Replace curve25519 ref implementation with latest ref10 from Supercop.

AUTHORS

@@ -44,9 +44,9 @@ crypto_auth/hmacsha512
 ------------------
 Colin Percival
 
-crypto_scalarmult/curve25519/ref
+crypto_scalarmult/curve25519/ref10
 --------------------------------
-Matthew Dempsky (Mochi Media)
+Daniel J. Bernstein
 
 crypto_scalarmult/curve25519/donna_c64
 --------------------------------------

src/libsodium/Makefile.am

@@ -208,9 +208,24 @@ libsodium_la_SOURCES += \
 	crypto_scalarmult/curve25519/donna_c64/smult_curve25519_donna_c64.c
 else
 libsodium_la_SOURCES += \
-	crypto_scalarmult/curve25519/ref/api.h \
-	crypto_scalarmult/curve25519/ref/base_curve25519_ref.c \
-	crypto_scalarmult/curve25519/ref/smult_curve25519_ref.c
+	crypto_scalarmult/curve25519/ref10/api.h \
+	crypto_scalarmult/curve25519/ref10/base.c \
+	crypto_scalarmult/curve25519/ref10/fe.h \
+	crypto_scalarmult/curve25519/ref10/fe_0.c \
+	crypto_scalarmult/curve25519/ref10/fe_1.c \
+	crypto_scalarmult/curve25519/ref10/fe_add.c \
+	crypto_scalarmult/curve25519/ref10/fe_copy.c \
+	crypto_scalarmult/curve25519/ref10/fe_cswap.c \
+	crypto_scalarmult/curve25519/ref10/fe_frombytes.c \
+	crypto_scalarmult/curve25519/ref10/fe_invert.c \
+	crypto_scalarmult/curve25519/ref10/fe_mul.c \
+	crypto_scalarmult/curve25519/ref10/fe_mul121666.c \
+	crypto_scalarmult/curve25519/ref10/fe_sq.c \
+	crypto_scalarmult/curve25519/ref10/fe_sub.c \
+	crypto_scalarmult/curve25519/ref10/fe_tobytes.c \
+	crypto_scalarmult/curve25519/ref10/montgomery.h \
+	crypto_scalarmult/curve25519/ref10/pow225521.h \
+	crypto_scalarmult/curve25519/ref10/scalarmult.c
 endif
 
 if HAVE_AMD64_ASM

src/libsodium/crypto_scalarmult/curve25519/ref10/api.h

@@ -0,0 +1,5 @@
+
+#include "crypto_scalarmult_curve25519.h"
+
+#define crypto_scalarmult crypto_scalarmult_curve25519
+#define crypto_scalarmult_base crypto_scalarmult_curve25519_base

src/libsodium/crypto_scalarmult/curve25519/ref10/base.c

@@ -0,0 +1,14 @@
+
+#include "api.h"
+#include "crypto_scalarmult.h"
+
+#ifndef HAVE_TI_MODE
+
+static const unsigned char basepoint[32] = {9};
+
+int crypto_scalarmult_base(unsigned char *q,const unsigned char *n)
+{
+  return crypto_scalarmult(q,n,basepoint);
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe.h

@@ -0,0 +1,44 @@
+#ifndef FE_H
+#define FE_H
+
+#include "crypto_int32.h"
+
+typedef crypto_int32 fe[10];
+
+/*
+fe means field element.
+Here the field is \Z/(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.
+*/
+
+#define fe_frombytes crypto_scalarmult_curve25519_ref10_fe_frombytes
+#define fe_tobytes crypto_scalarmult_curve25519_ref10_fe_tobytes
+#define fe_copy crypto_scalarmult_curve25519_ref10_fe_copy
+#define fe_0 crypto_scalarmult_curve25519_ref10_fe_0
+#define fe_1 crypto_scalarmult_curve25519_ref10_fe_1
+#define fe_cswap crypto_scalarmult_curve25519_ref10_fe_cswap
+#define fe_add crypto_scalarmult_curve25519_ref10_fe_add
+#define fe_sub crypto_scalarmult_curve25519_ref10_fe_sub
+#define fe_mul crypto_scalarmult_curve25519_ref10_fe_mul
+#define fe_sq crypto_scalarmult_curve25519_ref10_fe_sq
+#define fe_mul121666 crypto_scalarmult_curve25519_ref10_fe_mul121666
+#define fe_invert crypto_scalarmult_curve25519_ref10_fe_invert
+
+extern void fe_frombytes(fe,const unsigned char *);
+extern void fe_tobytes(unsigned char *,fe);
+
+extern void fe_copy(fe,fe);
+extern void fe_0(fe);
+extern void fe_1(fe);
+extern void fe_cswap(fe,fe,unsigned int);
+
+extern void fe_add(fe,fe,fe);
+extern void fe_sub(fe,fe,fe);
+extern void fe_mul(fe,fe,fe);
+extern void fe_sq(fe,fe);
+extern void fe_mul121666(fe,fe);
+extern void fe_invert(fe,fe);
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_0.c

