * 683901
+ s12 = 0
+
+ carry[0] = (s0 + (1 << 20)) >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[2] = (s2 + (1 << 20)) >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[4] = (s4 + (1 << 20)) >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[6] = (s6 + (1 << 20)) >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[8] = (s8 + (1 << 20)) >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[10] = (s10 + (1 << 20)) >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+
+ carry[1] = (s1 + (1 << 20)) >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[3] = (s3 + (1 << 20)) >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[5] = (s5 + (1 << 20)) >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[7] = (s7 + (1 << 20)) >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[9] = (s9 + (1 << 20)) >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[11] = (s11 + (1 << 20)) >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+
+ s0 += s12 * 666643
+ s1 += s12 * 470296
+ s2 += s12 * 654183
+ s3 -= s12 * 997805
+ s4 += s12 * 136657
+ s5 -= s12 * 683901
+ s12 = 0
+
+ carry[0] = s0 >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[1] = s1 >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[2] = s2 >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[3] = s3 >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[4] = s4 >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[5] = s5 >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[6] = s6 >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[7] = s7 >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[8] = s8 >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[9] = s9 >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[10] = s10 >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+ carry[11] = s11 >> 21
+ s12 += carry[11]
+ s11 -= carry[11] << 21
+
+ s0 += s12 * 666643
+ s1 += s12 * 470296
+ s2 += s12 * 654183
+ s3 -= s12 * 997805
+ s4 += s12 * 136657
+ s5 -= s12 * 683901
+ s12 = 0
+
+ carry[0] = s0 >> 21
+ s1 += carry[0]
+ s0 -= carry[0] << 21
+ carry[1] = s1 >> 21
+ s2 += carry[1]
+ s1 -= carry[1] << 21
+ carry[2] = s2 >> 21
+ s3 += carry[2]
+ s2 -= carry[2] << 21
+ carry[3] = s3 >> 21
+ s4 += carry[3]
+ s3 -= carry[3] << 21
+ carry[4] = s4 >> 21
+ s5 += carry[4]
+ s4 -= carry[4] << 21
+ carry[5] = s5 >> 21
+ s6 += carry[5]
+ s5 -= carry[5] << 21
+ carry[6] = s6 >> 21
+ s7 += carry[6]
+ s6 -= carry[6] << 21
+ carry[7] = s7 >> 21
+ s8 += carry[7]
+ s7 -= carry[7] << 21
+ carry[8] = s8 >> 21
+ s9 += carry[8]
+ s8 -= carry[8] << 21
+ carry[9] = s9 >> 21
+ s10 += carry[9]
+ s9 -= carry[9] << 21
+ carry[10] = s10 >> 21
+ s11 += carry[10]
+ s10 -= carry[10] << 21
+
+ out[0] = byte(s0 >> 0)
+ out[1] = byte(s0 >> 8)
+ out[2] = byte((s0 >> 16) | (s1 << 5))
+ out[3] = byte(s1 >> 3)
+ out[4] = byte(s1 >> 11)
+ out[5] = byte((s1 >> 19) | (s2 << 2))
+ out[6] = byte(s2 >> 6)
+ out[7] = byte((s2 >> 14) | (s3 << 7))
+ out[8] = byte(s3 >> 1)
+ out[9] = byte(s3 >> 9)
+ out[10] = byte((s3 >> 17) | (s4 << 4))
+ out[11] = byte(s4 >> 4)
+ out[12] = byte(s4 >> 12)
+ out[13] = byte((s4 >> 20) | (s5 << 1))
+ out[14] = byte(s5 >> 7)
+ out[15] = byte((s5 >> 15) | (s6 << 6))
+ out[16] = byte(s6 >> 2)
+ out[17] = byte(s6 >> 10)
+ out[18] = byte((s6 >> 18) | (s7 << 3))
+ out[19] = byte(s7 >> 5)
+ out[20] = byte(s7 >> 13)
+ out[21] = byte(s8 >> 0)
+ out[22] = byte(s8 >> 8)
+ out[23] = byte((s8 >> 16) | (s9 << 5))
+ out[24] = byte(s9 >> 3)
+ out[25] = byte(s9 >> 11)
+ out[26] = byte((s9 >> 19) | (s10 << 2))
+ out[27] = byte(s10 >> 6)
+ out[28] = byte((s10 >> 14) | (s11 << 7))
+ out[29] = byte(s11 >> 1)
+ out[30] = byte(s11 >> 9)
+ out[31] = byte(s11 >> 17)
+}
+
+// nonAdjacentForm computes a width-w non-adjacent form for this scalar.
+//
+// w must be between 2 and 8, or nonAdjacentForm will panic.
+func (s *Scalar) nonAdjacentForm(w uint) [256]int8 {
+ // This implementation is adapted from the one
+ // in curve25519-dalek and is documented there:
+ // https://github.com/dalek-cryptography/curve25519-dalek/blob/f630041af28e9a405255f98a8a93adca18e4315b/src/scalar.rs#L800-L871
+ if s.s[31] > 127 {
+ panic("scalar has high bit set illegally")
+ }
+ if w < 2 {
+ panic("w must be at least 2 by the definition of NAF")
+ } else if w > 8 {
+ panic("NAF digits must fit in int8")
+ }
+
+ var naf [256]int8
+ var digits [5]uint64
+
+ for i := 0; i < 4; i++ {
+ digits[i] = binary.LittleEndian.Uint64(s.s[i*8:])
+ }
+
+ width := uint64(1 << w)
+ windowMask := uint64(width - 1)
+
+ pos := uint(0)
+ carry := uint64(0)
+ for pos < 256 {
+ indexU64 := pos / 64
+ indexBit := pos % 64
+ var bitBuf uint64
+ if indexBit < 64-w {
+ // This window's bits are contained in a single u64
+ bitBuf = digits[indexU64] >> indexBit
+ } else {
+ // Combine the current 64 bits with bits from the next 64
+ bitBuf = (digits[indexU64] >> indexBit) | (digits[1+indexU64] << (64 - indexBit))
+ }
+
+ // Add carry into the current window
+ window := carry + (bitBuf & windowMask)
+
+ if window&1 == 0 {
+ // If the window value is even, preserve the carry and continue.
+ // Why is the carry preserved?
+ // If carry == 0 and window & 1 == 0,
+ // then the next carry should be 0
+ // If carry == 1 and window & 1 == 0,
+ // then bit_buf & 1 == 1 so the next carry should be 1
+ pos += 1
+ continue
+ }
+
+ if window < width/2 {
+ carry = 0
+ naf[pos] = int8(window)
+ } else {
+ carry = 1
+ naf[pos] = int8(window) - int8(width)
+ }
+
+ pos += w
+ }
+ return naf
+}
+
+func (s *Scalar) signedRadix16() [64]int8 {
+ if s.s[31] > 127 {
+ panic("scalar has high bit set illegally")
+ }
+
+ var digits [64]int8
+
+ // Compute unsigned radix-16 digits:
+ for i := 0; i < 32; i++ {
+ digits[2*i] = int8(s.s[i] & 15)
+ digits[2*i+1] = int8((s.s[i] >> 4) & 15)
+ }
+
+ // Recenter coefficients:
+ for i := 0; i < 63; i++ {
+ carry := (digits[i] + 8) >> 4
+ digits[i] -= carry << 4
+ digits[i+1] += carry
+ }
+
+ return digits
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-23 09:07:52 +0000