[obfs4/master] common: Replace the extra25519 import with an internal package

10 Apr 2020

commit 2d8f3c8bbfd7a7ca931738a64c2f6e97b7332d9e
Author: Yawning Angel <yawning@schwanenlied.me>
Date:   Fri Apr 10 11:36:29 2020 +0000

    common: Replace the extra25519 import with an internal package
    
    I really didn't want to do this, but this should make `go get` work
    again, and maybe people will leave me alone.
---
 ChangeLog                              |    1 +
 common/ntor/ntor.go                    |    9 +-
 go.mod                                 |    3 +-
 go.sum                                 |    2 -
 internal/README-extra25519.md          |   21 +
 internal/edwards25519/const.go         | 1411 +++++++++++++++++++++++++
 internal/edwards25519/edwards25519.go  | 1773 ++++++++++++++++++++++++++++++++
 internal/extra25519/extra25519.go      |  291 ++++++
 internal/extra25519/extra25519_test.go |   61 ++
 9 files changed, 3565 insertions(+), 7 deletions(-)

diff --git a/ChangeLog b/ChangeLog
index fb2372f..eb4efc7 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,5 @@
 Changes in version 0.0.12 - UNRELEASED:
+ - Replace the extra25519 import with an internal package.
 
 Changes in version 0.0.11 - 2019-06-21:
  - Update my e-mail address.
diff --git a/common/ntor/ntor.go b/common/ntor/ntor.go
index 15f7f38..851cc1e 100644
--- a/common/ntor/ntor.go
+++ b/common/ntor/ntor.go
@@ -43,10 +43,11 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/agl/ed25519/extra25519"
-	"gitlab.com/yawning/obfs4.git/common/csrand"
 	"golang.org/x/crypto/curve25519"
 	"golang.org/x/crypto/hkdf"
+
+	"gitlab.com/yawning/obfs4.git/common/csrand"
+	"gitlab.com/yawning/obfs4.git/internal/extra25519"
 )
 
 const (
@@ -203,7 +204,7 @@ func (repr *Representative) Bytes() *[RepresentativeLength]byte {
 func (repr *Representative) ToPublic() *PublicKey {
 	pub := new(PublicKey)
 
-	extra25519.RepresentativeToPublicKey(pub.Bytes(), repr.Bytes())
+	extra25519.UnsafeBrokenRepresentativeToPublicKey(pub.Bytes(), repr.Bytes())
 	return pub
 }
 
@@ -275,7 +276,7 @@ func NewKeypair(elligator bool) (*Keypair, error) {
 
 		if elligator {
 			// Apply the Elligator transform.  This fails ~50% of the time.
-			if !extra25519.ScalarBaseMult(keypair.public.Bytes(),
+			if !extra25519.UnsafeBrokenScalarBaseMult(keypair.public.Bytes(),
 				keypair.representative.Bytes(),
 				keypair.private.Bytes()) {
 				continue
diff --git a/go.mod b/go.mod
index 888ea8c..a90d67d 100644
--- a/go.mod
+++ b/go.mod
@@ -2,9 +2,10 @@ module gitlab.com/yawning/obfs4.git
 
 require (
 	git.torproject.org/pluggable-transports/goptlib.git v1.0.0
-	github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412
 	github.com/dchest/siphash v1.2.1
 	gitlab.com/yawning/utls.git v0.0.11-1
 	golang.org/x/crypto v0.0.0-20190325154230-a5d413f7728c
 	golang.org/x/net v0.0.0-20190328230028-74de082e2cca
 )
+
+go 1.13
diff --git a/go.sum b/go.sum
index 68b4e92..bffa15e 100644
--- a/go.sum
+++ b/go.sum
@@ -2,8 +2,6 @@ git.schwanenlied.me/yawning/bsaes.git v0.0.0-20190320102049-26d1add596b6 h1:zOrl
 git.schwanenlied.me/yawning/bsaes.git v0.0.0-20190320102049-26d1add596b6/go.mod h1:BWqTsj8PgcPriQJGl7el20J/7TuT1d/hSyFDXMEpoEo=
 git.torproject.org/pluggable-transports/goptlib.git v1.0.0 h1:ElTwFFPKf/tA6x5nuIk9g49JZzS4T5WN+eTQTjqd00A=
 git.torproject.org/pluggable-transports/goptlib.git v1.0.0/go.mod h1:YT4XMSkuEXbtqlydr9+OxqFAyspUv0Gr9qhM3B++o/Q=
-github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 h1:w1UutsfOrms1J05zt7ISrnJIXKzwaspym5BTKGx93EI=
-github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412/go.mod h1:WPjqKcmVOxf0XSf3YxCJs6N6AOSrOx3obionmG7T0y0=
 github.com/dchest/siphash v1.2.1 h1:4cLinnzVJDKxTCl9B01807Yiy+W7ZzVHj/KIroQRvT4=
 github.com/dchest/siphash v1.2.1/go.mod h1:q+IRvb2gOSrUnYoPqHiyHXS0FOBBOdl6tONBlVnOnt4=
 github.com/dsnet/compress v0.0.1 h1:PlZu0n3Tuv04TzpfPbrnI0HW/YwodEXDS+oPKahKF0Q=
diff --git a/internal/README-extra25519.md b/internal/README-extra25519.md
new file mode 100644
index 0000000..f02418c
--- /dev/null
+++ b/internal/README-extra25519.md
@@ -0,0 +1,21 @@
+This includes a copy of the edwards25519 and extra25519 packages authored
+by agl, that formerly lived at github.com/agl/ed25519 as of the commit
+5312a61534124124185d41f09206b9fef1d88403 with the following changes:
+
+ * Import paths fixed up.
+
+ * The unused Ed25519->X25519 key conversion routines were removed.
+
+ * `UnsafeBroken` was prefixed to the routines that are known to be
+   severely flawed.
+
+The only reason this is being done (despite agl's wishes that the code
+base dies, which I wanted to respect) is so people stop bothering me
+about it.
