benchmark OpenSSL p256 C code

5 files changed, 1514 insertions, 0 deletions

diff --git a/third_party/openssl-nistp256c64/LICENSE b/third_party/openssl-nistp256c64/LICENSE
new file mode 100644
index 000000000..8fbabd8af
--- /dev/null
+++ b/third_party/openssl-nistp256c64/LICENSE
@@ -0,0 +1,125 @@
+
+  LICENSE ISSUES
+  ==============
+
+  The OpenSSL toolkit stays under a double license, i.e. both the conditions of
+  the OpenSSL License and the original SSLeay license apply to the toolkit.
+  See below for the actual license texts.
+
+  OpenSSL License
+  ---------------
+
+/* ====================================================================
+ * Copyright (c) 1998-2017 The OpenSSL Project.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer. 
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ *    software must display the following acknowledgment:
+ *    "This product includes software developed by the OpenSSL Project
+ *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ *    endorse or promote products derived from this software without
+ *    prior written permission. For written permission, please contact
+ *    openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ *    nor may "OpenSSL" appear in their names without prior written
+ *    permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ *    acknowledgment:
+ *    "This product includes software developed by the OpenSSL Project
+ *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com).  This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+ Original SSLeay License
+ -----------------------
+
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
+ * All rights reserved.
+ *
+ * This package is an SSL implementation written
+ * by Eric Young (eay@cryptsoft.com).
+ * The implementation was written so as to conform with Netscapes SSL.
+ * 
+ * This library is free for commercial and non-commercial use as long as
+ * the following conditions are aheared to.  The following conditions
+ * apply to all code found in this distribution, be it the RC4, RSA,
+ * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
+ * included with this distribution is covered by the same copyright terms
+ * except that the holder is Tim Hudson (tjh@cryptsoft.com).
+ * 
+ * Copyright remains Eric Young's, and as such any Copyright notices in
+ * the code are not to be removed.
+ * If this package is used in a product, Eric Young should be given attribution
+ * as the author of the parts of the library used.
+ * This can be in the form of a textual message at program startup or
+ * in documentation (online or textual) provided with the package.
+ * 
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *    "This product includes cryptographic software written by
+ *     Eric Young (eay@cryptsoft.com)"
+ *    The word 'cryptographic' can be left out if the rouines from the library
+ *    being used are not cryptographic related :-).
+ * 4. If you include any Windows specific code (or a derivative thereof) from 
+ *    the apps directory (application code) you must include an acknowledgement:
+ *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
+ * 
+ * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ * 
+ * The licence and distribution terms for any publically available version or
+ * derivative of this code cannot be changed.  i.e. this code cannot simply be
+ * copied and put under another distribution licence
+ * [including the GNU Public Licence.]
+ */
+
diff --git a/third_party/openssl-nistp256c64/bench_madd.c b/third_party/openssl-nistp256c64/bench_madd.c
new file mode 100644
index 000000000..e2dc8e880
--- /dev/null
+++ b/third_party/openssl-nistp256c64/bench_madd.c
@@ -0,0 +1,16 @@
+#include <stdint.h>
+#include "ecp_nistp256.h"
+
+void bench_madd(unsigned char* buf) {
+  uint128_t* x3 = (uint128_t*) buf;
+  uint128_t* y3 = (uint128_t*) (buf + 1*sizeof(felem));
+  uint128_t* z3 = (uint128_t*) (buf + 2*sizeof(felem));
+  uint128_t* x1 = (uint128_t*) (buf + 3*sizeof(felem));
+  uint128_t* y1 = (uint128_t*) (buf + 4*sizeof(felem));
+  uint128_t* z1 = (uint128_t*) (buf + 5*sizeof(felem));
+  int mixed = 1;
+  uint64_t* x2 = (uint64_t*) (buf + 6*sizeof(felem));
+  uint64_t* y2 = (uint64_t*) (buf + 6*sizeof(felem) + sizeof(smallfelem));
+  smallfelem z2 = {1, 0, 0, 0};
+  point_add(x3, y3, z3, x1, y1, z1, mixed, x2, y2, z2);
+}
diff --git a/third_party/openssl-nistp256c64/compiler.sh b/third_party/openssl-nistp256c64/compiler.sh
new file mode 100755
index 000000000..e64df574a
--- /dev/null
+++ b/third_party/openssl-nistp256c64/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 $@
diff --git a/third_party/openssl-nistp256c64/ecp_nistp256.c b/third_party/openssl-nistp256c64/ecp_nistp256.c
new file mode 100644
index 000000000..9d5f36905
--- /dev/null
+++ b/third_party/openssl-nistp256c64/ecp_nistp256.c
@@ -0,0 +1,1314 @@
+/*
+ * Copyright 2011-2016 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
+ */
+
+/* Copyright 2011 Google Inc.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ *
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS,
+ *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ */
+
+/*
+ * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication
+ *
+ * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c.
+ * Otherwise based on Emilia's P224 work, which was inspired by my curve25519
+ * work which got its smarts from Daniel J. Bernstein's work on the same.
+ */
+
+# include <stdint.h>
+# include <string.h>
+# include <openssl/err.h>
+# include "ecp_nistp256.h"
+
+
+/*
+ * These are the parameters of P256, taken from FIPS 186-3, page 86. These
+ * values are big-endian.
+ */
+static const felem_bytearray nistp256_curve_params[5] = {
+    {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+    {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */
+    {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7,
+     0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc,
+     0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6,
+     0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b},
+    {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */
+     0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2,
+     0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0,
+     0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96},
+    {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */
+     0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16,
+     0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce,
+     0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5}
+};
+
+/*-
+
+/* This is the value of the prime as four 64-bit words, little-endian. */
+static const u64 kPrime[4] =
+    { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul };
+static const u64 bottom63bits = 0x7ffffffffffffffful;
+
+/*
+ * bin32_to_felem takes a little-endian byte array and converts it into felem
+ * form. This assumes that the CPU is little-endian.
+ */
+static void bin32_to_felem(felem out, const u8 in[32])
+{
+    out[0] = *((u64 *)&in[0]);
+    out[1] = *((u64 *)&in[8]);
+    out[2] = *((u64 *)&in[16]);
+    out[3] = *((u64 *)&in[24]);
+}
+
+/*
+ * smallfelem_to_bin32 takes a smallfelem and serialises into a little
+ * endian, 32 byte array. This assumes that the CPU is little-endian.
