benchmark OpenSSL curve25519

5 files changed, 1138 insertions, 0 deletions

diff --git a/third_party/openssl-curve25519/compiler.sh b/third_party/openssl-curve25519/compiler.sh
new file mode 100755
index 000000000..29885a152
--- /dev/null
+++ b/third_party/openssl-curve25519/compiler.sh
@@ -0,0 +1,4 @@
+#!/bin/sh
+set -eu
+
+gcc -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes -lcrypto $@
diff --git a/third_party/openssl-curve25519/crypto_scalarmult_bench.c b/third_party/openssl-curve25519/crypto_scalarmult_bench.c
new file mode 100644
index 000000000..b7d717158
--- /dev/null
+++ b/third_party/openssl-curve25519/crypto_scalarmult_bench.c
@@ -0,0 +1,5 @@
+#include "ec_curve25519.h"
+
+void crypto_scalarmult_bench(unsigned char* buf) {
+  x25519_scalar_mult(buf, buf+32, buf+64);
+}
diff --git a/third_party/openssl-curve25519/ec_curve25519.c b/third_party/openssl-curve25519/ec_curve25519.c
new file mode 100644
index 000000000..7d00cc53f
--- /dev/null
+++ b/third_party/openssl-curve25519/ec_curve25519.c
@@ -0,0 +1,1126 @@
+/*
+ * Copyright 2016 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the OpenSSL license (the "License").  You may not use
+ * this file except in compliance with the License.  You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
+ * 20141124 (http://bench.cr.yp.to/supercop.html).
+ *
+ * The field functions are shared by Ed25519 and X25519 where possible. */
+
+#include <stdint.h>
+#include <string.h>
+#include "ec_curve25519.h"
+
+
+/* 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.  */
+typedef int32_t fe[10];
+
+static const int64_t kBottom25Bits = 0x1ffffffLL;
+static const int64_t kBottom26Bits = 0x3ffffffLL;
+static const int64_t kTop39Bits = 0xfffffffffe000000LL;
+static const int64_t kTop38Bits = 0xfffffffffc000000LL;
+
+static uint64_t load_3(const uint8_t *in) {
+  uint64_t result;
+  result = (uint64_t)in[0];
+  result |= ((uint64_t)in[1]) << 8;
+  result |= ((uint64_t)in[2]) << 16;
+  return result;
+}
+
+static uint64_t load_4(const uint8_t *in) {
+  uint64_t result;
+  result = (uint64_t)in[0];
+  result |= ((uint64_t)in[1]) << 8;
+  result |= ((uint64_t)in[2]) << 16;
+  result |= ((uint64_t)in[3]) << 24;
+  return result;
+}
+
+static void fe_frombytes(fe h, const uint8_t *s) {
+  /* Ignores top bit of h. */
+  int64_t h0 = load_4(s);
+  int64_t h1 = load_3(s + 4) << 6;
+  int64_t h2 = load_3(s + 7) << 5;
+  int64_t h3 = load_3(s + 10) << 3;
+  int64_t h4 = load_3(s + 13) << 2;
+  int64_t h5 = load_4(s + 16);
+  int64_t h6 = load_3(s + 20) << 7;
+  int64_t h7 = load_3(s + 23) << 5;
+  int64_t h8 = load_3(s + 26) << 4;
+  int64_t h9 = (load_3(s + 29) & 8388607) << 2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+  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;
+}
+
+/* Preconditions:
+ *  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,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|<2^231 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. */
+static void fe_tobytes(uint8_t *s, const fe h) {
+  int32_t h0 = h[0];
+  int32_t h1 = h[1];
+  int32_t h2 = h[2];
+  int32_t h3 = h[3];
+  int32_t h4 = h[4];
+  int32_t h5 = h[5];
+  int32_t h6 = h[6];
+  int32_t h7 = h[7];
+  int32_t h8 = h[8];
+  int32_t h9 = h[9];
+  int32_t q;
+
+  q = (19 * h9 + (((int32_t) 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. */
+