+
+Do not ask me questions about this.
+Do not use it in other projects.
+Do not use it in anything new.
+Do not expect me to maintain this beyond ensuring it continues to build.
+
+All I want is to be left alone.
diff --git a/internal/edwards25519/const.go b/internal/edwards25519/const.go
new file mode 100644
index 0000000..ea5b77a
--- /dev/null
+++ b/internal/edwards25519/const.go
@@ -0,0 +1,1411 @@
+// Copyright 2013 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
+
+var d = FieldElement{
+	-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116,
+}
+
+var d2 = FieldElement{
+	-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199,
+}
+
+var SqrtM1 = FieldElement{
+	-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482,
+}
+
+var A = FieldElement{
+	486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+}
+
+var bi = [8]PreComputedGroupElement{
+	{
+		FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
+		FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
+		FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
+	},
+	{
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+	},
+	{
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+	},
+}
+
+var base = [32][8]PreComputedGroupElement{
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+		},
+		{
+			FieldElement{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313},
+			FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
+			FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577},
+		},
+		{
+			FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
+			FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
+			FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476},
+		},
+	},
+}
diff --git a/internal/edwards25519/edwards25519.go b/internal/edwards25519/edwards25519.go
new file mode 100644
index 0000000..9079818
--- /dev/null
+++ b/internal/edwards25519/edwards25519.go
@@ -0,0 +1,1773 @@
+// Copyright 2013 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 implements operations in GF(2**255-19) and on an
+// Edwards curve that is isomorphic to curve25519. See
+// http://ed25519.cr.yp.to/.
+package edwards25519
+
+// This code is a port of the public domain, "ref10" implementation of ed25519
+// from SUPERCOP.
+
+// 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
+
+var zero FieldElement
+
+func FeZero(fe *FieldElement) {
+	copy(fe[:], zero[:])
+}
+
+func FeOne(fe *FieldElement) {
+	FeZero(fe)
+	fe[0] = 1
+}
+
+func FeAdd(dst, a, b *FieldElement) {
+	dst[0] = a[0] + b[0]
+	dst[1] = a[1] + b[1]
+	dst[2] = a[2] + b[2]
+	dst[3] = a[3] + b[3]
+	dst[4] = a[4] + b[4]
+	dst[5] = a[5] + b[5]
+	dst[6] = a[6] + b[6]
+	dst[7] = a[7] + b[7]
+	dst[8] = a[8] + b[8]
+	dst[9] = a[9] + b[9]
+}
+
+func FeSub(dst, a, b *FieldElement) {
+	dst[0] = a[0] - b[0]
+	dst[1] = a[1] - b[1]
+	dst[2] = a[2] - b[2]
+	dst[3] = a[3] - b[3]
+	dst[4] = a[4] - b[4]
+	dst[5] = a[5] - b[5]
+	dst[6] = a[6] - b[6]
+	dst[7] = a[7] - b[7]
+	dst[8] = a[8] - b[8]
+	dst[9] = a[9] - b[9]
+}
+
+func FeCopy(dst, src *FieldElement) {
+	copy(dst[:], src[:])
+}
+
+// Replace (f,g) with (g,g) if b == 1;
+// replace (f,g) with (f,g) if b == 0.
+//
+// Preconditions: b in {0,1}.
+func FeCMove(f, g *FieldElement, b int32) {
+	b = -b
+	f[0] ^= b & (f[0] ^ g[0])
+	f[1] ^= b & (f[1] ^ g[1])
+	f[2] ^= b & (f[2] ^ g[2])
+	f[3] ^= b & (f[3] ^ g[3])
+	f[4] ^= b & (f[4] ^ g[4])
+	f[5] ^= b & (f[5] ^ g[5])
+	f[6] ^= b & (f[6] ^ g[6])
+	f[7] ^= b & (f[7] ^ g[7])
+	f[8] ^= b & (f[8] ^ g[8])
+	f[9] ^= b & (f[9] ^ g[9])
+}
+
+func load3(in []byte) int64 {
+	var r int64
+	r = int64(in[0])
+	r |= int64(in[1]) << 8
+	r |= int64(in[2]) << 16
+	return r
+}
+
+func load4(in []byte) int64 {
+	var r int64
+	r = int64(in[0])
+	r |= int64(in[1]) << 8
+	r |= int64(in[2]) << 16
+	r |= int64(in[3]) << 24
+	return r
+}
+
+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:]) & 8388607) << 2
+
+	FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, 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.
+//
+//   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)
+}
+
+func FeIsNegative(f *FieldElement) byte {
+	var s [32]byte
+	FeToBytes(&s, f)
+	return s[0] & 1
+}
+
+func FeIsNonZero(f *FieldElement) int32 {
+	var s [32]byte
+	FeToBytes(&s, f)
+	var x uint8
+	for _, b := range s {
+		x |= b
+	}
+	x |= x >> 4
+	x |= x >> 2
+	x |= x >> 1
+	return int32(x & 1)
+}
+
+// FeNeg sets h = -f
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+func FeNeg(h, f *FieldElement) {
+	h[0] = -f[0]
+	h[1] = -f[1]
+	h[2] = -f[2]
+	h[3] = -f[3]
+	h[4] = -f[4]
+	h[5] = -f[5]
+	h[6] = -f[6]
+	h[7] = -f[7]
+	h[8] = -f[8]
+	h[9] = -f[9]
+}
+
+func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
+	var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 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
+	*/
+
+	c0 = (h0 + (1 << 25)) >> 26
+	h1 += c0
+	h0 -= c0 << 26
+	c4 = (h4 + (1 << 25)) >> 26
+	h5 += c4
+	h4 -= c4 << 26
+	/* |h0| <= 2^25 */
+	/* |h4| <= 2^25 */
+	/* |h1| <= 1.51*2^58 */
+	/* |h5| <= 1.51*2^58 */
+
+	c1 = (h1 + (1 << 24)) >> 25
+	h2 += c1
+	h1 -= c1 << 25
+	c5 = (h5 + (1 << 24)) >> 25
+	h6 += c5
+	h5 -= c5 << 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 */
+
+	c2 = (h2 + (1 << 25)) >> 26
+	h3 += c2
+	h2 -= c2 << 26
+	c6 = (h6 + (1 << 25)) >> 26
+	h7 += c6
+	h6 -= c6 << 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 */
+
+	c3 = (h3 + (1 << 24)) >> 25
+	h4 += c3
+	h3 -= c3 << 25
+	c7 = (h7 + (1 << 24)) >> 25
+	h8 += c7
+	h7 -= c7 << 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 */
+
+	c4 = (h4 + (1 << 25)) >> 26
+	h5 += c4
+	h4 -= c4 << 26
+	c8 = (h8 + (1 << 25)) >> 26
+	h9 += c8
+	h8 -= c8 << 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 */
+
+	c9 = (h9 + (1 << 24)) >> 25
+	h0 += c9 * 19
+	h9 -= c9 << 25
+	/* |h9| <= 2^24; from now on fits into int32 unchanged */
+	/* |h0| <= 1.8*2^37 */
+
+	c0 = (h0 + (1 << 25)) >> 26
+	h1 += c0
+	h0 -= c0 << 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)
+}
+
+// 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.
