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Diffstat (limited to 'vendor/golang.org/x/crypto/curve25519/curve25519.go')
-rw-r--r--vendor/golang.org/x/crypto/curve25519/curve25519.go881
1 files changed, 71 insertions, 810 deletions
diff --git a/vendor/golang.org/x/crypto/curve25519/curve25519.go b/vendor/golang.org/x/crypto/curve25519/curve25519.go
index 75f24bab..4b9a655d 100644
--- a/vendor/golang.org/x/crypto/curve25519/curve25519.go
+++ b/vendor/golang.org/x/crypto/curve25519/curve25519.go
@@ -1,834 +1,95 @@
-// Copyright 2013 The Go Authors. All rights reserved.
+// Copyright 2019 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.
-// We have an implementation in amd64 assembly so this code is only run on
-// non-amd64 platforms. The amd64 assembly does not support gccgo.
-// +build !amd64 gccgo appengine
-
-package curve25519
+// Package curve25519 provides an implementation of the X25519 function, which
+// performs scalar multiplication on the elliptic curve known as Curve25519.
+// See RFC 7748.
+package curve25519 // import "golang.org/x/crypto/curve25519"
import (
- "encoding/binary"
+ "crypto/subtle"
+ "fmt"
)
-// This code is a port of the public domain, "ref10" implementation of
-// curve25519 from SUPERCOP 20130419 by D. J. Bernstein.
-
-// fieldElement represents an element of the field GF(2^255 - 19). An element
-// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
-// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
-// context.
-type fieldElement [10]int32
-
-func feZero(fe *fieldElement) {
- for i := range fe {
- fe[i] = 0
- }
-}
-
-func feOne(fe *fieldElement) {
- feZero(fe)
- fe[0] = 1
-}
-
-func feAdd(dst, a, b *fieldElement) {
- for i := range dst {
- dst[i] = a[i] + b[i]
- }
-}
-
-func feSub(dst, a, b *fieldElement) {
- for i := range dst {
- dst[i] = a[i] - b[i]
- }
-}
-
-func feCopy(dst, src *fieldElement) {
- for i := range dst {
- dst[i] = src[i]
- }
-}
-
-// feCSwap replaces (f,g) with (g,f) if b == 1; replaces (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-func feCSwap(f, g *fieldElement, b int32) {
- b = -b
- for i := range f {
- t := b & (f[i] ^ g[i])
- f[i] ^= t
- g[i] ^= t
- }
-}
-
-// load3 reads a 24-bit, little-endian value from in.
-func load3(in []byte) int64 {
- var r int64
- r = int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- return r
-}
-
-// load4 reads a 32-bit, little-endian value from in.
-func load4(in []byte) int64 {
- return int64(binary.LittleEndian.Uint32(in))
-}
-
-func feFromBytes(dst *fieldElement, src *[32]byte) {
- h0 := load4(src[:])
- h1 := load3(src[4:]) << 6
- h2 := load3(src[7:]) << 5
- h3 := load3(src[10:]) << 3
- h4 := load3(src[13:]) << 2
- h5 := load4(src[16:])
- h6 := load3(src[20:]) << 7
- h7 := load3(src[23:]) << 5
- h8 := load3(src[26:]) << 4
- h9 := (load3(src[29:]) & 0x7fffff) << 2
-
- var carry [10]int64
- carry[9] = (h9 + 1<<24) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
- carry[1] = (h1 + 1<<24) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[3] = (h3 + 1<<24) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[5] = (h5 + 1<<24) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
- carry[7] = (h7 + 1<<24) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
-
- carry[0] = (h0 + 1<<25) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[2] = (h2 + 1<<25) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[4] = (h4 + 1<<25) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[6] = (h6 + 1<<25) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
- carry[8] = (h8 + 1<<25) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
-
- dst[0] = int32(h0)
- dst[1] = int32(h1)
- dst[2] = int32(h2)
- dst[3] = int32(h3)
- dst[4] = int32(h4)
- dst[5] = int32(h5)
- dst[6] = int32(h6)
- dst[7] = int32(h7)
- dst[8] = int32(h8)
- dst[9] = int32(h9)
-}
-
-// feToBytes marshals h to s.
-// Preconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Write p=2^255-19; q=floor(h/p).
-// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
-//
-// Proof:
-// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
-// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
-//
-// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
-// Then 0<y<1.