+  h1 += h0 >> 26; h0 &= kBottom26Bits;
+  h2 += h1 >> 25; h1 &= kBottom25Bits;
+  h3 += h2 >> 26; h2 &= kBottom26Bits;
+  h4 += h3 >> 25; h3 &= kBottom25Bits;
+  h5 += h4 >> 26; h4 &= kBottom26Bits;
+  h6 += h5 >> 25; h5 &= kBottom25Bits;
+  h7 += h6 >> 26; h6 &= kBottom26Bits;
+  h8 += h7 >> 25; h7 &= kBottom25Bits;
+  h9 += h8 >> 26; h8 &= kBottom26Bits;
+                  h9 &= kBottom25Bits;
+                  /* 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) | ((uint32_t)(h1) << 2);
+  s[4] = h1 >> 6;
+  s[5] = h1 >> 14;
+  s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
+  s[7] = h2 >> 5;
+  s[8] = h2 >> 13;
+  s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
+  s[10] = h3 >> 3;
+  s[11] = h3 >> 11;
+  s[12] = (h3 >> 19) | ((uint32_t)(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) | ((uint32_t)(h6) << 1);
+  s[20] = h6 >> 7;
+  s[21] = h6 >> 15;
+  s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
+  s[23] = h7 >> 5;
+  s[24] = h7 >> 13;
+  s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
+  s[26] = h8 >> 4;
+  s[27] = h8 >> 12;
+  s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
+  s[29] = h9 >> 2;
+  s[30] = h9 >> 10;
+  s[31] = h9 >> 18;
+}
+
+/* h = f */
+static void fe_copy(fe h, const fe f) {
+  memmove(h, f, sizeof(int32_t) * 10);
+}
+
+/* h = 0 */
+static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
+
+/* h = 1 */
+static void fe_1(fe h) {
+  memset(h, 0, sizeof(int32_t) * 10);
+  h[0] = 1;
+}
+
+/* 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. */
+static void fe_add(fe h, const fe f, const fe g) {
+  unsigned i;
+  for (i = 0; i < 10; i++) {
+    h[i] = f[i] + g[i];
+  }
+}
+
+/* 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. */
+static void fe_sub(fe h, const fe f, const fe g) {
+  unsigned i;
+  for (i = 0; i < 10; i++) {
+    h[i] = f[i] - g[i];
+  }
+}
+
+/* h = f * g
+ * Can overlap h with f or g.
+ *
+ * Preconditions:
+ *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+ *    |g| 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.
+ *
+ * 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. */
+static void fe_mul(fe h, const fe f, const fe g) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t g0 = g[0];
+  int32_t g1 = g[1];
+  int32_t g2 = g[2];
+  int32_t g3 = g[3];
+  int32_t g4 = g[4];
+  int32_t g5 = g[5];
+  int32_t g6 = g[6];
+  int32_t g7 = g[7];
+  int32_t g8 = g[8];
+  int32_t g9 = g[9];
+  int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+  int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+  int32_t g3_19 = 19 * g3;
+  int32_t g4_19 = 19 * g4;
+  int32_t g5_19 = 19 * g5;
+  int32_t g6_19 = 19 * g6;
+  int32_t g7_19 = 19 * g7;
+  int32_t g8_19 = 19 * g8;
+  int32_t g9_19 = 19 * g9;
+  int32_t f1_2 = 2 * f1;
+  int32_t f3_2 = 2 * f3;
+  int32_t f5_2 = 2 * f5;
+  int32_t f7_2 = 2 * f7;
+  int32_t f9_2 = 2 * f9;
+  int64_t f0g0    = f0   * (int64_t) g0;
+  int64_t f0g1    = f0   * (int64_t) g1;
+  int64_t f0g2    = f0   * (int64_t) g2;
+  int64_t f0g3    = f0   * (int64_t) g3;
+  int64_t f0g4    = f0   * (int64_t) g4;
+  int64_t f0g5    = f0   * (int64_t) g5;
+  int64_t f0g6    = f0   * (int64_t) g6;
+  int64_t f0g7    = f0   * (int64_t) g7;
+  int64_t f0g8    = f0   * (int64_t) g8;
+  int64_t f0g9    = f0   * (int64_t) g9;
+  int64_t f1g0    = f1   * (int64_t) g0;
