Bug 1550579 - Replace arm32 curve25519 ref implementation with fiat-crypto r=jcj,mt,mhoyeNSS_3_45_BETA2

This patch changes the 32-bit Curve25519 implementation in NSS from ref to fiat-crypto (https://github.com/mit-plv/fiat-crypto). There is no HACL* variant available for 32-bit platforms.

A helpful benchmark comparison is here: https://bench.cr.yp.to/impl-scalarmult/curve25519.html. fiat-crypto proved to be ~5-8% faster than ref10 in my tests.

**Notes about this patch: **
1) MIT license is listed as compatible in https://docs.google.com/document/d/1Oguqp43W4_ChyroJ9AJAzG1jSwkUWfKvBKVvrDxVsMg/, but mhoye will have to approve before landing

Differential Revision: https://phabricator.services.mozilla.com/D33725

1 files changed, 1131 insertions, 312 deletions

diff --git a/lib/freebl/ecl/curve25519_32.c b/lib/freebl/ecl/curve25519_32.c
index 0122961e6..909efb7ed 100644
--- a/lib/freebl/ecl/curve25519_32.c
+++ b/lib/freebl/ecl/curve25519_32.c
@@ -1,390 +1,1209 @@
-/* This Source Code Form is subject to the terms of the Mozilla Public
- * License, v. 2.0. If a copy of the MPL was not distributed with this
- * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
+// The MIT License (MIT)
+//
+// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
 
 /*
- * Derived from public domain code by Matthew Dempsky and D. J. Bernstein.
+ * Derived from machine-generated code via Fiat-Crypto:
+ * https://github.com/mit-plv/fiat-crypto and https://github.com/briansmith/ring
+ *
+ * The below captures notable changes:
+ *
+ *  1. Convert custom integer types to stdint.h types
  */
 
 #include "ecl-priv.h"
-#include "mpi.h"
 
-#include <stdint.h>
-#include <stdio.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].
+ * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
+ * Multiplication and carrying produce fe from fe_loose.
+ */
+typedef struct fe {
+    uint32_t v[10];
+} fe;
+
+/* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc
+ * Addition and subtraction produce fe_loose from (fe, fe).
+ */
+typedef struct fe_loose {
+    uint32_t v[10];
+} fe_loose;
+
+#define assert_fe(f)                                                         \
+    do {                                                                     \
+        for (unsigned _assert_fe_i = 0; _assert_fe_i < 10; _assert_fe_i++) { \
+            PORT_Assert(f[_assert_fe_i] <=                                   \
+                        ((_assert_fe_i & 1) ? 0x2333333u : 0x4666666u));     \
+        }                                                                    \
+    } while (0)
 
-typedef uint32_t elem[32];
+#define assert_fe_loose(f)                                                   \
+    do {                                                                     \
+        for (unsigned _assert_fe_i = 0; _assert_fe_i < 10; _assert_fe_i++) { \
+            PORT_Assert(f[_assert_fe_i] <=                                   \
+                        ((_assert_fe_i & 1) ? 0x6999999u : 0xd333332u));     \
+        }                                                                    \
+    } while (0)
 
 /*
- * Add two field elements.
- * out = a + b
+ * The function fiat_25519_subborrowx_u26 is a subtraction with borrow.
+ * Postconditions:
+ *   out1 = (-arg1 + arg2 + -arg3) mod 2^26
+ *   out2 = -⌊(-arg1 + arg2 + -arg3) / 2^26⌋
+ *
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x3ffffff]
+ *   arg3: [0x0 ~> 0x3ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x3ffffff]
+ *   out2: [0x0 ~> 0x1]
  */
 static void
-add(elem out, const elem a, const elem b)
-{
-    uint32_t j;
-    uint32_t u = 0;
-    for (j = 0; j < 31; ++j) {
-        u += a[j] + b[j];
-        out[j] = u & 0xFF;
-        u >>= 8;
-    }
-    u += a[31] + b[31];
-    out[31] = u;
+fiat_25519_subborrowx_u26(uint32_t *out1, uint8_t *out2, uint8_t arg1, uint32_t arg2, uint32_t arg3)
+{
+    int32_t x1 = ((int32_t)(arg2 - arg1) - (int32_t)arg3);
+    int8_t x2 = (int8_t)(x1 >> 26);
+    uint32_t x3 = (x1 & UINT32_C(0x3ffffff));
+    *out1 = x3;
+    *out2 = (uint8_t)(0x0 - x2);
 }
 