+ */
+static void smallfelem_to_bin32(u8 out[32], const smallfelem in)
+{
+    *((u64 *)&out[0]) = in[0];
+    *((u64 *)&out[8]) = in[1];
+    *((u64 *)&out[16]) = in[2];
+    *((u64 *)&out[24]) = in[3];
+}
+
+/*-
+ * Field operations
+ * ----------------
+ */
+
+static void smallfelem_one(smallfelem out)
+{
+    out[0] = 1;
+    out[1] = 0;
+    out[2] = 0;
+    out[3] = 0;
+}
+
+static void smallfelem_assign(smallfelem out, const smallfelem in)
+{
+    out[0] = in[0];
+    out[1] = in[1];
+    out[2] = in[2];
+    out[3] = in[3];
+}
+
+static void felem_assign(felem out, const felem in)
+{
+    out[0] = in[0];
+    out[1] = in[1];
+    out[2] = in[2];
+    out[3] = in[3];
+}
+
+/* felem_sum sets out = out + in. */
+static void felem_sum(felem out, const felem in)
+{
+    out[0] += in[0];
+    out[1] += in[1];
+    out[2] += in[2];
+    out[3] += in[3];
+}
+
+/* felem_small_sum sets out = out + in. */
+static void felem_small_sum(felem out, const smallfelem in)
+{
+    out[0] += in[0];
+    out[1] += in[1];
+    out[2] += in[2];
+    out[3] += in[3];
+}
+
+/* felem_scalar sets out = out * scalar */
+static void felem_scalar(felem out, const u64 scalar)
+{
+    out[0] *= scalar;
+    out[1] *= scalar;
+    out[2] *= scalar;
+    out[3] *= scalar;
+}
+
+/* longfelem_scalar sets out = out * scalar */
+static void longfelem_scalar(longfelem out, const u64 scalar)
+{
+    out[0] *= scalar;
+    out[1] *= scalar;
+    out[2] *= scalar;
+    out[3] *= scalar;
+    out[4] *= scalar;
+    out[5] *= scalar;
+    out[6] *= scalar;
+    out[7] *= scalar;
+}
+
+# define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9)
+# define two105 (((limb)1) << 105)
+# define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9)
+
+/* zero105 is 0 mod p */
+static const felem zero105 =
+    { two105m41m9, two105, two105m41p9, two105m41p9 };
+
+/*-
+ * smallfelem_neg sets |out| to |-small|
+ * On exit:
+ *   out[i] < out[i] + 2^105
+ */
+static void smallfelem_neg(felem out, const smallfelem small)
+{
+    /* In order to prevent underflow, we subtract from 0 mod p. */
+    out[0] = zero105[0] - small[0];
+    out[1] = zero105[1] - small[1];
+    out[2] = zero105[2] - small[2];
+    out[3] = zero105[3] - small[3];
+}
+
+/*-
+ * felem_diff subtracts |in| from |out|
+ * On entry:
+ *   in[i] < 2^104
+ * On exit:
+ *   out[i] < out[i] + 2^105
+ */
+static void felem_diff(felem out, const felem in)
+{
+    /*
+     * In order to prevent underflow, we add 0 mod p before subtracting.
+     */
+    out[0] += zero105[0];
+    out[1] += zero105[1];
+    out[2] += zero105[2];
+    out[3] += zero105[3];
+
+    out[0] -= in[0];
+    out[1] -= in[1];
+    out[2] -= in[2];
+    out[3] -= in[3];
+}
+
+# define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11)
+# define two107 (((limb)1) << 107)
+# define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11)
+
+/* zero107 is 0 mod p */
+static const felem zero107 =
+    { two107m43m11, two107, two107m43p11, two107m43p11 };
+
+/*-
+ * An alternative felem_diff for larger inputs |in|
+ * felem_diff_zero107 subtracts |in| from |out|
+ * On entry:
+ *   in[i] < 2^106
+ * On exit:
+ *   out[i] < out[i] + 2^107
+ */
+static void felem_diff_zero107(felem out, const felem in)
+{
+    /*
+     * In order to prevent underflow, we add 0 mod p before subtracting.
+     */
+    out[0] += zero107[0];
+    out[1] += zero107[1];
+    out[2] += zero107[2];
+    out[3] += zero107[3];
+
+    out[0] -= in[0];
+    out[1] -= in[1];
+    out[2] -= in[2];
+    out[3] -= in[3];
+}
+
+/*-
+ * longfelem_diff subtracts |in| from |out|
+ * On entry:
+ *   in[i] < 7*2^67
+ * On exit:
+ *   out[i] < out[i] + 2^70 + 2^40
+ */
+static void longfelem_diff(longfelem out, const longfelem in)
+{
+    static const limb two70m8p6 =
+        (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6);
+    static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40);
+    static const limb two70 = (((limb) 1) << 70);
+    static const limb two70m40m38p6 =
+        (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) +
+        (((limb) 1) << 6);
+    static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6);
+
+    /* add 0 mod p to avoid underflow */
+    out[0] += two70m8p6;
+    out[1] += two70p40;
+    out[2] += two70;
+    out[3] += two70m40m38p6;
+    out[4] += two70m6;
+    out[5] += two70m6;
+    out[6] += two70m6;
+    out[7] += two70m6;
+
+    /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */
+    out[0] -= in[0];
+    out[1] -= in[1];
+    out[2] -= in[2];
+    out[3] -= in[3];
+    out[4] -= in[4];
+    out[5] -= in[5];
+    out[6] -= in[6];
+    out[7] -= in[7];
+}
+
+# define two64m0 (((limb)1) << 64) - 1
+# define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1
+# define two64m46 (((limb)1) << 64) - (((limb)1) << 46)
+# define two64m32 (((limb)1) << 64) - (((limb)1) << 32)
+
+/* zero110 is 0 mod p */
+static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 };
+
+/*-
+ * felem_shrink converts an felem into a smallfelem. The result isn't quite
+ * minimal as the value may be greater than p.