+// ScalarMult sets dst to the product scalar * point.
//
-// Write r=h-pq.
-// Have 0<=r<=p-1=2^255-20.
-// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
-//
-// Write x=r+19(2^-255)r+y.
-// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
-//
-// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
-// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
-func feToBytes(s *[32]byte, h *fieldElement) {
- var carry [10]int32
-
- q := (19*h[9] + (1 << 24)) >> 25
- q = (h[0] + q) >> 26
- q = (h[1] + q) >> 25
- q = (h[2] + q) >> 26
- q = (h[3] + q) >> 25
- q = (h[4] + q) >> 26
- q = (h[5] + q) >> 25
- q = (h[6] + q) >> 26
- q = (h[7] + q) >> 25
- q = (h[8] + q) >> 26
- q = (h[9] + q) >> 25
-
- // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
- h[0] += 19 * q
- // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
-
- carry[0] = h[0] >> 26
- h[1] += carry[0]
- h[0] -= carry[0] << 26
- carry[1] = h[1] >> 25
- h[2] += carry[1]
- h[1] -= carry[1] << 25
- carry[2] = h[2] >> 26
- h[3] += carry[2]
- h[2] -= carry[2] << 26
- carry[3] = h[3] >> 25
- h[4] += carry[3]
- h[3] -= carry[3] << 25
- carry[4] = h[4] >> 26
- h[5] += carry[4]
- h[4] -= carry[4] << 26
- carry[5] = h[5] >> 25
- h[6] += carry[5]
- h[5] -= carry[5] << 25
- carry[6] = h[6] >> 26
- h[7] += carry[6]
- h[6] -= carry[6] << 26
- carry[7] = h[7] >> 25
- h[8] += carry[7]
- h[7] -= carry[7] << 25
- carry[8] = h[8] >> 26
- h[9] += carry[8]
- h[8] -= carry[8] << 26
- carry[9] = h[9] >> 25
- h[9] -= carry[9] << 25
- // h10 = carry9
-
- // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- // Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
- // evidently 2^255 h10-2^255 q = 0.
- // Goal: Output h[0]+...+2^230 h[9].
-
- s[0] = byte(h[0] >> 0)
- s[1] = byte(h[0] >> 8)
- s[2] = byte(h[0] >> 16)
- s[3] = byte((h[0] >> 24) | (h[1] << 2))
- s[4] = byte(h[1] >> 6)
- s[5] = byte(h[1] >> 14)
- s[6] = byte((h[1] >> 22) | (h[2] << 3))
- s[7] = byte(h[2] >> 5)
- s[8] = byte(h[2] >> 13)
- s[9] = byte((h[2] >> 21) | (h[3] << 5))
- s[10] = byte(h[3] >> 3)
- s[11] = byte(h[3] >> 11)
- s[12] = byte((h[3] >> 19) | (h[4] << 6))
- s[13] = byte(h[4] >> 2)
- s[14] = byte(h[4] >> 10)
- s[15] = byte(h[4] >> 18)
- s[16] = byte(h[5] >> 0)
- s[17] = byte(h[5] >> 8)
- s[18] = byte(h[5] >> 16)
- s[19] = byte((h[5] >> 24) | (h[6] << 1))
- s[20] = byte(h[6] >> 7)
- s[21] = byte(h[6] >> 15)
- s[22] = byte((h[6] >> 23) | (h[7] << 3))
- s[23] = byte(h[7] >> 5)
- s[24] = byte(h[7] >> 13)
- s[25] = byte((h[7] >> 21) | (h[8] << 4))
- s[26] = byte(h[8] >> 4)
- s[27] = byte(h[8] >> 12)
- s[28] = byte((h[8] >> 20) | (h[9] << 6))
- s[29] = byte(h[9] >> 2)
- s[30] = byte(h[9] >> 10)
- s[31] = byte(h[9] >> 18)
+// Deprecated: when provided a low-order point, ScalarMult will set dst to all
+// zeroes, irrespective of the scalar. Instead, use the X25519 function, which
+// will return an error.
+func ScalarMult(dst, scalar, point *[32]byte) {
+ scalarMult(dst, scalar, point)
}
-// feMul calculates h = f * g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Notes on implementation strategy:
-//
-// Using schoolbook multiplication.