+//
+// 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 := int64(f[0])
+	f1 := int64(f[1])
+	f2 := int64(f[2])
+	f3 := int64(f[3])
+	f4 := int64(f[4])
+	f5 := int64(f[5])
+	f6 := int64(f[6])
+	f7 := int64(f[7])
+	f8 := int64(f[8])
+	f9 := int64(f[9])
+
+	f1_2 := int64(2 * f[1])
+	f3_2 := int64(2 * f[3])
+	f5_2 := int64(2 * f[5])
+	f7_2 := int64(2 * f[7])
+	f9_2 := int64(2 * f[9])
+
+	g0 := int64(g[0])
+	g1 := int64(g[1])
+	g2 := int64(g[2])
+	g3 := int64(g[3])
+	g4 := int64(g[4])
+	g5 := int64(g[5])
+	g6 := int64(g[6])
+	g7 := int64(g[7])
+	g8 := int64(g[8])
+	g9 := int64(g[9])
+
+	g1_19 := int64(19 * g[1]) /* 1.4*2^29 */
+	g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */
+	g3_19 := int64(19 * g[3])
+	g4_19 := int64(19 * g[4])
+	g5_19 := int64(19 * g[5])
+	g6_19 := int64(19 * g[6])
+	g7_19 := int64(19 * g[7])
+	g8_19 := int64(19 * g[8])
+	g9_19 := int64(19 * g[9])
+
+	h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19
+	h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19
+	h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19
+	h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19
+	h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19
+	h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19
+	h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19
+	h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19
+	h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19
+	h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0
+
+	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
+	f0 := int64(f[0])
+	f1 := int64(f[1])
+	f2 := int64(f[2])
+	f3 := int64(f[3])
+	f4 := int64(f[4])
+	f5 := int64(f[5])
+	f6 := int64(f[6])
+	f7 := int64(f[7])
+	f8 := int64(f[8])
+	f9 := int64(f[9])
+	f0_2 := int64(2 * f[0])
+	f1_2 := int64(2 * f[1])
+	f2_2 := int64(2 * f[2])
+	f3_2 := int64(2 * f[3])
+	f4_2 := int64(2 * f[4])
+	f5_2 := int64(2 * f[5])
+	f6_2 := int64(2 * f[6])
+	f7_2 := int64(2 * f[7])
+	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
+
+	h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38
+	h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19
+	h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19
+	h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38
+	h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38
+	h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19
+	h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19
+	h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38
+	h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38
+	h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5
+
+	return
+}
+
+// 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) {
+	h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
+	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+// FeSquare2 sets h = 2 * f * f
+//
+// Can overlap h with f.
+//
+// Preconditions:
+//    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+// See fe_mul.c for discussion of implementation strategy.
+func FeSquare2(h, f *FieldElement) {
+	h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
+
+	h0 += h0
+	h1 += h1
+	h2 += h2
+	h3 += h3
+	h4 += h4
+	h5 += h5
+	h6 += h6
+	h7 += h7
+	h8 += h8
+	h9 += h9
+
+	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+func FeInvert(out, z *FieldElement) {
+	var t0, t1, t2, t3 FieldElement
+	var i int
+
+	FeSquare(&t0, z)        // 2^1
+	FeSquare(&t1, &t0)      // 2^2
+	for i = 1; i < 2; i++ { // 2^3
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, z, &t1)      // 2^3 + 2^0
+	FeMul(&t0, &t0, &t1)    // 2^3 + 2^1 + 2^0
+	FeSquare(&t2, &t0)      // 2^4 + 2^2 + 2^1
+	FeMul(&t1, &t1, &t2)    // 2^4 + 2^3 + 2^2 + 2^1 + 2^0
+	FeSquare(&t2, &t1)      // 5,4,3,2,1
+	for i = 1; i < 5; i++ { // 9,8,7,6,5
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)     // 9,8,7,6,5,4,3,2,1,0
+	FeSquare(&t2, &t1)       // 10..1
+	for i = 1; i < 10; i++ { // 19..10
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t2, &t2, &t1)     // 19..0
+	FeSquare(&t3, &t2)       // 20..1
+	for i = 1; i < 20; i++ { // 39..20
+		FeSquare(&t3, &t3)
+	}
+	FeMul(&t2, &t3, &t2)     // 39..0
+	FeSquare(&t2, &t2)       // 40..1
+	for i = 1; i < 10; i++ { // 49..10
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)     // 49..0
+	FeSquare(&t2, &t1)       // 50..1
+	for i = 1; i < 50; i++ { // 99..50
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t2, &t2, &t1)      // 99..0
+	FeSquare(&t3, &t2)        // 100..1
+	for i = 1; i < 100; i++ { // 199..100
+		FeSquare(&t3, &t3)
+	}
+	FeMul(&t2, &t3, &t2)     // 199..0
+	FeSquare(&t2, &t2)       // 200..1
+	for i = 1; i < 50; i++ { // 249..50
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)    // 249..0
+	FeSquare(&t1, &t1)      // 250..1
+	for i = 1; i < 5; i++ { // 254..5
+		FeSquare(&t1, &t1)
+	}
+	FeMul(out, &t1, &t0) // 254..5,3,1,0
+}
+
+func fePow22523(out, z *FieldElement) {
+	var t0, t1, t2 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(&t0, &t0)
+	for i = 1; i < 1; i++ {
+		FeSquare(&t0, &t0)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t1, &t0)
+	for i = 1; i < 5; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t1, &t0)
+	for i = 1; i < 10; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, &t1, &t0)
+	FeSquare(&t2, &t1)
+	for i = 1; i < 20; i++ {
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)
+	FeSquare(&t1, &t1)
+	for i = 1; i < 10; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t1, &t0)
+	for i = 1; i < 50; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, &t1, &t0)
+	FeSquare(&t2, &t1)
+	for i = 1; i < 100; i++ {
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)
+	FeSquare(&t1, &t1)
+	for i = 1; i < 50; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t0, &t0)
+	for i = 1; i < 2; i++ {
+		FeSquare(&t0, &t0)
+	}
+	FeMul(out, &t0, z)
+}
+
+// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 *
+// y^2 where d = -121665/121666.