+  int64_t f1g1_2  = f1_2 * (int64_t) g1;
+  int64_t f1g2    = f1   * (int64_t) g2;
+  int64_t f1g3_2  = f1_2 * (int64_t) g3;
+  int64_t f1g4    = f1   * (int64_t) g4;
+  int64_t f1g5_2  = f1_2 * (int64_t) g5;
+  int64_t f1g6    = f1   * (int64_t) g6;
+  int64_t f1g7_2  = f1_2 * (int64_t) g7;
+  int64_t f1g8    = f1   * (int64_t) g8;
+  int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+  int64_t f2g0    = f2   * (int64_t) g0;
+  int64_t f2g1    = f2   * (int64_t) g1;
+  int64_t f2g2    = f2   * (int64_t) g2;
+  int64_t f2g3    = f2   * (int64_t) g3;
+  int64_t f2g4    = f2   * (int64_t) g4;
+  int64_t f2g5    = f2   * (int64_t) g5;
+  int64_t f2g6    = f2   * (int64_t) g6;
+  int64_t f2g7    = f2   * (int64_t) g7;
+  int64_t f2g8_19 = f2   * (int64_t) g8_19;
+  int64_t f2g9_19 = f2   * (int64_t) g9_19;
+  int64_t f3g0    = f3   * (int64_t) g0;
+  int64_t f3g1_2  = f3_2 * (int64_t) g1;
+  int64_t f3g2    = f3   * (int64_t) g2;
+  int64_t f3g3_2  = f3_2 * (int64_t) g3;
+  int64_t f3g4    = f3   * (int64_t) g4;
+  int64_t f3g5_2  = f3_2 * (int64_t) g5;
+  int64_t f3g6    = f3   * (int64_t) g6;
+  int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+  int64_t f3g8_19 = f3   * (int64_t) g8_19;
+  int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+  int64_t f4g0    = f4   * (int64_t) g0;
+  int64_t f4g1    = f4   * (int64_t) g1;
+  int64_t f4g2    = f4   * (int64_t) g2;
+  int64_t f4g3    = f4   * (int64_t) g3;
+  int64_t f4g4    = f4   * (int64_t) g4;
+  int64_t f4g5    = f4   * (int64_t) g5;
+  int64_t f4g6_19 = f4   * (int64_t) g6_19;
+  int64_t f4g7_19 = f4   * (int64_t) g7_19;
+  int64_t f4g8_19 = f4   * (int64_t) g8_19;
+  int64_t f4g9_19 = f4   * (int64_t) g9_19;
+  int64_t f5g0    = f5   * (int64_t) g0;
+  int64_t f5g1_2  = f5_2 * (int64_t) g1;
+  int64_t f5g2    = f5   * (int64_t) g2;
+  int64_t f5g3_2  = f5_2 * (int64_t) g3;
+  int64_t f5g4    = f5   * (int64_t) g4;
+  int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+  int64_t f5g6_19 = f5   * (int64_t) g6_19;
+  int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+  int64_t f5g8_19 = f5   * (int64_t) g8_19;
+  int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+  int64_t f6g0    = f6   * (int64_t) g0;
+  int64_t f6g1    = f6   * (int64_t) g1;
+  int64_t f6g2    = f6   * (int64_t) g2;
+  int64_t f6g3    = f6   * (int64_t) g3;
+  int64_t f6g4_19 = f6   * (int64_t) g4_19;
+  int64_t f6g5_19 = f6   * (int64_t) g5_19;
+  int64_t f6g6_19 = f6   * (int64_t) g6_19;
+  int64_t f6g7_19 = f6   * (int64_t) g7_19;
+  int64_t f6g8_19 = f6   * (int64_t) g8_19;
+  int64_t f6g9_19 = f6   * (int64_t) g9_19;
+  int64_t f7g0    = f7   * (int64_t) g0;
+  int64_t f7g1_2  = f7_2 * (int64_t) g1;
+  int64_t f7g2    = f7   * (int64_t) g2;
+  int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+  int64_t f7g4_19 = f7   * (int64_t) g4_19;
+  int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+  int64_t f7g6_19 = f7   * (int64_t) g6_19;
+  int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+  int64_t f7g8_19 = f7   * (int64_t) g8_19;
+  int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+  int64_t f8g0    = f8   * (int64_t) g0;
+  int64_t f8g1    = f8   * (int64_t) g1;
+  int64_t f8g2_19 = f8   * (int64_t) g2_19;
+  int64_t f8g3_19 = f8   * (int64_t) g3_19;
+  int64_t f8g4_19 = f8   * (int64_t) g4_19;
+  int64_t f8g5_19 = f8   * (int64_t) g5_19;