@@ -0,0 +1,23 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+h = 0
+*/
+
+void fe_0(fe h)
+{
+  h[0] = 0;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_1.c

@@ -0,0 +1,23 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+h = 1
+*/
+
+void fe_1(fe h)
+{
+  h[0] = 1;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_add.c

@@ -0,0 +1,61 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+h = f + g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| 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*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h,fe f,fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 + g0;
+  crypto_int32 h1 = f1 + g1;
+  crypto_int32 h2 = f2 + g2;
+  crypto_int32 h3 = f3 + g3;
+  crypto_int32 h4 = f4 + g4;
+  crypto_int32 h5 = f5 + g5;
+  crypto_int32 h6 = f6 + g6;
+  crypto_int32 h7 = f7 + g7;
+  crypto_int32 h8 = f8 + g8;
+  crypto_int32 h9 = f9 + g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_copy.c

@@ -0,0 +1,33 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+h = f
+*/
+
+void fe_copy(fe h,fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  h[0] = f0;
+  h[1] = f1;
+  h[2] = f2;
+  h[3] = f3;
+  h[4] = f4;
+  h[5] = f5;
+  h[6] = f6;
+  h[7] = f7;
+  h[8] = f8;
+  h[9] = f9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_cswap.c

@@ -0,0 +1,77 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+Replace (f,g) with (g,f) if b == 1;
+replace (f,g) with (f,g) if b == 0.
+
+Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,fe g,unsigned int b)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 x0 = f0 ^ g0;
+  crypto_int32 x1 = f1 ^ g1;
+  crypto_int32 x2 = f2 ^ g2;
+  crypto_int32 x3 = f3 ^ g3;
+  crypto_int32 x4 = f4 ^ g4;
+  crypto_int32 x5 = f5 ^ g5;
+  crypto_int32 x6 = f6 ^ g6;
+  crypto_int32 x7 = f7 ^ g7;
+  crypto_int32 x8 = f8 ^ g8;
+  crypto_int32 x9 = f9 ^ g9;
+  b = -b;
+  x0 &= b;
+  x1 &= b;
+  x2 &= b;
+  x3 &= b;
+  x4 &= b;
+  x5 &= b;
+  x6 &= b;
+  x7 &= b;
+  x8 &= b;
+  x9 &= b;
+  f[0] = f0 ^ x0;
+  f[1] = f1 ^ x1;
+  f[2] = f2 ^ x2;
+  f[3] = f3 ^ x3;
+  f[4] = f4 ^ x4;
+  f[5] = f5 ^ x5;
+  f[6] = f6 ^ x6;
+  f[7] = f7 ^ x7;
+  f[8] = f8 ^ x8;
+  f[9] = f9 ^ x9;
+  g[0] = g0 ^ x0;
+  g[1] = g1 ^ x1;
+  g[2] = g2 ^ x2;
+  g[3] = g3 ^ x3;
+  g[4] = g4 ^ x4;
+  g[5] = g5 ^ x5;
+  g[6] = g6 ^ x6;
+  g[7] = g7 ^ x7;
+  g[8] = g8 ^ x8;
+  g[9] = g9 ^ x9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_frombytes.c

@@ -0,0 +1,73 @@
+#include "fe.h"
+#include "crypto_int64.h"
+#include "crypto_uint64.h"
+
+#ifndef HAVE_TI_MODE
+
+static crypto_uint64 load_3(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  return result;
+}
+
+static crypto_uint64 load_4(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  result |= ((crypto_uint64) in[3]) << 24;
+  return result;
+}
+
+void fe_frombytes(fe h,const unsigned char *s)
+{
+  crypto_int64 h0 = load_4(s);
+  crypto_int64 h1 = load_3(s + 4) << 6;
+  crypto_int64 h2 = load_3(s + 7) << 5;
+  crypto_int64 h3 = load_3(s + 10) << 3;
+  crypto_int64 h4 = load_3(s + 13) << 2;
+  crypto_int64 h5 = load_4(s + 16);
+  crypto_int64 h6 = load_3(s + 20) << 7;
+  crypto_int64 h7 = load_3(s + 23) << 5;
+  crypto_int64 h8 = load_3(s + 26) << 4;
+  crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_invert.c