+//
+// Several representations are used:
+//   ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z
+//   ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+//   CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+//   PreComputedGroupElement: (y+x,y-x,2dxy)
+
+type ProjectiveGroupElement struct {
+	X, Y, Z FieldElement
+}
+
+type ExtendedGroupElement struct {
+	X, Y, Z, T FieldElement
+}
+
+type CompletedGroupElement struct {
+	X, Y, Z, T FieldElement
+}
+
+type PreComputedGroupElement struct {
+	yPlusX, yMinusX, xy2d FieldElement
+}
+
+type CachedGroupElement struct {
+	yPlusX, yMinusX, Z, T2d FieldElement
+}
+
+func (p *ProjectiveGroupElement) Zero() {
+	FeZero(&p.X)
+	FeOne(&p.Y)
+	FeOne(&p.Z)
+}
+
+func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) {
+	var t0 FieldElement
+
+	FeSquare(&r.X, &p.X)
+	FeSquare(&r.Z, &p.Y)
+	FeSquare2(&r.T, &p.Z)
+	FeAdd(&r.Y, &p.X, &p.Y)
+	FeSquare(&t0, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.X)
+	FeSub(&r.Z, &r.Z, &r.X)
+	FeSub(&r.X, &t0, &r.Y)
+	FeSub(&r.T, &r.T, &r.Z)
+}
+
+func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) {
+	var recip, x, y FieldElement
+
+	FeInvert(&recip, &p.Z)
+	FeMul(&x, &p.X, &recip)
+	FeMul(&y, &p.Y, &recip)
+	FeToBytes(s, &y)
+	s[31] ^= FeIsNegative(&x) << 7
+}
+
+func (p *ExtendedGroupElement) Zero() {
+	FeZero(&p.X)
+	FeOne(&p.Y)
+	FeOne(&p.Z)
+	FeZero(&p.T)
+}
+
+func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) {
+	var q ProjectiveGroupElement
+	p.ToProjective(&q)
+	q.Double(r)
+}
+
+func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) {
+	FeAdd(&r.yPlusX, &p.Y, &p.X)
+	FeSub(&r.yMinusX, &p.Y, &p.X)
+	FeCopy(&r.Z, &p.Z)
+	FeMul(&r.T2d, &p.T, &d2)
+}
+
+func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) {
+	FeCopy(&r.X, &p.X)
+	FeCopy(&r.Y, &p.Y)
+	FeCopy(&r.Z, &p.Z)
+}
+
+func (p *ExtendedGroupElement) ToBytes(s *[32]byte) {
+	var recip, x, y FieldElement
+
+	FeInvert(&recip, &p.Z)
+	FeMul(&x, &p.X, &recip)
+	FeMul(&y, &p.Y, &recip)
+	FeToBytes(s, &y)
+	s[31] ^= FeIsNegative(&x) << 7
+}
+
+func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool {
+	var u, v, v3, vxx, check FieldElement
+
+	FeFromBytes(&p.Y, s)
+	FeOne(&p.Z)
+	FeSquare(&u, &p.Y)
+	FeMul(&v, &u, &d)
+	FeSub(&u, &u, &p.Z) // y = y^2-1
+	FeAdd(&v, &v, &p.Z) // v = dy^2+1
+
+	FeSquare(&v3, &v)
+	FeMul(&v3, &v3, &v) // v3 = v^3
+	FeSquare(&p.X, &v3)
+	FeMul(&p.X, &p.X, &v)
+	FeMul(&p.X, &p.X, &u) // x = uv^7
+
+	fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8)
+	FeMul(&p.X, &p.X, &v3)
+	FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8)
+
+	var tmpX, tmp2 [32]byte
+
+	FeSquare(&vxx, &p.X)
+	FeMul(&vxx, &vxx, &v)
+	FeSub(&check, &vxx, &u) // vx^2-u
+	if FeIsNonZero(&check) == 1 {
+		FeAdd(&check, &vxx, &u) // vx^2+u
+		if FeIsNonZero(&check) == 1 {
+			return false
+		}
+		FeMul(&p.X, &p.X, &SqrtM1)
+
+		FeToBytes(&tmpX, &p.X)
+		for i, v := range tmpX {
+			tmp2[31-i] = v
+		}
+	}
+
+	if FeIsNegative(&p.X) != (s[31] >> 7) {
+		FeNeg(&p.X, &p.X)
+	}
+
+	FeMul(&p.T, &p.X, &p.Y)
+	return true
+}
+
+func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) {
+	FeMul(&r.X, &p.X, &p.T)
+	FeMul(&r.Y, &p.Y, &p.Z)
+	FeMul(&r.Z, &p.Z, &p.T)
+}
+
+func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) {
+	FeMul(&r.X, &p.X, &p.T)
+	FeMul(&r.Y, &p.Y, &p.Z)
+	FeMul(&r.Z, &p.Z, &p.T)
+	FeMul(&r.T, &p.X, &p.Y)
+}
+
+func (p *PreComputedGroupElement) Zero() {
+	FeOne(&p.yPlusX)
+	FeOne(&p.yMinusX)
+	FeZero(&p.xy2d)
+}
+
+func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yPlusX)
+	FeMul(&r.Y, &r.Y, &q.yMinusX)
+	FeMul(&r.T, &q.T2d, &p.T)
+	FeMul(&r.X, &p.Z, &q.Z)