+  int64_t f8g6_19 = f8   * (int64_t) g6_19;
+  int64_t f8g7_19 = f8   * (int64_t) g7_19;
+  int64_t f8g8_19 = f8   * (int64_t) g8_19;
+  int64_t f8g9_19 = f8   * (int64_t) g9_19;
+  int64_t f9g0    = f9   * (int64_t) g0;
+  int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+  int64_t f9g2_19 = f9   * (int64_t) g2_19;
+  int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+  int64_t f9g4_19 = f9   * (int64_t) g4_19;
+  int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+  int64_t f9g6_19 = f9   * (int64_t) g6_19;
+  int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+  int64_t f9g8_19 = f9   * (int64_t) g8_19;
+  int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+  int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
+  int64_t h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
+  int64_t h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
+  int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
+  int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
+  int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
+  int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
+  int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
+  int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
+  int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
+   *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
+   * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
+   *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+  /* |h0| <= 2^25 */
+  /* |h4| <= 2^25 */
+  /* |h1| <= 1.71*2^59 */
+  /* |h5| <= 1.71*2^59 */
+
+  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+  /* |h1| <= 2^24; from now on fits into int32 */
+  /* |h5| <= 2^24; from now on fits into int32 */
+  /* |h2| <= 1.41*2^60 */
+  /* |h6| <= 1.41*2^60 */
+
+  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+  /* |h2| <= 2^25; from now on fits into int32 unchanged */
+  /* |h6| <= 2^25; from now on fits into int32 unchanged */
+  /* |h3| <= 1.71*2^59 */
+  /* |h7| <= 1.71*2^59 */
+
+  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+  /* |h3| <= 2^24; from now on fits into int32 unchanged */
+  /* |h7| <= 2^24; from now on fits into int32 unchanged */
+  /* |h4| <= 1.72*2^34 */
+  /* |h8| <= 1.41*2^60 */
+
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+  /* |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| <= 1.71*2^59 */
+
+  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+  /* |h9| <= 2^24; from now on fits into int32 unchanged */
+  /* |h0| <= 1.1*2^39 */
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+  /* |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;
+}
+
+/* h = 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. */
+static void fe_sq(fe h, const fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t f0_2 = 2 * f0;
+  int32_t f1_2 = 2 * f1;
+  int32_t f2_2 = 2 * f2;
+  int32_t f3_2 = 2 * f3;
+  int32_t f4_2 = 2 * f4;
+  int32_t f5_2 = 2 * f5;
+  int32_t f6_2 = 2 * f6;
+  int32_t f7_2 = 2 * f7;
+  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+  int64_t f0f0    = f0   * (int64_t) f0;
+  int64_t f0f1_2  = f0_2 * (int64_t) f1;
+  int64_t f0f2_2  = f0_2 * (int64_t) f2;
+  int64_t f0f3_2  = f0_2 * (int64_t) f3;
+  int64_t f0f4_2  = f0_2 * (int64_t) f4;
+  int64_t f0f5_2  = f0_2 * (int64_t) f5;