-// Karatsuba would save a little in some cost models.
+// ScalarBaseMult sets dst to the product scalar * base where base is the
+// standard generator.
//
-// Most multiplications by 2 and 19 are 32-bit precomputations;
-// cheaper than 64-bit postcomputations.
-//
-// There is one remaining multiplication by 19 in the carry chain;
-// one *19 precomputation can be merged into this,
-// but the resulting data flow is considerably less clean.
-//
-// There are 12 carries below.
-// 10 of them are 2-way parallelizable and vectorizable.
-// Can get away with 11 carries, but then data flow is much deeper.
-//
-// With tighter constraints on inputs can squeeze carries into int32.
-func feMul(h, f, g *fieldElement) {
- f0 := f[0]
- f1 := f[1]
- f2 := f[2]
- f3 := f[3]
- f4 := f[4]
- f5 := f[5]
- f6 := f[6]
- f7 := f[7]
- f8 := f[8]
- f9 := f[9]
- g0 := g[0]
- g1 := g[1]
- g2 := g[2]
- g3 := g[3]
- g4 := g[4]
- g5 := g[5]
- g6 := g[6]
- g7 := g[7]
- g8 := g[8]
- g9 := g[9]
- g1_19 := 19 * g1 // 1.4*2^29
- g2_19 := 19 * g2 // 1.4*2^30; still ok
- g3_19 := 19 * g3
- g4_19 := 19 * g4
- g5_19 := 19 * g5
- g6_19 := 19 * g6
- g7_19 := 19 * g7
- g8_19 := 19 * g8
- g9_19 := 19 * g9
- f1_2 := 2 * f1
- f3_2 := 2 * f3
- f5_2 := 2 * f5
- f7_2 := 2 * f7
- f9_2 := 2 * f9
- f0g0 := int64(f0) * int64(g0)
- f0g1 := int64(f0) * int64(g1)
- f0g2 := int64(f0) * int64(g2)
- f0g3 := int64(f0) * int64(g3)
- f0g4 := int64(f0) * int64(g4)
- f0g5 := int64(f0) * int64(g5)
- f0g6 := int64(f0) * int64(g6)
- f0g7 := int64(f0) * int64(g7)
- f0g8 := int64(f0) * int64(g8)
- f0g9 := int64(f0) * int64(g9)
- f1g0 := int64(f1) * int64(g0)
- f1g1_2 := int64(f1_2) * int64(g1)
- f1g2 := int64(f1) * int64(g2)
- f1g3_2 := int64(f1_2) * int64(g3)
- f1g4 := int64(f1) * int64(g4)
- f1g5_2 := int64(f1_2) * int64(g5)
- f1g6 := int64(f1) * int64(g6)
- f1g7_2 := int64(f1_2) * int64(g7)
- f1g8 := int64(f1) * int64(g8)
- f1g9_38 := int64(f1_2) * int64(g9_19)
- f2g0 := int64(f2) * int64(g0)
- f2g1 := int64(f2) * int64(g1)
- f2g2 := int64(f2) * int64(g2)
- f2g3 := int64(f2) * int64(g3)
- f2g4 := int64(f2) * int64(g4)
- f2g5 := int64(f2) * int64(g5)
- f2g6 := int64(f2) * int64(g6)
- f2g7 := int64(f2) * int64(g7)
- f2g8_19 := int64(f2) * int64(g8_19)
- f2g9_19 := int64(f2) * int64(g9_19)
- f3g0 := int64(f3) * int64(g0)
- f3g1_2 := int64(f3_2) * int64(g1)
- f3g2 := int64(f3) * int64(g2)
- f3g3_2 := int64(f3_2) * int64(g3)
- f3g4 := int64(f3) * int64(g4)
- f3g5_2 := int64(f3_2) * int64(g5)
- f3g6 := int64(f3) * int64(g6)
- f3g7_38 := int64(f3_2) * int64(g7_19)
- f3g8_19 := int64(f3) * int64(g8_19)
- f3g9_38 := int64(f3_2) * int64(g9_19)
- f4g0 := int64(f4) * int64(g0)
- f4g1 := int64(f4) * int64(g1)
- f4g2 := int64(f4) * int64(g2)
- f4g3 := int64(f4) * int64(g3)
- f4g4 := int64(f4) * int64(g4)
- f4g5 := int64(f4) * int64(g5)
- f4g6_19 := int64(f4) * int64(g6_19)
- f4g7_19 := int64(f4) * int64(g7_19)
- f4g8_19 := int64(f4) * int64(g8_19)
- f4g9_19 := int64(f4) * int64(g9_19)
- f5g0 := int64(f5) * int64(g0)
- f5g1_2 := int64(f5_2) * int64(g1)
- f5g2 := int64(f5) * int64(g2)
- f5g3_2 := int64(f5_2) * int64(g3)
- f5g4 := int64(f5) * int64(g4)
- f5g5_38 := int64(f5_2) * int64(g5_19)
- f5g6_19 := int64(f5) * int64(g6_19)
- f5g7_38 := int64(f5_2) * int64(g7_19)
- f5g8_19 := int64(f5) * int64(g8_19)
- f5g9_38 := int64(f5_2) * int64(g9_19)
- f6g0 := int64(f6) * int64(g0)
- f6g1 := int64(f6) * int64(g1)
- f6g2 := int64(f6) * int64(g2)
- f6g3 := int64(f6) * int64(g3)
- f6g4_19 := int64(f6) * int64(g4_19)
- f6g5_19 := int64(f6) * int64(g5_19)
- f6g6_19 := int64(f6) * int64(g6_19)
- f6g7_19 := int64(f6) * int64(g7_19)
- f6g8_19 := int64(f6) * int64(g8_19)
- f6g9_19 := int64(f6) * int64(g9_19)
- f7g0 := int64(f7) * int64(g0)
- f7g1_2 := int64(f7_2) * int64(g1)