+	FeAdd(&t0, &r.X, &r.X)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeAdd(&r.Z, &t0, &r.T)
+	FeSub(&r.T, &t0, &r.T)
+}
+
+func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yMinusX)
+	FeMul(&r.Y, &r.Y, &q.yPlusX)
+	FeMul(&r.T, &q.T2d, &p.T)
+	FeMul(&r.X, &p.Z, &q.Z)
+	FeAdd(&t0, &r.X, &r.X)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeSub(&r.Z, &t0, &r.T)
+	FeAdd(&r.T, &t0, &r.T)
+}
+
+func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yPlusX)
+	FeMul(&r.Y, &r.Y, &q.yMinusX)
+	FeMul(&r.T, &q.xy2d, &p.T)
+	FeAdd(&t0, &p.Z, &p.Z)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeAdd(&r.Z, &t0, &r.T)
+	FeSub(&r.T, &t0, &r.T)
+}
+
+func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yMinusX)
+	FeMul(&r.Y, &r.Y, &q.yPlusX)
+	FeMul(&r.T, &q.xy2d, &p.T)
+	FeAdd(&t0, &p.Z, &p.Z)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeSub(&r.Z, &t0, &r.T)
+	FeAdd(&r.T, &t0, &r.T)
+}
+
+func slide(r *[256]int8, a *[32]byte) {
+	for i := range r {
+		r[i] = int8(1 & (a[i>>3] >> uint(i&7)))
+	}
+
+	for i := range r {
+		if r[i] != 0 {
+			for b := 1; b <= 6 && i+b < 256; b++ {
+				if r[i+b] != 0 {
+					if r[i]+(r[i+b]<<uint(b)) <= 15 {
+						r[i] += r[i+b] << uint(b)
+						r[i+b] = 0
+					} else if r[i]-(r[i+b]<<uint(b)) >= -15 {
+						r[i] -= r[i+b] << uint(b)
+						for k := i + b; k < 256; k++ {
+							if r[k] == 0 {
+								r[k] = 1
+								break
+							}
+							r[k] = 0
+						}
+					} else {
+						break
+					}
+				}
+			}
+		}
+	}
+}
+
+// GeDoubleScalarMultVartime sets r = a*A + b*B
+// where a = a[0]+256*a[1]+...+256^31 a[31].
+// and b = b[0]+256*b[1]+...+256^31 b[31].
+// B is the Ed25519 base point (x,4/5) with x positive.
+func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) {
+	var aSlide, bSlide [256]int8
+	var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A
+	var t CompletedGroupElement
+	var u, A2 ExtendedGroupElement
+	var i int
+
+	slide(&aSlide, a)
+	slide(&bSlide, b)
+
+	A.ToCached(&Ai[0])
+	A.Double(&t)
+	t.ToExtended(&A2)
+
+	for i := 0; i < 7; i++ {
+		geAdd(&t, &A2, &Ai[i])
+		t.ToExtended(&u)
+		u.ToCached(&Ai[i+1])
+	}
+
+	r.Zero()
+
+	for i = 255; i >= 0; i-- {
+		if aSlide[i] != 0 || bSlide[i] != 0 {
+			break
+		}
+	}
+
+	for ; i >= 0; i-- {
+		r.Double(&t)
+
+		if aSlide[i] > 0 {
+			t.ToExtended(&u)
+			geAdd(&t, &u, &Ai[aSlide[i]/2])
+		} else if aSlide[i] < 0 {
+			t.ToExtended(&u)
+			geSub(&t, &u, &Ai[(-aSlide[i])/2])
+		}
+
+		if bSlide[i] > 0 {
+			t.ToExtended(&u)
+			geMixedAdd(&t, &u, &bi[bSlide[i]/2])
+		} else if bSlide[i] < 0 {
+			t.ToExtended(&u)
+			geMixedSub(&t, &u, &bi[(-bSlide[i])/2])
+		}
+
+		t.ToProjective(r)
+	}
+}
+
+// equal returns 1 if b == c and 0 otherwise.
+func equal(b, c int32) int32 {
+	x := uint32(b ^ c)
+	x--
+	return int32(x >> 31)
+}
+
+// negative returns 1 if b < 0 and 0 otherwise.
+func negative(b int32) int32 {
+	return (b >> 31) & 1
+}
+
+func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) {
+	FeCMove(&t.yPlusX, &u.yPlusX, b)
+	FeCMove(&t.yMinusX, &u.yMinusX, b)
+	FeCMove(&t.xy2d, &u.xy2d, b)
+}
+
+func selectPoint(t *PreComputedGroupElement, pos int32, b int32) {
+	var minusT PreComputedGroupElement
+	bNegative := negative(b)
+	bAbs := b - (((-bNegative) & b) << 1)
+
+	t.Zero()
+	for i := int32(0); i < 8; i++ {
+		PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1))
+	}
+	FeCopy(&minusT.yPlusX, &t.yMinusX)
+	FeCopy(&minusT.yMinusX, &t.yPlusX)
+	FeNeg(&minusT.xy2d, &t.xy2d)
+	PreComputedGroupElementCMove(t, &minusT, bNegative)
+}
+
+// GeScalarMultBase computes h = a*B, where
+//   a = a[0]+256*a[1]+...+256^31 a[31]
+//   B is the Ed25519 base point (x,4/5) with x positive.