+  int64_t f0f6_2  = f0_2 * (int64_t) f6;
+  int64_t f0f7_2  = f0_2 * (int64_t) f7;
+  int64_t f0f8_2  = f0_2 * (int64_t) f8;
+  int64_t f0f9_2  = f0_2 * (int64_t) f9;
+  int64_t f1f1_2  = f1_2 * (int64_t) f1;
+  int64_t f1f2_2  = f1_2 * (int64_t) f2;
+  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+  int64_t f1f4_2  = f1_2 * (int64_t) f4;
+  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+  int64_t f1f6_2  = f1_2 * (int64_t) f6;
+  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+  int64_t f1f8_2  = f1_2 * (int64_t) f8;
+  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+  int64_t f2f2    = f2   * (int64_t) f2;
+  int64_t f2f3_2  = f2_2 * (int64_t) f3;
+  int64_t f2f4_2  = f2_2 * (int64_t) f4;
+  int64_t f2f5_2  = f2_2 * (int64_t) f5;
+  int64_t f2f6_2  = f2_2 * (int64_t) f6;
+  int64_t f2f7_2  = f2_2 * (int64_t) f7;
+  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+  int64_t f2f9_38 = f2   * (int64_t) f9_38;
+  int64_t f3f3_2  = f3_2 * (int64_t) f3;
+  int64_t f3f4_2  = f3_2 * (int64_t) f4;
+  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+  int64_t f3f6_2  = f3_2 * (int64_t) f6;
+  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+  int64_t f4f4    = f4   * (int64_t) f4;
+  int64_t f4f5_2  = f4_2 * (int64_t) f5;
+  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+  int64_t f4f7_38 = f4   * (int64_t) f7_38;
+  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+  int64_t f4f9_38 = f4   * (int64_t) f9_38;
+  int64_t f5f5_38 = f5   * (int64_t) f5_38;
+  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+  int64_t f6f6_19 = f6   * (int64_t) f6_19;
+  int64_t f6f7_38 = f6   * (int64_t) f7_38;
+  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+  int64_t f6f9_38 = f6   * (int64_t) f9_38;
+  int64_t f7f7_38 = f7   * (int64_t) f7_38;
+  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+  int64_t f8f8_19 = f8   * (int64_t) f8_19;
+  int64_t f8f9_38 = f8   * (int64_t) f9_38;
+  int64_t f9f9_38 = f9   * (int64_t) f9_38;
+  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+
+  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+
+  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+
+  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+
+  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;
+}
+
+static void fe_invert(fe out, const fe z) {
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+  /*
+   * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
+   * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
+   */
+
+  /* t0 = z ** 2 */
+  fe_sq(t0, z);
+
+  /* t1 = t0 ** (2 ** 2) = z ** 8 */
+  fe_sq(t1, t0);
+  fe_sq(t1, t1);
+
+  /* t1 = z * t1 = z ** 9 */
+  fe_mul(t1, z, t1);
+  /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
+  fe_mul(t0, t0, t1);
+
+  /* t2 = t0 ** 2 = z ** 22 */
+  fe_sq(t2, t0);
+
+  /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
+  fe_mul(t1, t1, t2);
+
+  /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
+  fe_sq(t2, t1);
+  for (i = 1; i < 5; ++i) {
+    fe_sq(t2, t2);
+  }
+
+  /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
+  fe_mul(t1, t2, t1);
+
+  /* Continuing similarly... */
+
+  /* t2 = z ** (2 ** 20 - 1) */
+  fe_sq(t2, t1);
+  for (i = 1; i < 10; ++i) {
+    fe_sq(t2, t2);
+  }
+  fe_mul(t2, t2, t1);
+
+  /* t2 = z ** (2 ** 40 - 1) */
+  fe_sq(t3, t2);
+  for (i = 1; i < 20; ++i) {