 /*
- * Subtract two field elements.
- * out = a - b
+ * The function fiat_25519_subborrowx_u25 is a subtraction with borrow.
+ * Postconditions:
+ *   out1 = (-arg1 + arg2 + -arg3) mod 2^25
+ *   out2 = -⌊(-arg1 + arg2 + -arg3) / 2^25⌋
+ *
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x1ffffff]
+ *   arg3: [0x0 ~> 0x1ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x1ffffff]
+ *   out2: [0x0 ~> 0x1]
  */
 static void
-sub(elem out, const elem a, const elem b)
-{
-    uint32_t j;
-    uint32_t u;
-    u = 218;
-    for (j = 0; j < 31; ++j) {
-        u += a[j] + 0xFF00 - b[j];
-        out[j] = u & 0xFF;
-        u >>= 8;
-    }
-    u += a[31] - b[31];
-    out[31] = u;
+fiat_25519_subborrowx_u25(uint32_t *out1, uint8_t *out2, uint8_t arg1, uint32_t arg2, uint32_t arg3)
+{
+    int32_t x1 = ((int32_t)(arg2 - arg1) - (int32_t)arg3);
+    int8_t x2 = (int8_t)(x1 >> 25);
+    uint32_t x3 = (x1 & UINT32_C(0x1ffffff));
+    *out1 = x3;
+    *out2 = (uint8_t)(0x0 - x2);
 }
 
 /*
- * "Squeeze" an element after multiplication (and square).
+ * The function fiat_25519_addcarryx_u26 is an addition with carry.
+ * Postconditions:
+ *   out1 = (arg1 + arg2 + arg3) mod 2^26
+ *   out2 = ⌊(arg1 + arg2 + arg3) / 2^26⌋
+ *
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x3ffffff]
+ *   arg3: [0x0 ~> 0x3ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x3ffffff]
+ *   out2: [0x0 ~> 0x1]
  */
 static void
-squeeze(elem a)
-{
-    uint32_t j;
-    uint32_t u;
-    u = 0;
-    for (j = 0; j < 31; ++j) {
-        u += a[j];
-        a[j] = u & 0xFF;
-        u >>= 8;
-    }
-    u += a[31];
-    a[31] = u & 0x7F;
-    u = 19 * (u >> 7);
-    for (j = 0; j < 31; ++j) {
-        u += a[j];
-        a[j] = u & 0xFF;
-        u >>= 8;
-    }
-    a[31] += u;
+fiat_25519_addcarryx_u26(uint32_t *out1, uint8_t *out2, uint8_t arg1, uint32_t arg2, uint32_t arg3)
+{
+    uint32_t x1 = ((arg1 + arg2) + arg3);
+    uint32_t x2 = (x1 & UINT32_C(0x3ffffff));
+    uint8_t x3 = (uint8_t)(x1 >> 26);
+    *out1 = x2;
+    *out2 = x3;
 }
 
-static const elem minusp = { 19, 0, 0, 0, 0, 0, 0, 0,
-                             0, 0, 0, 0, 0, 0, 0, 0,
-                             0, 0, 0, 0, 0, 0, 0, 0,
-                             0, 0, 0, 0, 0, 0, 0, 128 };
-
 /*
- * Reduce point a by 2^255-19
+ * The function fiat_25519_addcarryx_u25 is an addition with carry.
+ * Postconditions:
+ *   out1 = (arg1 + arg2 + arg3) mod 2^25
+ *   out2 = ⌊(arg1 + arg2 + arg3) / 2^25⌋
+ *
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x1ffffff]
+ *   arg3: [0x0 ~> 0x1ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x1ffffff]
+ *   out2: [0x0 ~> 0x1]
  */
 static void
-reduce(elem a)
+fiat_25519_addcarryx_u25(uint32_t *out1, uint8_t *out2, uint8_t arg1, uint32_t arg2, uint32_t arg3)
 {
-    elem aorig;
-    uint32_t j;
-    uint32_t negative;
+    uint32_t x1 = ((arg1 + arg2) + arg3);
+    uint32_t x2 = (x1 & UINT32_C(0x1ffffff));
+    uint8_t x3 = (uint8_t)(x1 >> 25);
+    *out1 = x2;
+    *out2 = x3;
+}
 