+//
+// Preconditions:
+//   a[31] <= 127
+func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) {
+	var e [64]int8
+
+	for i, v := range a {
+		e[2*i] = int8(v & 15)
+		e[2*i+1] = int8((v >> 4) & 15)
+	}
+
+	// each e[i] is between 0 and 15 and e[63] is between 0 and 7.
+
+	carry := int8(0)
+	for i := 0; i < 63; i++ {
+		e[i] += carry
+		carry = (e[i] + 8) >> 4
+		e[i] -= carry << 4
+	}
+	e[63] += carry
+	// each e[i] is between -8 and 8.
+
+	h.Zero()
+	var t PreComputedGroupElement
+	var r CompletedGroupElement
+	for i := int32(1); i < 64; i += 2 {
+		selectPoint(&t, i/2, int32(e[i]))
+		geMixedAdd(&r, h, &t)
+		r.ToExtended(h)
+	}
+
+	var s ProjectiveGroupElement
+
+	h.Double(&r)
+	r.ToProjective(&s)
+	s.Double(&r)
+	r.ToProjective(&s)
+	s.Double(&r)
+	r.ToProjective(&s)
+	s.Double(&r)
+	r.ToExtended(h)
+
+	for i := int32(0); i < 64; i += 2 {
+		selectPoint(&t, i/2, int32(e[i]))
+		geMixedAdd(&r, h, &t)
+		r.ToExtended(h)
+	}
+}
+
+// The scalars are GF(2^252 + 27742317777372353535851937790883648493).
+
+// 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)
+}
diff --git a/internal/extra25519/extra25519.go b/internal/extra25519/extra25519.go
new file mode 100644
index 0000000..7e1d227
--- /dev/null
+++ b/internal/extra25519/extra25519.go
@@ -0,0 +1,291 @@
+// Copyright 2013 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 extra25519
+
+import "gitlab.com/yawning/obfs4.git/internal/edwards25519"
+
+// sqrtMinusAPlus2 is sqrt(-(486662+2))
+var sqrtMinusAPlus2 = edwards25519.FieldElement{
+	-12222970, -8312128, -11511410, 9067497, -15300785, -241793, 25456130, 14121551, -12187136, 3972024,
+}
+
+// sqrtMinusHalf is sqrt(-1/2)
+var sqrtMinusHalf = edwards25519.FieldElement{
+	-17256545, 3971863, 28865457, -1750208, 27359696, -16640980, 12573105, 1002827, -163343, 11073975,
+}
+
+// halfQMinus1Bytes is (2^255-20)/2 expressed in little endian form.
+var halfQMinus1Bytes = [32]byte{
+	0xf6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f,
+}
+
+// feBytesLess returns one if a <= b and zero otherwise.
+func feBytesLE(a, b *[32]byte) int32 {
+	equalSoFar := int32(-1)
+	greater := int32(0)
+
+	for i := uint(31); i < 32; i-- {
+		x := int32(a[i])
+		y := int32(b[i])
+
+		greater = (^equalSoFar & greater) | (equalSoFar & ((x - y) >> 31))
+		equalSoFar = equalSoFar & (((x ^ y) - 1) >> 31)
+	}
+
+	return int32(^equalSoFar & 1 & greater)
+}
+
+// UnsafeBrokenScalarBaseMult computes a curve25519 public key from a private
+// key and also a uniform representative for that public key. Note that this
+// function will fail and return false for about half of private keys.
+// See http://elligator.cr.yp.to/elligator-20130828.pdf.
+func UnsafeBrokenScalarBaseMult(publicKey, representative, privateKey *[32]byte) bool {
+	var maskedPrivateKey [32]byte
+	copy(maskedPrivateKey[:], privateKey[:])
+
+	maskedPrivateKey[0] &= 248
+	maskedPrivateKey[31] &= 127
+	maskedPrivateKey[31] |= 64
+
+	var A edwards25519.ExtendedGroupElement
+	edwards25519.GeScalarMultBase(&A, &maskedPrivateKey)
+
+	var inv1 edwards25519.FieldElement
+	edwards25519.FeSub(&inv1, &A.Z, &A.Y)
+	edwards25519.FeMul(&inv1, &inv1, &A.X)
+	edwards25519.FeInvert(&inv1, &inv1)
+
+	var t0, u edwards25519.FieldElement
+	edwards25519.FeMul(&u, &inv1, &A.X)
+	edwards25519.FeAdd(&t0, &A.Y, &A.Z)
+	edwards25519.FeMul(&u, &u, &t0)
+
+	var v edwards25519.FieldElement
+	edwards25519.FeMul(&v, &t0, &inv1)
+	edwards25519.FeMul(&v, &v, &A.Z)
+	edwards25519.FeMul(&v, &v, &sqrtMinusAPlus2)
+
+	var b edwards25519.FieldElement
+	edwards25519.FeAdd(&b, &u, &edwards25519.A)
+
+	var c, b3, b7, b8 edwards25519.FieldElement
+	edwards25519.FeSquare(&b3, &b)   // 2
+	edwards25519.FeMul(&b3, &b3, &b) // 3
+	edwards25519.FeSquare(&c, &b3)   // 6
+	edwards25519.FeMul(&b7, &c, &b)  // 7
+	edwards25519.FeMul(&b8, &b7, &b) // 8
+	edwards25519.FeMul(&c, &b7, &u)
+	q58(&c, &c)
+
+	var chi edwards25519.FieldElement
+	edwards25519.FeSquare(&chi, &c)