+ *
+ * On entry:
+ *   in[i] < 2^109
+ * On exit:
+ *   out[i] < 2^64
+ */
+static void felem_shrink(smallfelem out, const felem in)
+{
+    felem tmp;
+    u64 a, b, mask;
+    s64 high, low;
+    static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */
+
+    /* Carry 2->3 */
+    tmp[3] = zero110[3] + in[3] + ((u64)(in[2] >> 64));
+    /* tmp[3] < 2^110 */
+
+    tmp[2] = zero110[2] + (u64)in[2];
+    tmp[0] = zero110[0] + in[0];
+    tmp[1] = zero110[1] + in[1];
+    /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */
+
+    /*
+     * We perform two partial reductions where we eliminate the high-word of
+     * tmp[3]. We don't update the other words till the end.
+     */
+    a = tmp[3] >> 64;           /* a < 2^46 */
+    tmp[3] = (u64)tmp[3];
+    tmp[3] -= a;
+    tmp[3] += ((limb) a) << 32;
+    /* tmp[3] < 2^79 */
+
+    b = a;
+    a = tmp[3] >> 64;           /* a < 2^15 */
+    b += a;                     /* b < 2^46 + 2^15 < 2^47 */
+    tmp[3] = (u64)tmp[3];
+    tmp[3] -= a;
+    tmp[3] += ((limb) a) << 32;
+    /* tmp[3] < 2^64 + 2^47 */
+
+    /*
+     * This adjusts the other two words to complete the two partial
+     * reductions.
+     */
+    tmp[0] += b;
+    tmp[1] -= (((limb) b) << 32);
+
+    /*
+     * In order to make space in tmp[3] for the carry from 2 -> 3, we
+     * conditionally subtract kPrime if tmp[3] is large enough.
+     */
+    high = tmp[3] >> 64;
+    /* As tmp[3] < 2^65, high is either 1 or 0 */
+    high <<= 63;
+    high >>= 63;
+    /*-
+     * high is:
+     *   all ones   if the high word of tmp[3] is 1
+     *   all zeros  if the high word of tmp[3] if 0 */
+    low = tmp[3];
+    mask = low >> 63;
+    /*-
+     * mask is:
+     *   all ones   if the MSB of low is 1
+     *   all zeros  if the MSB of low if 0 */
+    low &= bottom63bits;
+    low -= kPrime3Test;
+    /* if low was greater than kPrime3Test then the MSB is zero */
+    low = ~low;
+    low >>= 63;
+    /*-
+     * low is:
+     *   all ones   if low was > kPrime3Test
+     *   all zeros  if low was <= kPrime3Test */
+    mask = (mask & low) | high;
+    tmp[0] -= mask & kPrime[0];
+    tmp[1] -= mask & kPrime[1];
+    /* kPrime[2] is zero, so omitted */
+    tmp[3] -= mask & kPrime[3];
+    /* tmp[3] < 2**64 - 2**32 + 1 */
+
+    tmp[1] += ((u64)(tmp[0] >> 64));
+    tmp[0] = (u64)tmp[0];
+    tmp[2] += ((u64)(tmp[1] >> 64));
+    tmp[1] = (u64)tmp[1];
+    tmp[3] += ((u64)(tmp[2] >> 64));
+    tmp[2] = (u64)tmp[2];
+    /* tmp[i] < 2^64 */
+
+    out[0] = tmp[0];
+    out[1] = tmp[1];
+    out[2] = tmp[2];
+    out[3] = tmp[3];
+}
+
+/* smallfelem_expand converts a smallfelem to an felem */
+static void smallfelem_expand(felem out, const smallfelem in)
+{
+    out[0] = in[0];
+    out[1] = in[1];
+    out[2] = in[2];
+    out[3] = in[3];
+}
+
+/*-
+ * smallfelem_square sets |out| = |small|^2
+ * On entry:
+ *   small[i] < 2^64
+ * On exit:
+ *   out[i] < 7 * 2^64 < 2^67
+ */
+static void smallfelem_square(longfelem out, const smallfelem small)
+{
+    limb a;
+    u64 high, low;
+
+    a = ((uint128_t) small[0]) * small[0];
+    low = a;
+    high = a >> 64;
+    out[0] = low;
+    out[1] = high;
+
+    a = ((uint128_t) small[0]) * small[1];
+    low = a;
+    high = a >> 64;
+    out[1] += low;
+    out[1] += low;
+    out[2] = high;
+
+    a = ((uint128_t) small[0]) * small[2];
+    low = a;
+    high = a >> 64;
+    out[2] += low;
+    out[2] *= 2;
+    out[3] = high;
+
+    a = ((uint128_t) small[0]) * small[3];
+    low = a;
+    high = a >> 64;
+    out[3] += low;
+    out[4] = high;
+
+    a = ((uint128_t) small[1]) * small[2];
+    low = a;
+    high = a >> 64;
+    out[3] += low;
+    out[3] *= 2;
+    out[4] += high;
+
+    a = ((uint128_t) small[1]) * small[1];
+    low = a;
+    high = a >> 64;
+    out[2] += low;
+    out[3] += high;
+
+    a = ((uint128_t) small[1]) * small[3];
+    low = a;
+    high = a >> 64;
+    out[4] += low;
+    out[4] *= 2;
+    out[5] = high;
+
+    a = ((uint128_t) small[2]) * small[3];
+    low = a;
+    high = a >> 64;
+    out[5] += low;
+    out[5] *= 2;
+    out[6] = high;
+    out[6] += high;
+
+    a = ((uint128_t) small[2]) * small[2];
+    low = a;
+    high = a >> 64;
+    out[4] += low;
+    out[5] += high;
+
+    a = ((uint128_t) small[3]) * small[3];
+    low = a;
+    high = a >> 64;
+    out[6] += low;
+    out[7] = high;
+}
+
+/*-
+ * felem_square sets |out| = |in|^2
+ * On entry:
+ *   in[i] < 2^109
+ * On exit:
+ *   out[i] < 7 * 2^64 < 2^67
+ */
+static void felem_square(longfelem out, const felem in)
+{
+    u64 small[4];
+    felem_shrink(small, in);
+    smallfelem_square(out, small);
+}
+
+/*-
+ * smallfelem_mul sets |out| = |small1| * |small2|
+ * On entry:
+ *   small1[i] < 2^64
+ *   small2[i] < 2^64
+ * On exit:
+ *   out[i] < 7 * 2^64 < 2^67
+ */
+static void smallfelem_mul(longfelem out, const smallfelem small1,
+                           const smallfelem small2)
+{
+    limb a;
+    u64 high, low;
+
+    a = ((uint128_t) small1[0]) * small2[0];
+    low = a;
+    high = a >> 64;
+    out[0] = low;
+    out[1] = high;
+
+    a = ((uint128_t) small1[0]) * small2[1];
+    low = a;
+    high = a >> 64;
+    out[1] += low;
+    out[2] = high;
+
+    a = ((uint128_t) small1[1]) * small2[0];