-    for (j = 0; j < 32; ++j) {
-        aorig[j] = a[j];
-    }
-    add(a, a, minusp);
-    negative = 1 + ~((a[31] >> 7) & 1);
-    for (j = 0; j < 32; ++j) {
-        a[j] ^= negative & (aorig[j] ^ a[j]);
-    }
+/*
+ * The function fiat_25519_cmovznz_u32 is a single-word conditional move.
+ * Postconditions:
+ *   out1 = (if arg1 = 0 then arg2 else arg3)
+ *
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0xffffffff]
+ *   arg3: [0x0 ~> 0xffffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0xffffffff]
+ */
+static void
+fiat_25519_cmovznz_u32(uint32_t *out1, uint8_t arg1, uint32_t arg2, uint32_t arg3)
+{
+    uint8_t x1 = (!(!arg1));
+    uint32_t x2 = ((int8_t)(0x0 - x1) & UINT32_C(0xffffffff));
+    uint32_t x3 = ((x2 & arg3) | ((~x2) & arg2));
+    *out1 = x3;
 }
 
 /*
- * Multiplication and squeeze
- * out = a * b
+ * The function fiat_25519_from_bytes deserializes a field element from bytes in little-endian order.
+ * Postconditions:
+ *   eval out1 mod m = bytes_eval arg1 mod m
+ *
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
  */
 static void
-mult(elem out, const elem a, const elem b)
-{
-    uint32_t i;
-    uint32_t j;
-    uint32_t u;
-
-    for (i = 0; i < 32; ++i) {
-        u = 0;
-        for (j = 0; j <= i; ++j) {
-            u += a[j] * b[i - j];
-        }
-        for (j = i + 1; j < 32; ++j) {
-            u += 38 * a[j] * b[i + 32 - j];
-        }
-        out[i] = u;
-    }
-    squeeze(out);
+fiat_25519_from_bytes(uint32_t out1[10], const uint8_t arg1[32])
+{
+    uint32_t x1 = ((uint32_t)(arg1[31]) << 18);
+    uint32_t x2 = ((uint32_t)(arg1[30]) << 10);
+    uint32_t x3 = ((uint32_t)(arg1[29]) << 2);
+    uint32_t x4 = ((uint32_t)(arg1[28]) << 20);
+    uint32_t x5 = ((uint32_t)(arg1[27]) << 12);
+    uint32_t x6 = ((uint32_t)(arg1[26]) << 4);
+    uint32_t x7 = ((uint32_t)(arg1[25]) << 21);
+    uint32_t x8 = ((uint32_t)(arg1[24]) << 13);
+    uint32_t x9 = ((uint32_t)(arg1[23]) << 5);
+    uint32_t x10 = ((uint32_t)(arg1[22]) << 23);
+    uint32_t x11 = ((uint32_t)(arg1[21]) << 15);
+    uint32_t x12 = ((uint32_t)(arg1[20]) << 7);
+    uint32_t x13 = ((uint32_t)(arg1[19]) << 24);
+    uint32_t x14 = ((uint32_t)(arg1[18]) << 16);
+    uint32_t x15 = ((uint32_t)(arg1[17]) << 8);
+    uint8_t x16 = (arg1[16]);
+    uint32_t x17 = ((uint32_t)(arg1[15]) << 18);
+    uint32_t x18 = ((uint32_t)(arg1[14]) << 10);
+    uint32_t x19 = ((uint32_t)(arg1[13]) << 2);
+    uint32_t x20 = ((uint32_t)(arg1[12]) << 19);
+    uint32_t x21 = ((uint32_t)(arg1[11]) << 11);