+	edwards25519.FeSquare(&chi, &chi)
+
+	edwards25519.FeSquare(&t0, &u)
+	edwards25519.FeMul(&chi, &chi, &t0)
+
+	edwards25519.FeSquare(&t0, &b7) // 14
+	edwards25519.FeMul(&chi, &chi, &t0)
+	edwards25519.FeNeg(&chi, &chi)
+
+	var chiBytes [32]byte
+	edwards25519.FeToBytes(&chiBytes, &chi)
+	// chi[1] is either 0 or 0xff
+	if chiBytes[1] == 0xff {
+		return false
+	}
+
+	// Calculate r1 = sqrt(-u/(2*(u+A)))
+	var r1 edwards25519.FieldElement
+	edwards25519.FeMul(&r1, &c, &u)
+	edwards25519.FeMul(&r1, &r1, &b3)
+	edwards25519.FeMul(&r1, &r1, &sqrtMinusHalf)
+
+	var maybeSqrtM1 edwards25519.FieldElement
+	edwards25519.FeSquare(&t0, &r1)
+	edwards25519.FeMul(&t0, &t0, &b)
+	edwards25519.FeAdd(&t0, &t0, &t0)
+	edwards25519.FeAdd(&t0, &t0, &u)
+
+	edwards25519.FeOne(&maybeSqrtM1)
+	edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
+	edwards25519.FeMul(&r1, &r1, &maybeSqrtM1)
+
+	// Calculate r = sqrt(-(u+A)/(2u))
+	var r edwards25519.FieldElement
+	edwards25519.FeSquare(&t0, &c)   // 2
+	edwards25519.FeMul(&t0, &t0, &c) // 3
+	edwards25519.FeSquare(&t0, &t0)  // 6
+	edwards25519.FeMul(&r, &t0, &c)  // 7
+
+	edwards25519.FeSquare(&t0, &u)   // 2
+	edwards25519.FeMul(&t0, &t0, &u) // 3
+	edwards25519.FeMul(&r, &r, &t0)
+
+	edwards25519.FeSquare(&t0, &b8)   // 16
+	edwards25519.FeMul(&t0, &t0, &b8) // 24
+	edwards25519.FeMul(&t0, &t0, &b)  // 25
+	edwards25519.FeMul(&r, &r, &t0)
+	edwards25519.FeMul(&r, &r, &sqrtMinusHalf)
+
+	edwards25519.FeSquare(&t0, &r)
+	edwards25519.FeMul(&t0, &t0, &u)
+	edwards25519.FeAdd(&t0, &t0, &t0)
+	edwards25519.FeAdd(&t0, &t0, &b)
+	edwards25519.FeOne(&maybeSqrtM1)
+	edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0))
+	edwards25519.FeMul(&r, &r, &maybeSqrtM1)
+
+	var vBytes [32]byte
+	edwards25519.FeToBytes(&vBytes, &v)
+	vInSquareRootImage := feBytesLE(&vBytes, &halfQMinus1Bytes)
+	edwards25519.FeCMove(&r, &r1, vInSquareRootImage)
+
+	edwards25519.FeToBytes(publicKey, &u)
+	edwards25519.FeToBytes(representative, &r)
+	return true
+}
+
+// q58 calculates out = z^((p-5)/8).
+func q58(out, z *edwards25519.FieldElement) {
+	var t1, t2, t3 edwards25519.FieldElement
+	var i int
+
+	edwards25519.FeSquare(&t1, z)     // 2^1
+	edwards25519.FeMul(&t1, &t1, z)   // 2^1 + 2^0
+	edwards25519.FeSquare(&t1, &t1)   // 2^2 + 2^1
+	edwards25519.FeSquare(&t2, &t1)   // 2^3 + 2^2
+	edwards25519.FeSquare(&t2, &t2)   // 2^4 + 2^3
+	edwards25519.FeMul(&t2, &t2, &t1) // 4,3,2,1
+	edwards25519.FeMul(&t1, &t2, z)   // 4..0
+	edwards25519.FeSquare(&t2, &t1)   // 5..1
+	for i = 1; i < 5; i++ {           // 9,8,7,6,5
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
+	edwards25519.FeSquare(&t2, &t1)   // 10..1
+	for i = 1; i < 10; i++ {          // 19..10
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t2, &t2, &t1) // 19..0
+	edwards25519.FeSquare(&t3, &t2)   // 20..1
+	for i = 1; i < 20; i++ {          // 39..20
+		edwards25519.FeSquare(&t3, &t3)
+	}
+	edwards25519.FeMul(&t2, &t3, &t2) // 39..0
+	edwards25519.FeSquare(&t2, &t2)   // 40..1
+	for i = 1; i < 10; i++ {          // 49..10
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t1, &t2, &t1) // 49..0
+	edwards25519.FeSquare(&t2, &t1)   // 50..1
+	for i = 1; i < 50; i++ {          // 99..50
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t2, &t2, &t1) // 99..0
+	edwards25519.FeSquare(&t3, &t2)   // 100..1
+	for i = 1; i < 100; i++ {         // 199..100
+		edwards25519.FeSquare(&t3, &t3)
+	}
+	edwards25519.FeMul(&t2, &t3, &t2) // 199..0
+	edwards25519.FeSquare(&t2, &t2)   // 200..1
+	for i = 1; i < 50; i++ {          // 249..50
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t1, &t2, &t1) // 249..0
+	edwards25519.FeSquare(&t1, &t1)   // 250..1
+	edwards25519.FeSquare(&t1, &t1)   // 251..2
+	edwards25519.FeMul(out, &t1, z)   // 251..2,0
+}
+
+// chi calculates out = z^((p-1)/2). The result is either 1, 0, or -1 depending
+// on whether z is a non-zero square, zero, or a non-square.