+    low = a;
+    high = a >> 64;
+    out[1] += low;
+    out[2] += high;
+
+    a = ((uint128_t) small1[0]) * small2[2];
+    low = a;
+    high = a >> 64;
+    out[2] += low;
+    out[3] = high;
+
+    a = ((uint128_t) small1[1]) * small2[1];
+    low = a;
+    high = a >> 64;
+    out[2] += low;
+    out[3] += high;
+
+    a = ((uint128_t) small1[2]) * small2[0];
+    low = a;
+    high = a >> 64;
+    out[2] += low;
+    out[3] += high;
+
+    a = ((uint128_t) small1[0]) * small2[3];
+    low = a;
+    high = a >> 64;
+    out[3] += low;
+    out[4] = high;
+
+    a = ((uint128_t) small1[1]) * small2[2];
+    low = a;
+    high = a >> 64;
+    out[3] += low;
+    out[4] += high;
+
+    a = ((uint128_t) small1[2]) * small2[1];
+    low = a;
+    high = a >> 64;
+    out[3] += low;
+    out[4] += high;
+
+    a = ((uint128_t) small1[3]) * small2[0];
+    low = a;
+    high = a >> 64;
+    out[3] += low;
+    out[4] += high;
+
+    a = ((uint128_t) small1[1]) * small2[3];
+    low = a;
+    high = a >> 64;
+    out[4] += low;
+    out[5] = high;
+
+    a = ((uint128_t) small1[2]) * small2[2];
+    low = a;
+    high = a >> 64;
+    out[4] += low;
+    out[5] += high;
+
+    a = ((uint128_t) small1[3]) * small2[1];
+    low = a;
+    high = a >> 64;
+    out[4] += low;
+    out[5] += high;
+
+    a = ((uint128_t) small1[2]) * small2[3];
+    low = a;
+    high = a >> 64;
+    out[5] += low;
+    out[6] = high;
+
+    a = ((uint128_t) small1[3]) * small2[2];
+    low = a;
+    high = a >> 64;
+    out[5] += low;
+    out[6] += high;
+
+    a = ((uint128_t) small1[3]) * small2[3];
+    low = a;
+    high = a >> 64;
+    out[6] += low;
+    out[7] = high;
+}
+
+/*-
+ * felem_mul sets |out| = |in1| * |in2|
+ * On entry:
+ *   in1[i] < 2^109
+ *   in2[i] < 2^109
+ * On exit:
+ *   out[i] < 7 * 2^64 < 2^67
+ */
+static void felem_mul(longfelem out, const felem in1, const felem in2)
+{
+    smallfelem small1, small2;
+    felem_shrink(small1, in1);
+    felem_shrink(small2, in2);
+    smallfelem_mul(out, small1, small2);
+}
+
+/*-
+ * felem_small_mul sets |out| = |small1| * |in2|
+ * On entry:
+ *   small1[i] < 2^64
+ *   in2[i] < 2^109
+ * On exit:
+ *   out[i] < 7 * 2^64 < 2^67
+ */
+static void felem_small_mul(longfelem out, const smallfelem small1,
+                            const felem in2)
+{
+    smallfelem small2;
+    felem_shrink(small2, in2);
+    smallfelem_mul(out, small1, small2);
+}
+
+# define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4)
+# define two100 (((limb)1) << 100)
+# define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4)
+/* zero100 is 0 mod p */
+static const felem zero100 =
+    { two100m36m4, two100, two100m36p4, two100m36p4 };
+
+/*-
+ * Internal function for the different flavours of felem_reduce.
+ * felem_reduce_ reduces the higher coefficients in[4]-in[7].
+ * On entry:
+ *   out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7]
+ *   out[1] >= in[7] + 2^32*in[4]
+ *   out[2] >= in[5] + 2^32*in[5]
+ *   out[3] >= in[4] + 2^32*in[5] + 2^32*in[6]
+ * On exit:
+ *   out[0] <= out[0] + in[4] + 2^32*in[5]
+ *   out[1] <= out[1] + in[5] + 2^33*in[6]
+ *   out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7]
+ *   out[3] <= out[3] + 2^32*in[4] + 3*in[7]
+ */
+static void felem_reduce_(felem out, const longfelem in)
+{
+    int128_t c;
+    /* combine common terms from below */
+    c = in[4] + (in[5] << 32);
+    out[0] += c;
+    out[3] -= c;
+
+    c = in[5] - in[7];
+    out[1] += c;
+    out[2] -= c;
+
+    /* the remaining terms */
+    /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */
+    out[1] -= (in[4] << 32);
+    out[3] += (in[4] << 32);
+
+    /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */
+    out[2] -= (in[5] << 32);
+
+    /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */
+    out[0] -= in[6];
+    out[0] -= (in[6] << 32);
+    out[1] += (in[6] << 33);
+    out[2] += (in[6] * 2);
+    out[3] -= (in[6] << 32);
+
+    /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */
+    out[0] -= in[7];
+    out[0] -= (in[7] << 32);
+    out[2] += (in[7] << 33);
+    out[3] += (in[7] * 3);
+}
+
+/*-
+ * felem_reduce converts a longfelem into an felem.
+ * To be called directly after felem_square or felem_mul.
+ * On entry:
+ *   in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64
+ *   in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64
+ * On exit:
+ *   out[i] < 2^101
+ */
+static void felem_reduce(felem out, const longfelem in)
+{
+    out[0] = zero100[0] + in[0];
+    out[1] = zero100[1] + in[1];
+    out[2] = zero100[2] + in[2];
+    out[3] = zero100[3] + in[3];
+
+    felem_reduce_(out, in);
+
+    /*-
+     * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0
+     * out[1] > 2^100 - 2^64 - 7*2^96 > 0
+     * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0
+     * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0
+     *
+     * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101
+     * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101
+     * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101
+     * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101
+     */
+}
+
+/*-
+ * felem_reduce_zero105 converts a larger longfelem into an felem.