@@ -0,0 +1,18 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+void fe_invert(fe out,fe z)
+{
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+#include "pow225521.h"
+
+  return;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_mul.c

@@ -0,0 +1,257 @@
+#include "fe.h"
+#include "crypto_int64.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+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.
+*/
+
+void fe_mul(fe h,fe f,fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 g1_19 = 19 * g1; /* 1.4*2^29 */
+  crypto_int32 g2_19 = 19 * g2; /* 1.4*2^30; still ok */
+  crypto_int32 g3_19 = 19 * g3;
+  crypto_int32 g4_19 = 19 * g4;
+  crypto_int32 g5_19 = 19 * g5;
+  crypto_int32 g6_19 = 19 * g6;
+  crypto_int32 g7_19 = 19 * g7;
+  crypto_int32 g8_19 = 19 * g8;
+  crypto_int32 g9_19 = 19 * g9;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f9_2 = 2 * f9;
+  crypto_int64 f0g0    = f0   * (crypto_int64) g0;
+  crypto_int64 f0g1    = f0   * (crypto_int64) g1;
+  crypto_int64 f0g2    = f0   * (crypto_int64) g2;
+  crypto_int64 f0g3    = f0   * (crypto_int64) g3;
+  crypto_int64 f0g4    = f0   * (crypto_int64) g4;
+  crypto_int64 f0g5    = f0   * (crypto_int64) g5;
+  crypto_int64 f0g6    = f0   * (crypto_int64) g6;
+  crypto_int64 f0g7    = f0   * (crypto_int64) g7;
+  crypto_int64 f0g8    = f0   * (crypto_int64) g8;
+  crypto_int64 f0g9    = f0   * (crypto_int64) g9;
+  crypto_int64 f1g0    = f1   * (crypto_int64) g0;
+  crypto_int64 f1g1_2  = f1_2 * (crypto_int64) g1;
+  crypto_int64 f1g2    = f1   * (crypto_int64) g2;
+  crypto_int64 f1g3_2  = f1_2 * (crypto_int64) g3;
+  crypto_int64 f1g4    = f1   * (crypto_int64) g4;
+  crypto_int64 f1g5_2  = f1_2 * (crypto_int64) g5;
+  crypto_int64 f1g6    = f1   * (crypto_int64) g6;
+  crypto_int64 f1g7_2  = f1_2 * (crypto_int64) g7;
+  crypto_int64 f1g8    = f1   * (crypto_int64) g8;
+  crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
+  crypto_int64 f2g0    = f2   * (crypto_int64) g0;
+  crypto_int64 f2g1    = f2   * (crypto_int64) g1;
+  crypto_int64 f2g2    = f2   * (crypto_int64) g2;
+  crypto_int64 f2g3    = f2   * (crypto_int64) g3;
+  crypto_int64 f2g4    = f2   * (crypto_int64) g4;
+  crypto_int64 f2g5    = f2   * (crypto_int64) g5;
+  crypto_int64 f2g6    = f2   * (crypto_int64) g6;
+  crypto_int64 f2g7    = f2   * (crypto_int64) g7;
+  crypto_int64 f2g8_19 = f2   * (crypto_int64) g8_19;
+  crypto_int64 f2g9_19 = f2   * (crypto_int64) g9_19;
+  crypto_int64 f3g0    = f3   * (crypto_int64) g0;
+  crypto_int64 f3g1_2  = f3_2 * (crypto_int64) g1;
+  crypto_int64 f3g2    = f3   * (crypto_int64) g2;
+  crypto_int64 f3g3_2  = f3_2 * (crypto_int64) g3;
+  crypto_int64 f3g4    = f3   * (crypto_int64) g4;
+  crypto_int64 f3g5_2  = f3_2 * (crypto_int64) g5;
+  crypto_int64 f3g6    = f3   * (crypto_int64) g6;
+  crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
+  crypto_int64 f3g8_19 = f3   * (crypto_int64) g8_19;
+  crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
+  crypto_int64 f4g0    = f4   * (crypto_int64) g0;
+  crypto_int64 f4g1    = f4   * (crypto_int64) g1;
+  crypto_int64 f4g2    = f4   * (crypto_int64) g2;
+  crypto_int64 f4g3    = f4   * (crypto_int64) g3;
+  crypto_int64 f4g4    = f4   * (crypto_int64) g4;
+  crypto_int64 f4g5    = f4   * (crypto_int64) g5;
+  crypto_int64 f4g6_19 = f4   * (crypto_int64) g6_19;
+  crypto_int64 f4g7_19 = f4   * (crypto_int64) g7_19;
+  crypto_int64 f4g8_19 = f4   * (crypto_int64) g8_19;
+  crypto_int64 f4g9_19 = f4   * (crypto_int64) g9_19;
+  crypto_int64 f5g0    = f5   * (crypto_int64) g0;
+  crypto_int64 f5g1_2  = f5_2 * (crypto_int64) g1;
+  crypto_int64 f5g2    = f5   * (crypto_int64) g2;
+  crypto_int64 f5g3_2  = f5_2 * (crypto_int64) g3;
+  crypto_int64 f5g4    = f5   * (crypto_int64) g4;
+  crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
+  crypto_int64 f5g6_19 = f5   * (crypto_int64) g6_19;
+  crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
+  crypto_int64 f5g8_19 = f5   * (crypto_int64) g8_19;