+    uint32_t x22 = ((uint32_t)(arg1[10]) << 3);
+    uint32_t x23 = ((uint32_t)(arg1[9]) << 21);
+    uint32_t x24 = ((uint32_t)(arg1[8]) << 13);
+    uint32_t x25 = ((uint32_t)(arg1[7]) << 5);
+    uint32_t x26 = ((uint32_t)(arg1[6]) << 22);
+    uint32_t x27 = ((uint32_t)(arg1[5]) << 14);
+    uint32_t x28 = ((uint32_t)(arg1[4]) << 6);
+    uint32_t x29 = ((uint32_t)(arg1[3]) << 24);
+    uint32_t x30 = ((uint32_t)(arg1[2]) << 16);
+    uint32_t x31 = ((uint32_t)(arg1[1]) << 8);
+    uint8_t x32 = (arg1[0]);
+    uint32_t x33 = (x32 + (x31 + (x30 + x29)));
+    uint8_t x34 = (uint8_t)(x33 >> 26);
+    uint32_t x35 = (x33 & UINT32_C(0x3ffffff));
+    uint32_t x36 = (x3 + (x2 + x1));
+    uint32_t x37 = (x6 + (x5 + x4));
+    uint32_t x38 = (x9 + (x8 + x7));
+    uint32_t x39 = (x12 + (x11 + x10));
+    uint32_t x40 = (x16 + (x15 + (x14 + x13)));
+    uint32_t x41 = (x19 + (x18 + x17));
+    uint32_t x42 = (x22 + (x21 + x20));
+    uint32_t x43 = (x25 + (x24 + x23));
+    uint32_t x44 = (x28 + (x27 + x26));
+    uint32_t x45 = (x34 + x44);
+    uint8_t x46 = (uint8_t)(x45 >> 25);
+    uint32_t x47 = (x45 & UINT32_C(0x1ffffff));
+    uint32_t x48 = (x46 + x43);
+    uint8_t x49 = (uint8_t)(x48 >> 26);
+    uint32_t x50 = (x48 & UINT32_C(0x3ffffff));
+    uint32_t x51 = (x49 + x42);
+    uint8_t x52 = (uint8_t)(x51 >> 25);
+    uint32_t x53 = (x51 & UINT32_C(0x1ffffff));
+    uint32_t x54 = (x52 + x41);
+    uint32_t x55 = (x54 & UINT32_C(0x3ffffff));
+    uint8_t x56 = (uint8_t)(x40 >> 25);
+    uint32_t x57 = (x40 & UINT32_C(0x1ffffff));
+    uint32_t x58 = (x56 + x39);
+    uint8_t x59 = (uint8_t)(x58 >> 26);
+    uint32_t x60 = (x58 & UINT32_C(0x3ffffff));
+    uint32_t x61 = (x59 + x38);
+    uint8_t x62 = (uint8_t)(x61 >> 25);
+    uint32_t x63 = (x61 & UINT32_C(0x1ffffff));
+    uint32_t x64 = (x62 + x37);
+    uint8_t x65 = (uint8_t)(x64 >> 26);
+    uint32_t x66 = (x64 & UINT32_C(0x3ffffff));
+    uint32_t x67 = (x65 + x36);
+    out1[0] = x35;
+    out1[1] = x47;
+    out1[2] = x50;
+    out1[3] = x53;
+    out1[4] = x55;
+    out1[5] = x57;
+    out1[6] = x60;
+    out1[7] = x63;
+    out1[8] = x66;
+    out1[9] = x67;
+}
+
+static void
+fe_frombytes_strict(fe *h, const uint8_t s[32])
+{
+    // |fiat_25519_from_bytes| requires the top-most bit be clear.
+    PORT_Assert((s[31] & 0x80) == 0);
+    fiat_25519_from_bytes(h->v, s);
+    assert_fe(h->v);
+}
+
+static inline void
+fe_frombytes(fe *h, const uint8_t *s)
+{
+    uint8_t s_copy[32];
+    memcpy(s_copy, s, 32);
+    s_copy[31] &= 0x7f;
+    fe_frombytes_strict(h, s_copy);
 }
 