+ * On entry:
+ *   in[0] < 2^71
+ * On exit:
+ *   out[i] < 2^106
+ */
+static void felem_reduce_zero105(felem out, const longfelem in)
+{
+    out[0] = zero105[0] + in[0];
+    out[1] = zero105[1] + in[1];
+    out[2] = zero105[2] + in[2];
+    out[3] = zero105[3] + in[3];
+
+    felem_reduce_(out, in);
+
+    /*-
+     * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0
+     * out[1] > 2^105 - 2^71 - 2^103 > 0
+     * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0
+     * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0
+     *
+     * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
+     * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106
+     * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106
+     * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106
+     */
+}
+
+/*
+ * subtract_u64 sets *result = *result - v and *carry to one if the
+ * subtraction underflowed.
+ */
+static void subtract_u64(u64 *result, u64 *carry, u64 v)
+{
+    uint128_t r = *result;
+    r -= v;
+    *carry = (r >> 64) & 1;
+    *result = (u64)r;
+}
+
+/*
+ * felem_contract converts |in| to its unique, minimal representation. On
+ * entry: in[i] < 2^109
+ */
+static void felem_contract(smallfelem out, const felem in)
+{
+    unsigned i;
+    u64 all_equal_so_far = 0, result = 0, carry;
+
+    felem_shrink(out, in);
+    /* small is minimal except that the value might be > p */
+
+    all_equal_so_far--;
+    /*
+     * We are doing a constant time test if out >= kPrime. We need to compare
+     * each u64, from most-significant to least significant. For each one, if
+     * all words so far have been equal (m is all ones) then a non-equal
+     * result is the answer. Otherwise we continue.
+     */
+    for (i = 3; i < 4; i--) {
+        u64 equal;
+        uint128_t a = ((uint128_t) kPrime[i]) - out[i];
+        /*
+         * if out[i] > kPrime[i] then a will underflow and the high 64-bits
+         * will all be set.
+         */
+        result |= all_equal_so_far & ((u64)(a >> 64));
+
+        /*
+         * if kPrime[i] == out[i] then |equal| will be all zeros and the
+         * decrement will make it all ones.
+         */
+        equal = kPrime[i] ^ out[i];
+        equal--;
+        equal &= equal << 32;
+        equal &= equal << 16;
+        equal &= equal << 8;
+        equal &= equal << 4;
+        equal &= equal << 2;
+        equal &= equal << 1;
+        equal = ((s64) equal) >> 63;
+
+        all_equal_so_far &= equal;
+    }
+
+    /*
+     * if all_equal_so_far is still all ones then the two values are equal
+     * and so out >= kPrime is true.
+     */
+    result |= all_equal_so_far;
+
+    /* if out >= kPrime then we subtract kPrime. */
+    subtract_u64(&out[0], &carry, result & kPrime[0]);
+    subtract_u64(&out[1], &carry, carry);
+    subtract_u64(&out[2], &carry, carry);
+    subtract_u64(&out[3], &carry, carry);
+
+    subtract_u64(&out[1], &carry, result & kPrime[1]);
+    subtract_u64(&out[2], &carry, carry);
+    subtract_u64(&out[3], &carry, carry);
+
+    subtract_u64(&out[2], &carry, result & kPrime[2]);
+    subtract_u64(&out[3], &carry, carry);
+
+    subtract_u64(&out[3], &carry, result & kPrime[3]);
+}
+
+static void smallfelem_square_contract(smallfelem out, const smallfelem in)
+{
+    longfelem longtmp;
+    felem tmp;
+
+    smallfelem_square(longtmp, in);
+    felem_reduce(tmp, longtmp);
+    felem_contract(out, tmp);
+}
+
+static void smallfelem_mul_contract(smallfelem out, const smallfelem in1,
+                                    const smallfelem in2)
+{
+    longfelem longtmp;
+    felem tmp;
+
+    smallfelem_mul(longtmp, in1, in2);
+    felem_reduce(tmp, longtmp);
+    felem_contract(out, tmp);
+}
+
+/*-
+ * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
+ * otherwise.
+ * On entry:
+ *   small[i] < 2^64
+ */
+static limb smallfelem_is_zero(const smallfelem small)
+{
+    limb result;
+    u64 is_p;
+
+    u64 is_zero = small[0] | small[1] | small[2] | small[3];
+    is_zero--;
+    is_zero &= is_zero << 32;
+    is_zero &= is_zero << 16;
+    is_zero &= is_zero << 8;
+    is_zero &= is_zero << 4;
+    is_zero &= is_zero << 2;
+    is_zero &= is_zero << 1;
+    is_zero = ((s64) is_zero) >> 63;
+
+    is_p = (small[0] ^ kPrime[0]) |
+        (small[1] ^ kPrime[1]) |
+        (small[2] ^ kPrime[2]) | (small[3] ^ kPrime[3]);
+    is_p--;
+    is_p &= is_p << 32;
+    is_p &= is_p << 16;
+    is_p &= is_p << 8;
+    is_p &= is_p << 4;
+    is_p &= is_p << 2;