+  crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
+  crypto_int64 f6g0    = f6   * (crypto_int64) g0;
+  crypto_int64 f6g1    = f6   * (crypto_int64) g1;
+  crypto_int64 f6g2    = f6   * (crypto_int64) g2;
+  crypto_int64 f6g3    = f6   * (crypto_int64) g3;
+  crypto_int64 f6g4_19 = f6   * (crypto_int64) g4_19;
+  crypto_int64 f6g5_19 = f6   * (crypto_int64) g5_19;
+  crypto_int64 f6g6_19 = f6   * (crypto_int64) g6_19;
+  crypto_int64 f6g7_19 = f6   * (crypto_int64) g7_19;
+  crypto_int64 f6g8_19 = f6   * (crypto_int64) g8_19;
+  crypto_int64 f6g9_19 = f6   * (crypto_int64) g9_19;
+  crypto_int64 f7g0    = f7   * (crypto_int64) g0;
+  crypto_int64 f7g1_2  = f7_2 * (crypto_int64) g1;
+  crypto_int64 f7g2    = f7   * (crypto_int64) g2;
+  crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
+  crypto_int64 f7g4_19 = f7   * (crypto_int64) g4_19;
+  crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
+  crypto_int64 f7g6_19 = f7   * (crypto_int64) g6_19;
+  crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
+  crypto_int64 f7g8_19 = f7   * (crypto_int64) g8_19;
+  crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
+  crypto_int64 f8g0    = f8   * (crypto_int64) g0;
+  crypto_int64 f8g1    = f8   * (crypto_int64) g1;
+  crypto_int64 f8g2_19 = f8   * (crypto_int64) g2_19;
+  crypto_int64 f8g3_19 = f8   * (crypto_int64) g3_19;
+  crypto_int64 f8g4_19 = f8   * (crypto_int64) g4_19;
+  crypto_int64 f8g5_19 = f8   * (crypto_int64) g5_19;
+  crypto_int64 f8g6_19 = f8   * (crypto_int64) g6_19;
+  crypto_int64 f8g7_19 = f8   * (crypto_int64) g7_19;
+  crypto_int64 f8g8_19 = f8   * (crypto_int64) g8_19;
+  crypto_int64 f8g9_19 = f8   * (crypto_int64) g9_19;
+  crypto_int64 f9g0    = f9   * (crypto_int64) g0;
+  crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
+  crypto_int64 f9g2_19 = f9   * (crypto_int64) g2_19;
+  crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
+  crypto_int64 f9g4_19 = f9   * (crypto_int64) g4_19;
+  crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
+  crypto_int64 f9g6_19 = f9   * (crypto_int64) g6_19;
+  crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
+  crypto_int64 f9g8_19 = f9   * (crypto_int64) g8_19;
+  crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
+  crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
+  crypto_int64 h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
+  crypto_int64 h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
+  crypto_int64 h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
+  crypto_int64 h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
+  crypto_int64 h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
+  crypto_int64 h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
+  crypto_int64 h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
+  crypto_int64 h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
+  crypto_int64 h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  /*
+  |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
+  */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  /* |h0| <= 2^25 */
+  /* |h4| <= 2^25 */
+  /* |h1| <= 1.51*2^58 */
+  /* |h5| <= 1.51*2^58 */
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 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 */
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 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 */
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 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 */
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 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 */
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  /* |h9| <= 2^24; from now on fits into int32 unchanged */
+  /* |h0| <= 1.8*2^37 */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  /* |h0| <= 2^25; from now on fits into int32 unchanged */
+  /* |h1| <= 1.01*2^24 */
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_mul121666.c