+    fe_sq(t3, t3);
+  }
+  fe_mul(t2, t3, t2);
+
+  /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
+  for (i = 0; i < 10; ++i) {
+    fe_sq(t2, t2);
+  }
+  /* t1 = z ** (2 ** 50 - 1) */
+  fe_mul(t1, t2, t1);
+
+  /* t2 = z ** (2 ** 100 - 1) */
+  fe_sq(t2, t1);
+  for (i = 1; i < 50; ++i) {
+    fe_sq(t2, t2);
+  }
+  fe_mul(t2, t2, t1);
+
+  /* t2 = z ** (2 ** 200 - 1) */
+  fe_sq(t3, t2);
+  for (i = 1; i < 100; ++i) {
+    fe_sq(t3, t3);
+  }
+  fe_mul(t2, t3, t2);
+
+  /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
+  fe_sq(t2, t2);
+  for (i = 1; i < 50; ++i) {
+    fe_sq(t2, t2);
+  }
+
+  /* t1 = z ** (2 ** 250 - 1) */
+  fe_mul(t1, t2, t1);
+
+  /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
+  fe_sq(t1, t1);
+  for (i = 1; i < 5; ++i) {
+    fe_sq(t1, t1);
+  }
+
+  /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
+  fe_mul(out, t1, t0);
+}
+
+/* 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. */
+static void fe_neg(fe h, const fe f) {
+  unsigned i;
+  for (i = 0; i < 10; i++) {
+    h[i] = -f[i];
+  }
+}
+
+/* Replace (f,g) with (g,g) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
+ *
+ * Preconditions: b in {0,1}. */
+static void fe_cmov(fe f, const fe g, unsigned b) {
+  size_t i;
+  b = 0-b;
+  for (i = 0; i < 10; i++) {
+    int32_t x = f[i] ^ g[i];
+    x &= b;
+    f[i] ^= x;
+  }
+}
+
+/* return 0 if f == 0
+ * return 1 if f != 0
+ *
+ * Preconditions:
+ *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
+static int fe_isnonzero(const fe f) {
+  uint8_t s[32];
+  static const uint8_t zero[32] = {0};
+  fe_tobytes(s, f);
+
+  return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
+}
+
+/* return 1 if f is in {1,3,5,...,q-2}
+ * return 0 if f is in {0,2,4,...,q-1}
+ *
+ * Preconditions:
+ *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
+static int fe_isnegative(const fe f) {
+  uint8_t s[32];
+  fe_tobytes(s, f);
+  return s[0] & 1;
+}
+
+/* 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. */
+static void fe_sq2(fe h, const fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t f0_2 = 2 * f0;
+  int32_t f1_2 = 2 * f1;
+  int32_t f2_2 = 2 * f2;
+  int32_t f3_2 = 2 * f3;
+  int32_t f4_2 = 2 * f4;
+  int32_t f5_2 = 2 * f5;
+  int32_t f6_2 = 2 * f6;
+  int32_t f7_2 = 2 * f7;
+  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+  int64_t f0f0    = f0   * (int64_t) f0;
+  int64_t f0f1_2  = f0_2 * (int64_t) f1;
+  int64_t f0f2_2  = f0_2 * (int64_t) f2;
+  int64_t f0f3_2  = f0_2 * (int64_t) f3;
+  int64_t f0f4_2  = f0_2 * (int64_t) f4;
+  int64_t f0f5_2  = f0_2 * (int64_t) f5;
+  int64_t f0f6_2  = f0_2 * (int64_t) f6;
+  int64_t f0f7_2  = f0_2 * (int64_t) f7;
+  int64_t f0f8_2  = f0_2 * (int64_t) f8;
+  int64_t f0f9_2  = f0_2 * (int64_t) f9;
+  int64_t f1f1_2  = f1_2 * (int64_t) f1;
+  int64_t f1f2_2  = f1_2 * (int64_t) f2;
+  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+  int64_t f1f4_2  = f1_2 * (int64_t) f4;
+  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+  int64_t f1f6_2  = f1_2 * (int64_t) f6;
+  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+  int64_t f1f8_2  = f1_2 * (int64_t) f8;
+  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+  int64_t f2f2    = f2   * (int64_t) f2;
+  int64_t f2f3_2  = f2_2 * (int64_t) f3;
+  int64_t f2f4_2  = f2_2 * (int64_t) f4;