+    is_p &= is_p << 1;
+    is_p = ((s64) is_p) >> 63;
+
+    is_zero |= is_p;
+
+    result = is_zero;
+    result |= ((limb) is_zero) << 64;
+    return result;
+}
+
+static int smallfelem_is_zero_int(const smallfelem small)
+{
+    return (int)(smallfelem_is_zero(small) & ((limb) 1));
+}
+
+/*-
+ * felem_inv calculates |out| = |in|^{-1}
+ *
+ * Based on Fermat's Little Theorem:
+ *   a^p = a (mod p)
+ *   a^{p-1} = 1 (mod p)
+ *   a^{p-2} = a^{-1} (mod p)
+ */
+static void felem_inv(felem out, const felem in)
+{
+    felem ftmp, ftmp2;
+    /* each e_I will hold |in|^{2^I - 1} */
+    felem e2, e4, e8, e16, e32, e64;
+    longfelem tmp;
+    unsigned i;
+
+    felem_square(tmp, in);
+    felem_reduce(ftmp, tmp);    /* 2^1 */
+    felem_mul(tmp, in, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^2 - 2^0 */
+    felem_assign(e2, ftmp);
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^3 - 2^1 */
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^4 - 2^2 */
+    felem_mul(tmp, ftmp, e2);
+    felem_reduce(ftmp, tmp);    /* 2^4 - 2^0 */
+    felem_assign(e4, ftmp);
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^5 - 2^1 */
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^6 - 2^2 */
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^7 - 2^3 */
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^8 - 2^4 */
+    felem_mul(tmp, ftmp, e4);
+    felem_reduce(ftmp, tmp);    /* 2^8 - 2^0 */
+    felem_assign(e8, ftmp);
+    for (i = 0; i < 8; i++) {
+        felem_square(tmp, ftmp);
+        felem_reduce(ftmp, tmp);
+    }                           /* 2^16 - 2^8 */
+    felem_mul(tmp, ftmp, e8);
+    felem_reduce(ftmp, tmp);    /* 2^16 - 2^0 */
+    felem_assign(e16, ftmp);
+    for (i = 0; i < 16; i++) {
+        felem_square(tmp, ftmp);
+        felem_reduce(ftmp, tmp);
+    }                           /* 2^32 - 2^16 */
+    felem_mul(tmp, ftmp, e16);
+    felem_reduce(ftmp, tmp);    /* 2^32 - 2^0 */
+    felem_assign(e32, ftmp);
+    for (i = 0; i < 32; i++) {
+        felem_square(tmp, ftmp);
+        felem_reduce(ftmp, tmp);
+    }                           /* 2^64 - 2^32 */
+    felem_assign(e64, ftmp);
+    felem_mul(tmp, ftmp, in);
+    felem_reduce(ftmp, tmp);    /* 2^64 - 2^32 + 2^0 */
+    for (i = 0; i < 192; i++) {
+        felem_square(tmp, ftmp);
+        felem_reduce(ftmp, tmp);
+    }                           /* 2^256 - 2^224 + 2^192 */
+
+    felem_mul(tmp, e64, e32);
+    felem_reduce(ftmp2, tmp);   /* 2^64 - 2^0 */
+    for (i = 0; i < 16; i++) {
+        felem_square(tmp, ftmp2);
+        felem_reduce(ftmp2, tmp);
+    }                           /* 2^80 - 2^16 */
+    felem_mul(tmp, ftmp2, e16);
+    felem_reduce(ftmp2, tmp);   /* 2^80 - 2^0 */
+    for (i = 0; i < 8; i++) {
+        felem_square(tmp, ftmp2);
+        felem_reduce(ftmp2, tmp);
+    }                           /* 2^88 - 2^8 */
+    felem_mul(tmp, ftmp2, e8);
+    felem_reduce(ftmp2, tmp);   /* 2^88 - 2^0 */
+    for (i = 0; i < 4; i++) {
+        felem_square(tmp, ftmp2);
+        felem_reduce(ftmp2, tmp);
+    }                           /* 2^92 - 2^4 */
+    felem_mul(tmp, ftmp2, e4);
+    felem_reduce(ftmp2, tmp);   /* 2^92 - 2^0 */
+    felem_square(tmp, ftmp2);
+    felem_reduce(ftmp2, tmp);   /* 2^93 - 2^1 */
+    felem_square(tmp, ftmp2);
+    felem_reduce(ftmp2, tmp);   /* 2^94 - 2^2 */
+    felem_mul(tmp, ftmp2, e2);
+    felem_reduce(ftmp2, tmp);   /* 2^94 - 2^0 */
+    felem_square(tmp, ftmp2);
+    felem_reduce(ftmp2, tmp);   /* 2^95 - 2^1 */
+    felem_square(tmp, ftmp2);
+    felem_reduce(ftmp2, tmp);   /* 2^96 - 2^2 */
+    felem_mul(tmp, ftmp2, in);
+    felem_reduce(ftmp2, tmp);   /* 2^96 - 3 */
+
+    felem_mul(tmp, ftmp2, ftmp);
+    felem_reduce(out, tmp);     /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */
+}
+
+static void smallfelem_inv_contract(smallfelem out, const smallfelem in)
+{
+    felem tmp;
+
+    smallfelem_expand(tmp, in);
+    felem_inv(tmp, tmp);
+    felem_contract(out, tmp);
+}
+
+/*-
+ * Group operations
+ * ----------------
+ *
+ * Building on top of the field operations we have the operations on the
+ * elliptic curve group itself. Points on the curve are represented in Jacobian
+ * coordinates
+ */
+
+/*-
+ * point_double calculates 2*(x_in, y_in, z_in)
+ *
+ * The method is taken from:
+ *   http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
+ *
+ * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed.
+ * while x_out == y_in is not (maybe this works, but it's not tested).