@@ -0,0 +1,74 @@
+#include "fe.h"
+#include "crypto_int64.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+h = f * 121666
+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.
+*/
+
+void fe_mul121666(fe h,fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int64 h0 = f0 * (crypto_int64) 121666;
+  crypto_int64 h1 = f1 * (crypto_int64) 121666;
+  crypto_int64 h2 = f2 * (crypto_int64) 121666;
+  crypto_int64 h3 = f3 * (crypto_int64) 121666;
+  crypto_int64 h4 = f4 * (crypto_int64) 121666;
+  crypto_int64 h5 = f5 * (crypto_int64) 121666;
+  crypto_int64 h6 = f6 * (crypto_int64) 121666;
+  crypto_int64 h7 = f7 * (crypto_int64) 121666;
+  crypto_int64 h8 = f8 * (crypto_int64) 121666;
+  crypto_int64 h9 = f9 * (crypto_int64) 121666;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_sq.c

@@ -0,0 +1,153 @@
+#include "fe.h"
+#include "crypto_int64.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+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.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h,fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 f0_2 = 2 * f0;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f2_2 = 2 * f2;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f4_2 = 2 * f4;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f6_2 = 2 * f6;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f5_38 = 38 * f5; /* 1.31*2^30 */
+  crypto_int32 f6_19 = 19 * f6; /* 1.31*2^30 */
+  crypto_int32 f7_38 = 38 * f7; /* 1.31*2^30 */
+  crypto_int32 f8_19 = 19 * f8; /* 1.31*2^30 */
+  crypto_int32 f9_38 = 38 * f9; /* 1.31*2^30 */
+  crypto_int64 f0f0    = f0   * (crypto_int64) f0;
+  crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
+  crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
+  crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
+  crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
+  crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
+  crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
+  crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
+  crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
+  crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
+  crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
+  crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
+  crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
+  crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
+  crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
+  crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
+  crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
+  crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
+  crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
+  crypto_int64 f2f2    = f2   * (crypto_int64) f2;
+  crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
+  crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
+  crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
+  crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
+  crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
+  crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
+  crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
+  crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
+  crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
+  crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
+  crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
+  crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
+  crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
+  crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
+  crypto_int64 f4f4    = f4   * (crypto_int64) f4;
+  crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
+  crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
+  crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
+  crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
+  crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
+  crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
+  crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
+  crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
+  crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
+  crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
+  crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
+  crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
+  crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
+  crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
+  crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
+  crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
+  crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
+  crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
+  crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
+  crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
+  crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_sub.c

@@ -0,0 +1,61 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| 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*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h,fe f,fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 - g0;
+  crypto_int32 h1 = f1 - g1;
+  crypto_int32 h2 = f2 - g2;
+  crypto_int32 h3 = f3 - g3;
+  crypto_int32 h4 = f4 - g4;
+  crypto_int32 h5 = f5 - g5;
+  crypto_int32 h6 = f6 - g6;
+  crypto_int32 h7 = f7 - g7;
+  crypto_int32 h8 = f8 - g8;
+  crypto_int32 h9 = f9 - g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/fe_tobytes.c