 /*
- * Multiplication
- * out = 121665 * a
+ * The function fiat_25519_to_bytes serializes a field element to bytes in little-endian order.
+ * Postconditions:
+ *   out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
+ *
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
  */
 static void
-mult121665(elem out, const elem a)
+fiat_25519_to_bytes(uint8_t out1[32], const uint32_t arg1[10])
 {
-    uint32_t j;
-    uint32_t u;
+    uint32_t x1;
+    uint8_t x2;
+    fiat_25519_subborrowx_u26(&x1, &x2, 0x0, (arg1[0]), UINT32_C(0x3ffffed));
+    uint32_t x3;
+    uint8_t x4;
+    fiat_25519_subborrowx_u25(&x3, &x4, x2, (arg1[1]), UINT32_C(0x1ffffff));
+    uint32_t x5;
+    uint8_t x6;
+    fiat_25519_subborrowx_u26(&x5, &x6, x4, (arg1[2]), UINT32_C(0x3ffffff));
+    uint32_t x7;
+    uint8_t x8;
+    fiat_25519_subborrowx_u25(&x7, &x8, x6, (arg1[3]), UINT32_C(0x1ffffff));
+    uint32_t x9;
+    uint8_t x10;
+    fiat_25519_subborrowx_u26(&x9, &x10, x8, (arg1[4]), UINT32_C(0x3ffffff));
+    uint32_t x11;
+    uint8_t x12;
+    fiat_25519_subborrowx_u25(&x11, &x12, x10, (arg1[5]), UINT32_C(0x1ffffff));
+    uint32_t x13;
+    uint8_t x14;
+    fiat_25519_subborrowx_u26(&x13, &x14, x12, (arg1[6]), UINT32_C(0x3ffffff));
+    uint32_t x15;
+    uint8_t x16;
+    fiat_25519_subborrowx_u25(&x15, &x16, x14, (arg1[7]), UINT32_C(0x1ffffff));
+    uint32_t x17;
+    uint8_t x18;
+    fiat_25519_subborrowx_u26(&x17, &x18, x16, (arg1[8]), UINT32_C(0x3ffffff));
+    uint32_t x19;
+    uint8_t x20;
+    fiat_25519_subborrowx_u25(&x19, &x20, x18, (arg1[9]), UINT32_C(0x1ffffff));
+    uint32_t x21;
+    fiat_25519_cmovznz_u32(&x21, x20, 0x0, UINT32_C(0xffffffff));
+    uint32_t x22;
+    uint8_t x23;
+    fiat_25519_addcarryx_u26(&x22, &x23, 0x0, x1, (x21 & UINT32_C(0x3ffffed)));
+    uint32_t x24;
+    uint8_t x25;
+    fiat_25519_addcarryx_u25(&x24, &x25, x23, x3, (x21 & UINT32_C(0x1ffffff)));
+    uint32_t x26;
+    uint8_t x27;
+    fiat_25519_addcarryx_u26(&x26, &x27, x25, x5, (x21 & UINT32_C(0x3ffffff)));
+    uint32_t x28;
+    uint8_t x29;
+    fiat_25519_addcarryx_u25(&x28, &x29, x27, x7, (x21 & UINT32_C(0x1ffffff)));
+    uint32_t x30;
+    uint8_t x31;
+    fiat_25519_addcarryx_u26(&x30, &x31, x29, x9, (x21 & UINT32_C(0x3ffffff)));
+    uint32_t x32;
+    uint8_t x33;
+    fiat_25519_addcarryx_u25(&x32, &x33, x31, x11, (x21 & UINT32_C(0x1ffffff)));
+    uint32_t x34;
+    uint8_t x35;
+    fiat_25519_addcarryx_u26(&x34, &x35, x33, x13, (x21 & UINT32_C(0x3ffffff)));
+    uint32_t x36;
+    uint8_t x37;
+    fiat_25519_addcarryx_u25(&x36, &x37, x35, x15, (x21 & UINT32_C(0x1ffffff)));
+    uint32_t x38;
+    uint8_t x39;
+    fiat_25519_addcarryx_u26(&x38, &x39, x37, x17, (x21 & UINT32_C(0x3ffffff)));
+    uint32_t x40;
+    uint8_t x41;
+    fiat_25519_addcarryx_u25(&x40, &x41, x39, x19, (x21 & UINT32_C(0x1ffffff)));
+    uint32_t x42 = (x40 << 6);
+    uint32_t x43 = (x38 << 4);
+    uint32_t x44 = (x36 << 3);