+func chi(out, z *edwards25519.FieldElement) {
+	var t0, t1, t2, t3 edwards25519.FieldElement
+	var i int
+
+	edwards25519.FeSquare(&t0, z)     // 2^1
+	edwards25519.FeMul(&t1, &t0, z)   // 2^1 + 2^0
+	edwards25519.FeSquare(&t0, &t1)   // 2^2 + 2^1
+	edwards25519.FeSquare(&t2, &t0)   // 2^3 + 2^2
+	edwards25519.FeSquare(&t2, &t2)   // 4,3
+	edwards25519.FeMul(&t2, &t2, &t0) // 4,3,2,1
+	edwards25519.FeMul(&t1, &t2, z)   // 4..0
+	edwards25519.FeSquare(&t2, &t1)   // 5..1
+	for i = 1; i < 5; i++ {           // 9,8,7,6,5
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
+	edwards25519.FeSquare(&t2, &t1)   // 10..1
+	for i = 1; i < 10; i++ {          // 19..10
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t2, &t2, &t1) // 19..0
+	edwards25519.FeSquare(&t3, &t2)   // 20..1
+	for i = 1; i < 20; i++ {          // 39..20
+		edwards25519.FeSquare(&t3, &t3)
+	}
+	edwards25519.FeMul(&t2, &t3, &t2) // 39..0
+	edwards25519.FeSquare(&t2, &t2)   // 40..1
+	for i = 1; i < 10; i++ {          // 49..10
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t1, &t2, &t1) // 49..0
+	edwards25519.FeSquare(&t2, &t1)   // 50..1
+	for i = 1; i < 50; i++ {          // 99..50
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t2, &t2, &t1) // 99..0
+	edwards25519.FeSquare(&t3, &t2)   // 100..1
+	for i = 1; i < 100; i++ {         // 199..100
+		edwards25519.FeSquare(&t3, &t3)
+	}
+	edwards25519.FeMul(&t2, &t3, &t2) // 199..0
+	edwards25519.FeSquare(&t2, &t2)   // 200..1
+	for i = 1; i < 50; i++ {          // 249..50
+		edwards25519.FeSquare(&t2, &t2)
+	}
+	edwards25519.FeMul(&t1, &t2, &t1) // 249..0
+	edwards25519.FeSquare(&t1, &t1)   // 250..1
+	for i = 1; i < 4; i++ {           // 253..4
+		edwards25519.FeSquare(&t1, &t1)
+	}
+	edwards25519.FeMul(out, &t1, &t0) // 253..4,2,1
+}
+
+// UnsafeBrokenRepresentativeToPublicKey converts a uniform representative
+// value for a curve25519 public key, as produced by UnsafeBrokenScalarBaseMult,
+// to a curve25519 public key.
+func UnsafeBrokenRepresentativeToPublicKey(publicKey, representative *[32]byte) {
+	var rr2, v, e edwards25519.FieldElement
+	edwards25519.FeFromBytes(&rr2, representative)
+
+	edwards25519.FeSquare2(&rr2, &rr2)
+	rr2[0]++
+	edwards25519.FeInvert(&rr2, &rr2)
+	edwards25519.FeMul(&v, &edwards25519.A, &rr2)
+	edwards25519.FeNeg(&v, &v)
+
+	var v2, v3 edwards25519.FieldElement
+	edwards25519.FeSquare(&v2, &v)
+	edwards25519.FeMul(&v3, &v, &v2)
+	edwards25519.FeAdd(&e, &v3, &v)
+	edwards25519.FeMul(&v2, &v2, &edwards25519.A)
+	edwards25519.FeAdd(&e, &v2, &e)
+	chi(&e, &e)
+	var eBytes [32]byte
+	edwards25519.FeToBytes(&eBytes, &e)
+	// eBytes[1] is either 0 (for e = 1) or 0xff (for e = -1)
+	eIsMinus1 := int32(eBytes[1]) & 1
+	var negV edwards25519.FieldElement
+	edwards25519.FeNeg(&negV, &v)
+	edwards25519.FeCMove(&v, &negV, eIsMinus1)
+
+	edwards25519.FeZero(&v2)
+	edwards25519.FeCMove(&v2, &edwards25519.A, eIsMinus1)
+	edwards25519.FeSub(&v, &v, &v2)
+
+	edwards25519.FeToBytes(publicKey, &v)
+}
diff --git a/internal/extra25519/extra25519_test.go b/internal/extra25519/extra25519_test.go
new file mode 100644
index 0000000..7cf1e97
--- /dev/null
+++ b/internal/extra25519/extra25519_test.go
@@ -0,0 +1,61 @@
+// Copyright 2013 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 extra25519
+
+import (
+	"bytes"
+	"crypto/rand"
+	"testing"
+
+	"golang.org/x/crypto/curve25519"
+)
+
+func TestElligator(t *testing.T) {
+	var publicKey, publicKey2, publicKey3, representative, privateKey [32]byte
+
+	for i := 0; i < 1000; i++ {
+		rand.Reader.Read(privateKey[:])
+
+		if !UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey) {
+			continue
+		}
+		UnsafeBrokenRepresentativeToPublicKey(&publicKey2, &representative)
+		if !bytes.Equal(publicKey[:], publicKey2[:]) {
+			t.Fatal("The resulting public key doesn't match the initial one.")
+		}
+
+		curve25519.ScalarBaseMult(&publicKey3, &privateKey)
+		if !bytes.Equal(publicKey[:], publicKey3[:]) {
+			t.Fatal("The public key doesn't match the value that curve25519 produced.")
+		}
+	}
+}
+
+func BenchmarkKeyGeneration(b *testing.B) {
+	var publicKey, representative, privateKey [32]byte
+
+	// Find the private key that results in a point that's in the image of the map.
+	for {
+		rand.Reader.Read(privateKey[:])
+		if UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey) {
+			break
+		}
+	}
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		UnsafeBrokenScalarBaseMult(&publicKey, &representative, &privateKey)
+	}
+}
+
+func BenchmarkMap(b *testing.B) {
+	var publicKey, representative [32]byte
+	rand.Reader.Read(representative[:])
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		UnsafeBrokenRepresentativeToPublicKey(&publicKey, &representative)
+	}
+}

    

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