@@ -0,0 +1,123 @@
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+/*
+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.
+*/
+
+void fe_tobytes(unsigned char *s,fe h)
+{
+  crypto_int32 h0 = h[0];
+  crypto_int32 h1 = h[1];
+  crypto_int32 h2 = h[2];
+  crypto_int32 h3 = h[3];
+  crypto_int32 h4 = h[4];
+  crypto_int32 h5 = h[5];
+  crypto_int32 h6 = h[6];
+  crypto_int32 h7 = h[7];
+  crypto_int32 h8 = h[8];
+  crypto_int32 h9 = h[9];
+  crypto_int32 q;
+  crypto_int32 carry0;
+  crypto_int32 carry1;
+  crypto_int32 carry2;
+  crypto_int32 carry3;
+  crypto_int32 carry4;
+  crypto_int32 carry5;
+  crypto_int32 carry6;
+  crypto_int32 carry7;
+  crypto_int32 carry8;
+  crypto_int32 carry9;
+
+  q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25;
+  q = (h0 + q) >> 26;
+  q = (h1 + q) >> 25;
+  q = (h2 + q) >> 26;
+  q = (h3 + q) >> 25;
+  q = (h4 + q) >> 26;
+  q = (h5 + q) >> 25;
+  q = (h6 + q) >> 26;
+  q = (h7 + q) >> 25;
+  q = (h8 + q) >> 26;
+  q = (h9 + q) >> 25;
+
+  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+  h0 += 19 * q;
+  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+
+  carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry9 = h9 >> 25;               h9 -= carry9 << 25;
+                  /* h10 = carry9 */
+
+  /*
+  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+  Have h0+...+2^230 h9 between 0 and 2^255-1;
+  evidently 2^255 h10-2^255 q = 0.
+  Goal: Output h0+...+2^230 h9.
+  */
+
+  s[0] = h0 >> 0;
+  s[1] = h0 >> 8;
+  s[2] = h0 >> 16;
+  s[3] = (h0 >> 24) | (h1 << 2);
+  s[4] = h1 >> 6;
+  s[5] = h1 >> 14;
+  s[6] = (h1 >> 22) | (h2 << 3);
+  s[7] = h2 >> 5;
+  s[8] = h2 >> 13;
+  s[9] = (h2 >> 21) | (h3 << 5);
+  s[10] = h3 >> 3;
+  s[11] = h3 >> 11;
+  s[12] = (h3 >> 19) | (h4 << 6);
+  s[13] = h4 >> 2;
+  s[14] = h4 >> 10;
+  s[15] = h4 >> 18;
+  s[16] = h5 >> 0;
+  s[17] = h5 >> 8;
+  s[18] = h5 >> 16;
+  s[19] = (h5 >> 24) | (h6 << 1);
+  s[20] = h6 >> 7;
+  s[21] = h6 >> 15;
+  s[22] = (h6 >> 23) | (h7 << 3);
+  s[23] = h7 >> 5;
+  s[24] = h7 >> 13;
+  s[25] = (h7 >> 21) | (h8 << 4);
+  s[26] = h8 >> 4;
+  s[27] = h8 >> 12;
+  s[28] = (h8 >> 20) | (h9 << 6);
+  s[29] = h9 >> 2;
+  s[30] = h9 >> 10;
+  s[31] = h9 >> 18;
+}
+
+#endif