- f7g2 := int64(f7) * int64(g2)
- f7g3_38 := int64(f7_2) * int64(g3_19)
- f7g4_19 := int64(f7) * int64(g4_19)
- f7g5_38 := int64(f7_2) * int64(g5_19)
- f7g6_19 := int64(f7) * int64(g6_19)
- f7g7_38 := int64(f7_2) * int64(g7_19)
- f7g8_19 := int64(f7) * int64(g8_19)
- f7g9_38 := int64(f7_2) * int64(g9_19)
- f8g0 := int64(f8) * int64(g0)
- f8g1 := int64(f8) * int64(g1)
- f8g2_19 := int64(f8) * int64(g2_19)
- f8g3_19 := int64(f8) * int64(g3_19)
- f8g4_19 := int64(f8) * int64(g4_19)
- f8g5_19 := int64(f8) * int64(g5_19)
- f8g6_19 := int64(f8) * int64(g6_19)
- f8g7_19 := int64(f8) * int64(g7_19)
- f8g8_19 := int64(f8) * int64(g8_19)
- f8g9_19 := int64(f8) * int64(g9_19)
- f9g0 := int64(f9) * int64(g0)
- f9g1_38 := int64(f9_2) * int64(g1_19)
- f9g2_19 := int64(f9) * int64(g2_19)
- f9g3_38 := int64(f9_2) * int64(g3_19)
- f9g4_19 := int64(f9) * int64(g4_19)
- f9g5_38 := int64(f9_2) * int64(g5_19)
- f9g6_19 := int64(f9) * int64(g6_19)
- f9g7_38 := int64(f9_2) * int64(g7_19)
- f9g8_19 := int64(f9) * int64(g8_19)
- f9g9_38 := int64(f9_2) * int64(g9_19)
- h0 := f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38
- h1 := f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19
- h2 := f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38
- h3 := f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19
- h4 := f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38
- h5 := f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19
- h6 := f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38
- h7 := f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19
- h8 := f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38
- h9 := f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0
- var carry [10]int64
-
- // |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
- // i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
- // |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
- // i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- // |h0| <= 2^25
- // |h4| <= 2^25
- // |h1| <= 1.51*2^58
- // |h5| <= 1.51*2^58
-
- carry[1] = (h1 + (1 << 24)) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[5] = (h5 + (1 << 24)) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
- // |h1| <= 2^24; from now on fits into int32
- // |h5| <= 2^24; from now on fits into int32
- // |h2| <= 1.21*2^59
- // |h6| <= 1.21*2^59
-
- carry[2] = (h2 + (1 << 25)) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[6] = (h6 + (1 << 25)) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
- // |h2| <= 2^25; from now on fits into int32 unchanged
- // |h6| <= 2^25; from now on fits into int32 unchanged
- // |h3| <= 1.51*2^58
- // |h7| <= 1.51*2^58
-
- carry[3] = (h3 + (1 << 24)) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[7] = (h7 + (1 << 24)) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
- // |h3| <= 2^24; from now on fits into int32 unchanged
- // |h7| <= 2^24; from now on fits into int32 unchanged
- // |h4| <= 1.52*2^33
- // |h8| <= 1.52*2^33
-
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[8] = (h8 + (1 << 25)) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
- // |h4| <= 2^25; from now on fits into int32 unchanged
- // |h8| <= 2^25; from now on fits into int32 unchanged
- // |h5| <= 1.01*2^24
- // |h9| <= 1.51*2^58
-
- carry[9] = (h9 + (1 << 24)) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
- // |h9| <= 2^24; from now on fits into int32 unchanged
- // |h0| <= 1.8*2^37
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- // |h0| <= 2^25; from now on fits into int32 unchanged
- // |h1| <= 1.01*2^24
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
+// It is recommended to use the X25519 function with Basepoint instead, as
+// copying into fixed size arrays can lead to unexpected bugs.