+ */
+static void
+point_double(felem x_out, felem y_out, felem z_out,
+             const felem x_in, const felem y_in, const felem z_in)
+{
+    longfelem tmp, tmp2;
+    felem delta, gamma, beta, alpha, ftmp, ftmp2;
+    smallfelem small1, small2;
+
+    felem_assign(ftmp, x_in);
+    /* ftmp[i] < 2^106 */
+    felem_assign(ftmp2, x_in);
+    /* ftmp2[i] < 2^106 */
+
+    /* delta = z^2 */
+    felem_square(tmp, z_in);
+    felem_reduce(delta, tmp);
+    /* delta[i] < 2^101 */
+
+    /* gamma = y^2 */
+    felem_square(tmp, y_in);
+    felem_reduce(gamma, tmp);
+    /* gamma[i] < 2^101 */
+    felem_shrink(small1, gamma);
+
+    /* beta = x*gamma */
+    felem_small_mul(tmp, small1, x_in);
+    felem_reduce(beta, tmp);
+    /* beta[i] < 2^101 */
+
+    /* alpha = 3*(x-delta)*(x+delta) */
+    felem_diff(ftmp, delta);
+    /* ftmp[i] < 2^105 + 2^106 < 2^107 */
+    felem_sum(ftmp2, delta);
+    /* ftmp2[i] < 2^105 + 2^106 < 2^107 */
+    felem_scalar(ftmp2, 3);
+    /* ftmp2[i] < 3 * 2^107 < 2^109 */
+    felem_mul(tmp, ftmp, ftmp2);
+    felem_reduce(alpha, tmp);
+    /* alpha[i] < 2^101 */
+    felem_shrink(small2, alpha);
+
+    /* x' = alpha^2 - 8*beta */
+    smallfelem_square(tmp, small2);
+    felem_reduce(x_out, tmp);
+    felem_assign(ftmp, beta);
+    felem_scalar(ftmp, 8);
+    /* ftmp[i] < 8 * 2^101 = 2^104 */
+    felem_diff(x_out, ftmp);
+    /* x_out[i] < 2^105 + 2^101 < 2^106 */
+
+    /* z' = (y + z)^2 - gamma - delta */
+    felem_sum(delta, gamma);
+    /* delta[i] < 2^101 + 2^101 = 2^102 */
+    felem_assign(ftmp, y_in);
+    felem_sum(ftmp, z_in);
+    /* ftmp[i] < 2^106 + 2^106 = 2^107 */
+    felem_square(tmp, ftmp);
+    felem_reduce(z_out, tmp);
+    felem_diff(z_out, delta);
+    /* z_out[i] < 2^105 + 2^101 < 2^106 */
+
+    /* y' = alpha*(4*beta - x') - 8*gamma^2 */
+    felem_scalar(beta, 4);
+    /* beta[i] < 4 * 2^101 = 2^103 */
+    felem_diff_zero107(beta, x_out);
+    /* beta[i] < 2^107 + 2^103 < 2^108 */
+    felem_small_mul(tmp, small2, beta);
+    /* tmp[i] < 7 * 2^64 < 2^67 */
+    smallfelem_square(tmp2, small1);
+    /* tmp2[i] < 7 * 2^64 */
+    longfelem_scalar(tmp2, 8);
+    /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */
+    longfelem_diff(tmp, tmp2);
+    /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
+    felem_reduce_zero105(y_out, tmp);
+    /* y_out[i] < 2^106 */
+}
+
+/*
+ * point_double_small is the same as point_double, except that it operates on
+ * smallfelems
+ */
+static void
+point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out,
+                   const smallfelem x_in, const smallfelem y_in,
+                   const smallfelem z_in)
+{
+    felem felem_x_out, felem_y_out, felem_z_out;
+    felem felem_x_in, felem_y_in, felem_z_in;
+
+    smallfelem_expand(felem_x_in, x_in);
+    smallfelem_expand(felem_y_in, y_in);
+    smallfelem_expand(felem_z_in, z_in);
+    point_double(felem_x_out, felem_y_out, felem_z_out,
+                 felem_x_in, felem_y_in, felem_z_in);
+    felem_shrink(x_out, felem_x_out);
+    felem_shrink(y_out, felem_y_out);
+    felem_shrink(z_out, felem_z_out);
+}
+
+/* copy_conditional copies in to out iff mask is all ones. */
+static void copy_conditional(felem out, const felem in, limb mask)
+{
+    unsigned i;
+    for (i = 0; i < NLIMBS; ++i) {
+        const limb tmp = mask & (in[i] ^ out[i]);
+        out[i] ^= tmp;
+    }
+}
+
+/* copy_small_conditional copies in to out iff mask is all ones. */
+static void copy_small_conditional(felem out, const smallfelem in, limb mask)
+{
+    unsigned i;
+    const u64 mask64 = mask;
+    for (i = 0; i < NLIMBS; ++i) {
+        out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask);
+    }
+}
+
+/*-
+ * point_add calculates (x1, y1, z1) + (x2, y2, z2)
+ *
+ * The method is taken from:
+ *   http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
+ * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
+ *
+ * This function includes a branch for checking whether the two input points
+ * are equal, (while not equal to the point at infinity). This case never
+ * happens during single point multiplication, so there is no timing leak for
+ * ECDH or ECDSA signing.
+ */
+void point_add(felem x3, felem y3, felem z3,
+                      const felem x1, const felem y1, const felem z1,
+                      const int mixed, const smallfelem x2,
+                      const smallfelem y2, const smallfelem z2)
+{
+    felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
+    longfelem tmp, tmp2;
+    smallfelem small1, small2, small3, small4, small5;
+    limb x_equal, y_equal, z1_is_zero, z2_is_zero;
+
+    felem_shrink(small3, z1);
+
+    z1_is_zero = smallfelem_is_zero(small3);
+    z2_is_zero = smallfelem_is_zero(z2);
+
+    /* ftmp = z1z1 = z1**2 */
+    smallfelem_square(tmp, small3);
+    felem_reduce(ftmp, tmp);
+    /* ftmp[i] < 2^101 */
+    felem_shrink(small1, ftmp);
+
+    if (!mixed) {
+        /* ftmp2 = z2z2 = z2**2 */
+        smallfelem_square(tmp, z2);
+        felem_reduce(ftmp2, tmp);
+        /* ftmp2[i] < 2^101 */
+        felem_shrink(small2, ftmp2);
+
+        felem_shrink(small5, x1);
+
+        /* u1 = ftmp3 = x1*z2z2 */
+        smallfelem_mul(tmp, small5, small2);
+        felem_reduce(ftmp3, tmp);
+        /* ftmp3[i] < 2^101 */
+
+        /* ftmp5 = z1 + z2 */
+        felem_assign(ftmp5, z1);
+        felem_small_sum(ftmp5, z2);
+        /* ftmp5[i] < 2^107 */
+
+        /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */
+        felem_square(tmp, ftmp5);
+        felem_reduce(ftmp5, tmp);