+  int64_t f2f5_2  = f2_2 * (int64_t) f5;
+  int64_t f2f6_2  = f2_2 * (int64_t) f6;
+  int64_t f2f7_2  = f2_2 * (int64_t) f7;
+  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+  int64_t f2f9_38 = f2   * (int64_t) f9_38;
+  int64_t f3f3_2  = f3_2 * (int64_t) f3;
+  int64_t f3f4_2  = f3_2 * (int64_t) f4;
+  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+  int64_t f3f6_2  = f3_2 * (int64_t) f6;
+  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+  int64_t f4f4    = f4   * (int64_t) f4;
+  int64_t f4f5_2  = f4_2 * (int64_t) f5;
+  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+  int64_t f4f7_38 = f4   * (int64_t) f7_38;
+  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+  int64_t f4f9_38 = f4   * (int64_t) f9_38;
+  int64_t f5f5_38 = f5   * (int64_t) f5_38;
+  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+  int64_t f6f6_19 = f6   * (int64_t) f6_19;
+  int64_t f6f7_38 = f6   * (int64_t) f7_38;
+  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+  int64_t f6f9_38 = f6   * (int64_t) f9_38;
+  int64_t f7f7_38 = f7   * (int64_t) f7_38;
+  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+  int64_t f8f8_19 = f8   * (int64_t) f8_19;
+  int64_t f8f9_38 = f8   * (int64_t) f9_38;
+  int64_t f9f9_38 = f9   * (int64_t) f9_38;
+  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  h0 += h0;
+  h1 += h1;
+  h2 += h2;
+  h3 += h3;
+  h4 += h4;
+  h5 += h5;
+  h6 += h6;
+  h7 += h7;
+  h8 += h8;
+  h9 += h9;
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+
+  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+
+  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+
+  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+
+  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;
+}
+
+static void fe_pow22523(fe out, const fe z) {
+  fe t0;
+  fe t1;
+  fe t2;
+  int i;
+
+  fe_sq(t0, z);
+  fe_sq(t1, t0);
+  for (i = 1; i < 2; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t1, z, t1);
+  fe_mul(t0, t0, t1);
+  fe_sq(t0, t0);
+  fe_mul(t0, t1, t0);
+  fe_sq(t1, t0);
+  for (i = 1; i < 5; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t0, t1, t0);
+  fe_sq(t1, t0);
+  for (i = 1; i < 10; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t1, t1, t0);
+  fe_sq(t2, t1);
+  for (i = 1; i < 20; ++i) {
+    fe_sq(t2, t2);
+  }
+  fe_mul(t1, t2, t1);
+  fe_sq(t1, t1);
+  for (i = 1; i < 10; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t0, t1, t0);
+  fe_sq(t1, t0);
+  for (i = 1; i < 50; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t1, t1, t0);
+  fe_sq(t2, t1);
+  for (i = 1; i < 100; ++i) {
+    fe_sq(t2, t2);
+  }
+  fe_mul(t1, t2, t1);
+  fe_sq(t1, t1);
+  for (i = 1; i < 50; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t0, t1, t0);
+  fe_sq(t0, t0);
+  for (i = 1; i < 2; ++i) {
+    fe_sq(t0, t0);
+  }
+  fe_mul(out, t0, z);
+}
+
+static uint8_t equal(signed char b, signed char c) {
+  uint8_t ub = b;
+  uint8_t uc = c;
+  uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
+  uint32_t y = x;      /* 0: yes; 1..255: no */
+  y -= 1;              /* 4294967295: yes; 0..254: no */
+  y >>= 31;            /* 1: yes; 0: no */
+  return y;
+}
+
+/* Replace (f,g) with (g,f) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
+ *
+ * Preconditions: b in {0,1}. */
+static void fe_cswap(fe f, fe g, unsigned int b) {
+  size_t i;
+  b = 0-b;