src/libsodium/crypto_scalarmult/curve25519/ref10/montgomery.h

@@ -0,0 +1,140 @@
+
+/* qhasm: fe X2 */
+
+/* qhasm: fe Z2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe X4 */
+
+/* qhasm: fe Z4 */
+
+/* qhasm: fe X5 */
+
+/* qhasm: fe Z5 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: fe E */
+
+/* qhasm: fe AA */
+
+/* qhasm: fe BB */
+
+/* qhasm: fe DA */
+
+/* qhasm: fe CB */
+
+/* qhasm: fe t0 */
+
+/* qhasm: fe t1 */
+
+/* qhasm: fe t2 */
+
+/* qhasm: fe t3 */
+
+/* qhasm: fe t4 */
+
+/* qhasm: enter ladder */
+
+/* qhasm: D = X3-Z3 */
+/* asm 1: fe_sub(>D=fe#5,<X3=fe#3,<Z3=fe#4); */
+/* asm 2: fe_sub(>D=tmp0,<X3=x3,<Z3=z3); */
+fe_sub(tmp0,x3,z3);
+
+/* qhasm: B = X2-Z2 */
+/* asm 1: fe_sub(>B=fe#6,<X2=fe#1,<Z2=fe#2); */
+/* asm 2: fe_sub(>B=tmp1,<X2=x2,<Z2=z2); */
+fe_sub(tmp1,x2,z2);
+
+/* qhasm: A = X2+Z2 */
+/* asm 1: fe_add(>A=fe#1,<X2=fe#1,<Z2=fe#2); */
+/* asm 2: fe_add(>A=x2,<X2=x2,<Z2=z2); */
+fe_add(x2,x2,z2);
+
+/* qhasm: C = X3+Z3 */
+/* asm 1: fe_add(>C=fe#2,<X3=fe#3,<Z3=fe#4); */
+/* asm 2: fe_add(>C=z2,<X3=x3,<Z3=z3); */
+fe_add(z2,x3,z3);
+
+/* qhasm: DA = D*A */
+/* asm 1: fe_mul(>DA=fe#4,<D=fe#5,<A=fe#1); */
+/* asm 2: fe_mul(>DA=z3,<D=tmp0,<A=x2); */
+fe_mul(z3,tmp0,x2);
+
+/* qhasm: CB = C*B */
+/* asm 1: fe_mul(>CB=fe#2,<C=fe#2,<B=fe#6); */
+/* asm 2: fe_mul(>CB=z2,<C=z2,<B=tmp1); */
+fe_mul(z2,z2,tmp1);
+
+/* qhasm: BB = B^2 */
+/* asm 1: fe_sq(>BB=fe#5,<B=fe#6); */
+/* asm 2: fe_sq(>BB=tmp0,<B=tmp1); */
+fe_sq(tmp0,tmp1);
+
+/* qhasm: AA = A^2 */
+/* asm 1: fe_sq(>AA=fe#6,<A=fe#1); */
+/* asm 2: fe_sq(>AA=tmp1,<A=x2); */
+fe_sq(tmp1,x2);
+
+/* qhasm: t0 = DA+CB */
+/* asm 1: fe_add(>t0=fe#3,<DA=fe#4,<CB=fe#2); */
+/* asm 2: fe_add(>t0=x3,<DA=z3,<CB=z2); */
+fe_add(x3,z3,z2);
+
+/* qhasm: assign x3 to t0 */
+
+/* qhasm: t1 = DA-CB */
+/* asm 1: fe_sub(>t1=fe#2,<DA=fe#4,<CB=fe#2); */
+/* asm 2: fe_sub(>t1=z2,<DA=z3,<CB=z2); */
+fe_sub(z2,z3,z2);
+
+/* qhasm: X4 = AA*BB */
+/* asm 1: fe_mul(>X4=fe#1,<AA=fe#6,<BB=fe#5); */
+/* asm 2: fe_mul(>X4=x2,<AA=tmp1,<BB=tmp0); */
+fe_mul(x2,tmp1,tmp0);
+
+/* qhasm: E = AA-BB */
+/* asm 1: fe_sub(>E=fe#6,<AA=fe#6,<BB=fe#5); */
+/* asm 2: fe_sub(>E=tmp1,<AA=tmp1,<BB=tmp0); */
+fe_sub(tmp1,tmp1,tmp0);
+
+/* qhasm: t2 = t1^2 */
+/* asm 1: fe_sq(>t2=fe#2,<t1=fe#2); */
+/* asm 2: fe_sq(>t2=z2,<t1=z2); */
+fe_sq(z2,z2);
+
+/* qhasm: t3 = a24*E */
+/* asm 1: fe_mul121666(>t3=fe#4,<E=fe#6); */
+/* asm 2: fe_mul121666(>t3=z3,<E=tmp1); */
+fe_mul121666(z3,tmp1);
+
+/* qhasm: X5 = t0^2 */
+/* asm 1: fe_sq(>X5=fe#3,<t0=fe#3); */
+/* asm 2: fe_sq(>X5=x3,<t0=x3); */
+fe_sq(x3,x3);
+
+/* qhasm: t4 = BB+t3 */
+/* asm 1: fe_add(>t4=fe#5,<BB=fe#5,<t3=fe#4); */
+/* asm 2: fe_add(>t4=tmp0,<BB=tmp0,<t3=z3); */
+fe_add(tmp0,tmp0,z3);
+
+/* qhasm: Z5 = X1*t2 */
+/* asm 1: fe_mul(>Z5=fe#4,x1,<t2=fe#2); */
+/* asm 2: fe_mul(>Z5=z3,x1,<t2=z2); */
+fe_mul(z3,x1,z2);
+
+/* qhasm: Z4 = E*t4 */
+/* asm 1: fe_mul(>Z4=fe#2,<E=fe#6,<t4=fe#5); */
+/* asm 2: fe_mul(>Z4=z2,<E=tmp1,<t4=tmp0); */
+fe_mul(z2,tmp1,tmp0);
+
+/* qhasm: return */