+func ScalarBaseMult(dst, scalar *[32]byte) {
+ ScalarMult(dst, scalar, &basePoint)
}
-// feSquare calculates h = f*f. Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func feSquare(h, f *fieldElement) {
- f0 := f[0]
- f1 := f[1]
- f2 := f[2]
- f3 := f[3]
- f4 := f[4]
- f5 := f[5]
- f6 := f[6]
- f7 := f[7]
- f8 := f[8]
- f9 := f[9]
- f0_2 := 2 * f0
- f1_2 := 2 * f1
- f2_2 := 2 * f2
- f3_2 := 2 * f3
- f4_2 := 2 * f4
- f5_2 := 2 * f5
- f6_2 := 2 * f6
- f7_2 := 2 * f7
- f5_38 := 38 * f5 // 1.31*2^30
- f6_19 := 19 * f6 // 1.31*2^30
- f7_38 := 38 * f7 // 1.31*2^30
- f8_19 := 19 * f8 // 1.31*2^30
- f9_38 := 38 * f9 // 1.31*2^30
- f0f0 := int64(f0) * int64(f0)
- f0f1_2 := int64(f0_2) * int64(f1)
- f0f2_2 := int64(f0_2) * int64(f2)
- f0f3_2 := int64(f0_2) * int64(f3)
- f0f4_2 := int64(f0_2) * int64(f4)
- f0f5_2 := int64(f0_2) * int64(f5)
- f0f6_2 := int64(f0_2) * int64(f6)
- f0f7_2 := int64(f0_2) * int64(f7)
- f0f8_2 := int64(f0_2) * int64(f8)
- f0f9_2 := int64(f0_2) * int64(f9)
- f1f1_2 := int64(f1_2) * int64(f1)
- f1f2_2 := int64(f1_2) * int64(f2)
- f1f3_4 := int64(f1_2) * int64(f3_2)
- f1f4_2 := int64(f1_2) * int64(f4)
- f1f5_4 := int64(f1_2) * int64(f5_2)
- f1f6_2 := int64(f1_2) * int64(f6)
- f1f7_4 := int64(f1_2) * int64(f7_2)
- f1f8_2 := int64(f1_2) * int64(f8)
- f1f9_76 := int64(f1_2) * int64(f9_38)
- f2f2 := int64(f2) * int64(f2)
- f2f3_2 := int64(f2_2) * int64(f3)
- f2f4_2 := int64(f2_2) * int64(f4)
- f2f5_2 := int64(f2_2) * int64(f5)
- f2f6_2 := int64(f2_2) * int64(f6)
- f2f7_2 := int64(f2_2) * int64(f7)
- f2f8_38 := int64(f2_2) * int64(f8_19)
- f2f9_38 := int64(f2) * int64(f9_38)
- f3f3_2 := int64(f3_2) * int64(f3)
- f3f4_2 := int64(f3_2) * int64(f4)
- f3f5_4 := int64(f3_2) * int64(f5_2)
- f3f6_2 := int64(f3_2) * int64(f6)
- f3f7_76 := int64(f3_2) * int64(f7_38)
- f3f8_38 := int64(f3_2) * int64(f8_19)
- f3f9_76 := int64(f3_2) * int64(f9_38)
- f4f4 := int64(f4) * int64(f4)
- f4f5_2 := int64(f4_2) * int64(f5)
- f4f6_38 := int64(f4_2) * int64(f6_19)
- f4f7_38 := int64(f4) * int64(f7_38)
- f4f8_38 := int64(f4_2) * int64(f8_19)
- f4f9_38 := int64(f4) * int64(f9_38)
- f5f5_38 := int64(f5) * int64(f5_38)
- f5f6_38 := int64(f5_2) * int64(f6_19)
- f5f7_76 := int64(f5_2) * int64(f7_38)
- f5f8_38 := int64(f5_2) * int64(f8_19)
- f5f9_76 := int64(f5_2) * int64(f9_38)
- f6f6_19 := int64(f6) * int64(f6_19)
- f6f7_38 := int64(f6) * int64(f7_38)
- f6f8_38 := int64(f6_2) * int64(f8_19)
- f6f9_38 := int64(f6) * int64(f9_38)
- f7f7_38 := int64(f7) * int64(f7_38)
- f7f8_38 := int64(f7_2) * int64(f8_19)
- f7f9_76 := int64(f7_2) * int64(f9_38)
- f8f8_19 := int64(f8) * int64(f8_19)
- f8f9_38 := int64(f8) * int64(f9_38)
- f9f9_38 := int64(f9) * int64(f9_38)
- h0 := f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38
- h1 := f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38
- h2 := f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19
- h3 := f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38
- h4 := f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38
- h5 := f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38
- h6 := f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19