+  for (i = 0; i < 10; i++) {
+    int32_t x = f[i] ^ g[i];
+    x &= b;
+    f[i] ^= x;
+    g[i] ^= x;
+  }
+}
+
+/* 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. */
+static void fe_mul121666(fe h, fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int64_t h0 = f0 * (int64_t) 121666;
+  int64_t h1 = f1 * (int64_t) 121666;
+  int64_t h2 = f2 * (int64_t) 121666;
+  int64_t h3 = f3 * (int64_t) 121666;
+  int64_t h4 = f4 * (int64_t) 121666;
+  int64_t h5 = f5 * (int64_t) 121666;
+  int64_t h6 = f6 * (int64_t) 121666;
+  int64_t h7 = f7 * (int64_t) 121666;
+  int64_t h8 = f8 * (int64_t) 121666;
+  int64_t h9 = f9 * (int64_t) 121666;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
+  carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
+  carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
+  carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
+  carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
+
+  carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
+  carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
+  carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
+  carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
+  carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
+
+  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;
+}
+
+static void x25519_scalar_mult_generic(uint8_t out[32],
+                                       const uint8_t scalar[32],
+                                       const uint8_t point[32]) {
+  fe x1, x2, z2, x3, z3, tmp0, tmp1;
+  uint8_t e[32];
+  unsigned swap = 0;
+  int pos;
+
+  memcpy(e, scalar, 32);
+  e[0] &= 248;
+  e[31] &= 127;
+  e[31] |= 64;
+  fe_frombytes(x1, point);
+  fe_1(x2);
+  fe_0(z2);
+  fe_copy(x3, x1);
+  fe_1(z3);
+
+  for (pos = 254; pos >= 0; --pos) {
+    unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+    swap ^= b;
+    fe_cswap(x2, x3, swap);
+    fe_cswap(z2, z3, swap);
+    swap = b;
+    fe_sub(tmp0, x3, z3);
+    fe_sub(tmp1, x2, z2);
+    fe_add(x2, x2, z2);
+    fe_add(z2, x3, z3);
+    fe_mul(z3, tmp0, x2);
+    fe_mul(z2, z2, tmp1);
+    fe_sq(tmp0, tmp1);
+    fe_sq(tmp1, x2);
+    fe_add(x3, z3, z2);
+    fe_sub(z2, z3, z2);
+    fe_mul(x2, tmp1, tmp0);
+    fe_sub(tmp1, tmp1, tmp0);
+    fe_sq(z2, z2);
+    fe_mul121666(z3, tmp1);
+    fe_sq(x3, x3);
+    fe_add(tmp0, tmp0, z3);
+    fe_mul(z3, x1, z2);
+    fe_mul(z2, tmp1, tmp0);
+  }
+  fe_cswap(x2, x3, swap);
+  fe_cswap(z2, z3, swap);
+
+  fe_invert(z2, z2);
+  fe_mul(x2, x2, z2);
+  fe_tobytes(out, x2);
+}
+
+void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
+                               const uint8_t point[32]) {
+  x25519_scalar_mult_generic(out, scalar, point);
+}
diff --git a/third_party/openssl-curve25519/ec_curve25519.h b/third_party/openssl-curve25519/ec_curve25519.h
new file mode 100644
index 000000000..60dc86e75
--- /dev/null
+++ b/third_party/openssl-curve25519/ec_curve25519.h
@@ -0,0 +1,2 @@
+#include <stdint.h>
+void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], const uint8_t point[32]);
diff --git a/third_party/openssl-curve25519/measurements.txt b/third_party/openssl-curve25519/measurements.txt
new file mode 100644
index 000000000..b28317900
--- /dev/null
+++ b/third_party/openssl-curve25519/measurements.txt
@@ -0,0 +1 @@
+359336	ashryn-noht-notb-ac-broadwell	2.50ghz	7.1.1	56d7eec6