src/libsodium/crypto_scalarmult/curve25519/ref10/pow225521.h

@@ -0,0 +1,160 @@
+
+/* qhasm: fe z1 */
+
+/* qhasm: fe z2 */
+
+/* qhasm: fe z8 */
+
+/* qhasm: fe z9 */
+
+/* qhasm: fe z11 */
+
+/* qhasm: fe z22 */
+
+/* qhasm: fe z_5_0 */
+
+/* qhasm: fe z_10_5 */
+
+/* qhasm: fe z_10_0 */
+
+/* qhasm: fe z_20_10 */
+
+/* qhasm: fe z_20_0 */
+
+/* qhasm: fe z_40_20 */
+
+/* qhasm: fe z_40_0 */
+
+/* qhasm: fe z_50_10 */
+
+/* qhasm: fe z_50_0 */
+
+/* qhasm: fe z_100_50 */
+
+/* qhasm: fe z_100_0 */
+
+/* qhasm: fe z_200_100 */
+
+/* qhasm: fe z_200_0 */
+
+/* qhasm: fe z_250_50 */
+
+/* qhasm: fe z_250_0 */
+
+/* qhasm: fe z_255_5 */
+
+/* qhasm: fe z_255_21 */
+
+/* qhasm: enter pow225521 */
+
+/* qhasm: z2 = z1^2^1 */
+/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
+/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
+fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z8 = z2^2^2 */
+/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
+/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
+fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+
+/* qhasm: z9 = z1*z8 */
+/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
+/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
+fe_mul(t1,z,t1);
+
+/* qhasm: z11 = z2*z9 */
+/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
+/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
+fe_mul(t0,t0,t1);
+
+/* qhasm: z22 = z11^2^1 */
+/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
+/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
+fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
+
+/* qhasm: z_5_0 = z9*z22 */
+/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
+/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
+fe_mul(t1,t1,t2);
+
+/* qhasm: z_10_5 = z_5_0^2^5 */
+/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
+/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
+fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
+
+/* qhasm: z_10_0 = z_10_5*z_5_0 */
+/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
+/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_20_10 = z_10_0^2^10 */
+/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
+/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
+fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_20_0 = z_20_10*z_10_0 */
+/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_40_20 = z_20_0^2^20 */
+/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
+/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
+fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
+
+/* qhasm: z_40_0 = z_40_20*z_20_0 */
+/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
+/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_50_10 = z_40_0^2^10 */
+/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
+/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
+fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_50_0 = z_50_10*z_10_0 */
+/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_100_50 = z_50_0^2^50 */
+/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
+/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
+fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_100_0 = z_100_50*z_50_0 */
+/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_200_100 = z_100_0^2^100 */
+/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
+/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
+fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
+
+/* qhasm: z_200_0 = z_200_100*z_100_0 */
+/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
+/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_250_50 = z_200_0^2^50 */
+/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
+/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
+fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_250_0 = z_250_50*z_50_0 */
+/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_255_5 = z_250_0^2^5 */
+/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
+/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
+fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+
+/* qhasm: z_255_21 = z_255_5*z11 */
+/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
+/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
+fe_mul(out,t1,t0);
+
+/* qhasm: return */

src/libsodium/crypto_scalarmult/curve25519/ref10/scalarmult.c

@@ -0,0 +1,54 @@
+
+#include "api.h"
+#include "crypto_scalarmult.h"
+#include "fe.h"
+
+#ifndef HAVE_TI_MODE
+
+int crypto_scalarmult(unsigned char *q,
+  const unsigned char *n,
+  const unsigned char *p)
+{
+  unsigned char e[32];
+  unsigned int i;
+  fe x1;
+  fe x2;
+  fe z2;
+  fe x3;
+  fe z3;
+  fe tmp0;
+  fe tmp1;
+  int pos;
+  unsigned int swap;
+  unsigned int b;
+
+  for (i = 0;i < 32;++i) e[i] = n[i];
+  e[0] &= 248;
+  e[31] &= 127;
+  e[31] |= 64;
+  fe_frombytes(x1,p);
+  fe_1(x2);
+  fe_0(z2);
+  fe_copy(x3,x1);
+  fe_1(z3);
+
+  swap = 0;
+  for (pos = 254;pos >= 0;--pos) {
+    b = e[pos / 8] >> (pos & 7);
+    b &= 1;
+    swap ^= b;
+    fe_cswap(x2,x3,swap);
+    fe_cswap(z2,z3,swap);
+    swap = b;
+#include "montgomery.h"
+  }
+  fe_cswap(x2,x3,swap);
+  fe_cswap(z2,z3,swap);
+
+  fe_invert(z2,z2);
+  fe_mul(x2,x2,z2);
+  fe_tobytes(q,x2);
+  return 0;
+}
+
+#endif