+        /* ftmp2 = z2z2 + z1z1 */
+        felem_sum(ftmp2, ftmp);
+        /* ftmp2[i] < 2^101 + 2^101 = 2^102 */
+        felem_diff(ftmp5, ftmp2);
+        /* ftmp5[i] < 2^105 + 2^101 < 2^106 */
+
+        /* ftmp2 = z2 * z2z2 */
+        smallfelem_mul(tmp, small2, z2);
+        felem_reduce(ftmp2, tmp);
+
+        /* s1 = ftmp2 = y1 * z2**3 */
+        felem_mul(tmp, y1, ftmp2);
+        felem_reduce(ftmp6, tmp);
+        /* ftmp6[i] < 2^101 */
+    } else {
+        /*
+         * We'll assume z2 = 1 (special case z2 = 0 is handled later)
+         */
+
+        /* u1 = ftmp3 = x1*z2z2 */
+        felem_assign(ftmp3, x1);
+        /* ftmp3[i] < 2^106 */
+
+        /* ftmp5 = 2z1z2 */
+        felem_assign(ftmp5, z1);
+        felem_scalar(ftmp5, 2);
+        /* ftmp5[i] < 2*2^106 = 2^107 */
+
+        /* s1 = ftmp2 = y1 * z2**3 */
+        felem_assign(ftmp6, y1);
+        /* ftmp6[i] < 2^106 */
+    }
+
+    /* u2 = x2*z1z1 */
+    smallfelem_mul(tmp, x2, small1);
+    felem_reduce(ftmp4, tmp);
+
+    /* h = ftmp4 = u2 - u1 */
+    felem_diff_zero107(ftmp4, ftmp3);
+    /* ftmp4[i] < 2^107 + 2^101 < 2^108 */
+    felem_shrink(small4, ftmp4);
+
+    x_equal = smallfelem_is_zero(small4);
+
+    /* z_out = ftmp5 * h */
+    felem_small_mul(tmp, small4, ftmp5);
+    felem_reduce(z_out, tmp);
+    /* z_out[i] < 2^101 */
+
+    /* ftmp = z1 * z1z1 */
+    smallfelem_mul(tmp, small1, small3);
+    felem_reduce(ftmp, tmp);
+
+    /* s2 = tmp = y2 * z1**3 */
+    felem_small_mul(tmp, y2, ftmp);
+    felem_reduce(ftmp5, tmp);
+
+    /* r = ftmp5 = (s2 - s1)*2 */
+    felem_diff_zero107(ftmp5, ftmp6);
+    /* ftmp5[i] < 2^107 + 2^107 = 2^108 */
+    felem_scalar(ftmp5, 2);
+    /* ftmp5[i] < 2^109 */
+    felem_shrink(small1, ftmp5);
+    y_equal = smallfelem_is_zero(small1);
+
+    if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
+        point_double(x3, y3, z3, x1, y1, z1);
+        return;
+    }
+
+    /* I = ftmp = (2h)**2 */
+    felem_assign(ftmp, ftmp4);
+    felem_scalar(ftmp, 2);
+    /* ftmp[i] < 2*2^108 = 2^109 */
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);
+
+    /* J = ftmp2 = h * I */
+    felem_mul(tmp, ftmp4, ftmp);
+    felem_reduce(ftmp2, tmp);
+
+    /* V = ftmp4 = U1 * I */
+    felem_mul(tmp, ftmp3, ftmp);
+    felem_reduce(ftmp4, tmp);
+
+    /* x_out = r**2 - J - 2V */
+    smallfelem_square(tmp, small1);
+    felem_reduce(x_out, tmp);
+    felem_assign(ftmp3, ftmp4);
+    felem_scalar(ftmp4, 2);
+    felem_sum(ftmp4, ftmp2);
+    /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */
+    felem_diff(x_out, ftmp4);
+    /* x_out[i] < 2^105 + 2^101 */
+
+    /* y_out = r(V-x_out) - 2 * s1 * J */
+    felem_diff_zero107(ftmp3, x_out);
+    /* ftmp3[i] < 2^107 + 2^101 < 2^108 */
+    felem_small_mul(tmp, small1, ftmp3);
+    felem_mul(tmp2, ftmp6, ftmp2);
+    longfelem_scalar(tmp2, 2);
+    /* tmp2[i] < 2*2^67 = 2^68 */
+    longfelem_diff(tmp, tmp2);
+    /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */
+    felem_reduce_zero105(y_out, tmp);
+    /* y_out[i] < 2^106 */
+
+    copy_small_conditional(x_out, x2, z1_is_zero);
+    copy_conditional(x_out, x1, z2_is_zero);
+    copy_small_conditional(y_out, y2, z1_is_zero);
+    copy_conditional(y_out, y1, z2_is_zero);
+    copy_small_conditional(z_out, z2, z1_is_zero);
+    copy_conditional(z_out, z1, z2_is_zero);
+    felem_assign(x3, x_out);
+    felem_assign(y3, y_out);
+    felem_assign(z3, z_out);
+}
diff --git a/third_party/openssl-nistp256c64/ecp_nistp256.h b/third_party/openssl-nistp256c64/ecp_nistp256.h
new file mode 100644
index 000000000..190b81b61
--- /dev/null
+++ b/third_party/openssl-nistp256c64/ecp_nistp256.h
@@ -0,0 +1,55 @@
+#include <stdint.h>
+
+# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
+  /* even with gcc, the typedef won't work for 32-bit platforms */
+typedef __uint128_t uint128_t;  /* nonstandard; implemented by gcc on 64-bit
+                                 * platforms */
+typedef __int128_t int128_t;
+# else
+#  error "Need GCC 3.1 or later to define type uint128_t"
+# endif
+
+typedef uint8_t u8;
+typedef uint32_t u32;
+typedef uint64_t u64;
+typedef int64_t s64;
+
+/*
+ * The representation of field elements.
+ * ------------------------------------
+ *
+ * We represent field elements with either four 128-bit values, eight 128-bit
+ * values, or four 64-bit values. The field element represented is:
+ *   v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192  (mod p)
+ * or:
+ *   v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512  (mod p)
+ *
+ * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits
+ * apart, but are 128-bits wide, the most significant bits of each limb overlap
+ * with the least significant bits of the next.
+ *
+ * A field element with four limbs is an 'felem'. One with eight limbs is a
+ * 'longfelem'
+ *
+ * A field element with four, 64-bit values is called a 'smallfelem'. Small
+ * values are used as intermediate values before multiplication.
+ */
+
+# define NLIMBS 4
+
+typedef uint128_t limb;
+typedef limb felem[NLIMBS];
+typedef limb longfelem[NLIMBS * 2];
+typedef u64 smallfelem[NLIMBS];
+
+/*
+ * The underlying field. P256 operates over GF(2^256-2^224+2^192+2^96-1). We
+ * can serialise an element of this field into 32 bytes. We call this an
+ * felem_bytearray.
+ */
+
+typedef u8 felem_bytearray[32];
+void point_add(felem x3, felem y3, felem z3,
+                      const felem x1, const felem y1, const felem z1,
+                      const int mixed, const smallfelem x2,
+                      const smallfelem y2, const smallfelem z2);