- h7 := f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38
- h8 := f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38
- h9 := f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2
- var carry [10]int64
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
-
- carry[1] = (h1 + (1 << 24)) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[5] = (h5 + (1 << 24)) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
-
- carry[2] = (h2 + (1 << 25)) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[6] = (h6 + (1 << 25)) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
-
- carry[3] = (h3 + (1 << 24)) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[7] = (h7 + (1 << 24)) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
+const (
+ // ScalarSize is the size of the scalar input to X25519.
+ ScalarSize = 32
+ // PointSize is the size of the point input to X25519.
+ PointSize = 32
+)
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[8] = (h8 + (1 << 25)) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
+// Basepoint is the canonical Curve25519 generator.
+var Basepoint []byte
- carry[9] = (h9 + (1 << 24)) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
+var basePoint = [32]byte{9, 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}
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
+func init() { Basepoint = basePoint[:] }
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
+func checkBasepoint() {
+ if subtle.ConstantTimeCompare(Basepoint, []byte{
+ 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ }) != 1 {
+ panic("curve25519: global Basepoint value was modified")
+ }
}
-// feMul121666 calculates h = f * 121666. Can overlap h with f.
+// X25519 returns the result of the scalar multiplication (scalar * point),
+// according to RFC 7748, Section 5. scalar, point and the return value are
+// slices of 32 bytes.
//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+// scalar can be generated at random, for example with crypto/rand. point should
+// be either Basepoint or the output of another X25519 call.
//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func feMul121666(h, f *fieldElement) {
- h0 := int64(f[0]) * 121666
- h1 := int64(f[1]) * 121666
- h2 := int64(f[2]) * 121666
- h3 := int64(f[3]) * 121666
- h4 := int64(f[4]) * 121666
- h5 := int64(f[5]) * 121666
- h6 := int64(f[6]) * 121666
- h7 := int64(f[7]) * 121666
- h8 := int64(f[8]) * 121666
- h9 := int64(f[9]) * 121666
- var carry [10]int64
-
- carry[9] = (h9 + (1 << 24)) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
- carry[1] = (h1 + (1 << 24)) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[3] = (h3 + (1 << 24)) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[5] = (h5 + (1 << 24)) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
- carry[7] = (h7 + (1 << 24)) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[2] = (h2 + (1 << 25)) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[6] = (h6 + (1 << 25)) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
- carry[8] = (h8 + (1 << 25)) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
-}
-
-// feInvert sets out = z^-1.
-func feInvert(out, z *fieldElement) {
- var t0, t1, t2, t3 fieldElement
- var i int
-
- feSquare(&t0, z)
- for i = 1; i < 1; i++ {
- feSquare(&t0, &t0)
- }
- feSquare(&t1, &t0)
- for i = 1; i < 2; i++ {
- feSquare(&t1, &t1)
- }
- feMul(&t1, z, &t1)
- feMul(&t0, &t0, &t1)
- feSquare(&t2, &t0)
- for i = 1; i < 1; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t1, &t2)
- feSquare(&t2, &t1)
- for i = 1; i < 5; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t2, &t1)
- feSquare(&t2, &t1)
- for i = 1; i < 10; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t2, &t2, &t1)
- feSquare(&t3, &t2)
- for i = 1; i < 20; i++ {
- feSquare(&t3, &t3)
- }
- feMul(&t2, &t3, &t2)
- feSquare(&t2, &t2)
- for i = 1; i < 10; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t2, &t1)
- feSquare(&t2, &t1)
- for i = 1; i < 50; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t2, &t2, &t1)
- feSquare(&t3, &t2)
- for i = 1; i < 100; i++ {
- feSquare(&t3, &t3)
- }
- feMul(&t2, &t3, &t2)
- feSquare(&t2, &t2)
- for i = 1; i < 50; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t2, &t1)
- feSquare(&t1, &t1)
- for i = 1; i < 5; i++ {
- feSquare(&t1, &t1)
- }
- feMul(out, &t1, &t0)
+// If point is Basepoint (but not if it's a different slice with the same
+// contents) a precomputed implementation might be used for performance.
+func X25519(scalar, point []byte) ([]byte, error) {
+ // Outline the body of function, to let the allocation be inlined in the
+ // caller, and possibly avoid escaping to the heap.
+ var dst [32]byte
+ return x25519(&dst, scalar, point)
}
-func scalarMult(out, in, base *[32]byte) {
- var e [32]byte
-
- copy(e[:], in[:])
- e[0] &= 248
- e[31] &= 127
- e[31] |= 64
-
- var x1, x2, z2, x3, z3, tmp0, tmp1 fieldElement
- feFromBytes(&x1, base)
- feOne(&x2)
- feCopy(&x3, &x1)
- feOne(&z3)
-
- swap := int32(0)
- for pos := 254; pos >= 0; pos-- {
- b := e[pos/8] >> uint(pos&7)
- b &= 1
- swap ^= int32(b)
- feCSwap(&x2, &x3, swap)
- feCSwap(&z2, &z3, swap)
- swap = int32(b)
-
- feSub(&tmp0, &x3, &z3)
- feSub(&tmp1, &x2, &z2)
- feAdd(&x2, &x2, &z2)
- feAdd(&z2, &x3, &z3)
- feMul(&z3, &tmp0, &x2)
- feMul(&z2, &z2, &tmp1)
- feSquare(&tmp0, &tmp1)
- feSquare(&tmp1, &x2)
- feAdd(&x3, &z3, &z2)
- feSub(&z2, &z3, &z2)
- feMul(&x2, &tmp1, &tmp0)
- feSub(&tmp1, &tmp1, &tmp0)
- feSquare(&z2, &z2)
- feMul121666(&z3, &tmp1)
- feSquare(&x3, &x3)
- feAdd(&tmp0, &tmp0, &z3)
- feMul(&z3, &x1, &z2)
- feMul(&z2, &tmp1, &tmp0)
- }
-
- feCSwap(&x2, &x3, swap)
- feCSwap(&z2, &z3, swap)
-
- feInvert(&z2, &z2)
- feMul(&x2, &x2, &z2)
- feToBytes(out, &x2)
+func x25519(dst *[32]byte, scalar, point []byte) ([]byte, error) {
+ var in [32]byte
+ if l := len(scalar); l != 32 {
+ return nil, fmt.Errorf("bad scalar length: %d, expected %d", l, 32)
+ }
+ if l := len(point); l != 32 {
+ return nil, fmt.Errorf("bad point length: %d, expected %d", l, 32)
+ }
+ copy(in[:], scalar)
+ if &point[0] == &Basepoint[0] {
+ checkBasepoint()
+ ScalarBaseMult(dst, &in)
+ } else {
+ var base, zero [32]byte
+ copy(base[:], point)
+ ScalarMult(dst, &in, &base)
+ if subtle.ConstantTimeCompare(dst[:], zero[:]) == 1 {
+ return nil, fmt.Errorf("bad input point: low order point")
+ }
+ }
+ return dst[:], nil
}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-15 05:36:15 +0000