+    uint32_t x45 = (x34 * (uint32_t)0x2);
+    uint32_t x46 = (x30 << 6);
+    uint32_t x47 = (x28 << 5);
+    uint32_t x48 = (x26 << 3);
+    uint32_t x49 = (x24 << 2);
+    uint32_t x50 = (x22 >> 8);
+    uint8_t x51 = (uint8_t)(x22 & UINT8_C(0xff));
+    uint32_t x52 = (x50 >> 8);
+    uint8_t x53 = (uint8_t)(x50 & UINT8_C(0xff));
+    uint8_t x54 = (uint8_t)(x52 >> 8);
+    uint8_t x55 = (uint8_t)(x52 & UINT8_C(0xff));
+    uint32_t x56 = (x54 + x49);
+    uint32_t x57 = (x56 >> 8);
+    uint8_t x58 = (uint8_t)(x56 & UINT8_C(0xff));
+    uint32_t x59 = (x57 >> 8);
+    uint8_t x60 = (uint8_t)(x57 & UINT8_C(0xff));
+    uint8_t x61 = (uint8_t)(x59 >> 8);
+    uint8_t x62 = (uint8_t)(x59 & UINT8_C(0xff));
+    uint32_t x63 = (x61 + x48);
+    uint32_t x64 = (x63 >> 8);
+    uint8_t x65 = (uint8_t)(x63 & UINT8_C(0xff));
+    uint32_t x66 = (x64 >> 8);
+    uint8_t x67 = (uint8_t)(x64 & UINT8_C(0xff));
+    uint8_t x68 = (uint8_t)(x66 >> 8);
+    uint8_t x69 = (uint8_t)(x66 & UINT8_C(0xff));
+    uint32_t x70 = (x68 + x47);
+    uint32_t x71 = (x70 >> 8);
+    uint8_t x72 = (uint8_t)(x70 & UINT8_C(0xff));
+    uint32_t x73 = (x71 >> 8);
+    uint8_t x74 = (uint8_t)(x71 & UINT8_C(0xff));
+    uint8_t x75 = (uint8_t)(x73 >> 8);
+    uint8_t x76 = (uint8_t)(x73 & UINT8_C(0xff));
+    uint32_t x77 = (x75 + x46);
+    uint32_t x78 = (x77 >> 8);
+    uint8_t x79 = (uint8_t)(x77 & UINT8_C(0xff));
+    uint32_t x80 = (x78 >> 8);
+    uint8_t x81 = (uint8_t)(x78 & UINT8_C(0xff));
+    uint8_t x82 = (uint8_t)(x80 >> 8);
+    uint8_t x83 = (uint8_t)(x80 & UINT8_C(0xff));
+    uint8_t x84 = (uint8_t)(x82 & UINT8_C(0xff));
+    uint32_t x85 = (x32 >> 8);
+    uint8_t x86 = (uint8_t)(x32 & UINT8_C(0xff));
+    uint32_t x87 = (x85 >> 8);
+    uint8_t x88 = (uint8_t)(x85 & UINT8_C(0xff));
+    uint8_t x89 = (uint8_t)(x87 >> 8);
+    uint8_t x90 = (uint8_t)(x87 & UINT8_C(0xff));
+    uint32_t x91 = (x89 + x45);
+    uint32_t x92 = (x91 >> 8);
+    uint8_t x93 = (uint8_t)(x91 & UINT8_C(0xff));
+    uint32_t x94 = (x92 >> 8);
+    uint8_t x95 = (uint8_t)(x92 & UINT8_C(0xff));
+    uint8_t x96 = (uint8_t)(x94 >> 8);
+    uint8_t x97 = (uint8_t)(x94 & UINT8_C(0xff));
+    uint32_t x98 = (x96 + x44);
+    uint32_t x99 = (x98 >> 8);
+    uint8_t x100 = (uint8_t)(x98 & UINT8_C(0xff));
+    uint32_t x101 = (x99 >> 8);
+    uint8_t x102 = (uint8_t)(x99 & UINT8_C(0xff));
+    uint8_t x103 = (uint8_t)(x101 >> 8);
+    uint8_t x104 = (uint8_t)(x101 & UINT8_C(0xff));
+    uint32_t x105 = (x103 + x43);
+    uint32_t x106 = (x105 >> 8);
+    uint8_t x107 = (uint8_t)(x105 & UINT8_C(0xff));
+    uint32_t x108 = (x106 >> 8);
+    uint8_t x109 = (uint8_t)(x106 & UINT8_C(0xff));
+    uint8_t x110 = (uint8_t)(x108 >> 8);
+    uint8_t x111 = (uint8_t)(x108 & UINT8_C(0xff));
+    uint32_t x112 = (x110 + x42);
+    uint32_t x113 = (x112 >> 8);
+    uint8_t x114 = (uint8_t)(x112 & UINT8_C(0xff));
+    uint32_t x115 = (x113 >> 8);
+    uint8_t x116 = (uint8_t)(x113 & UINT8_C(0xff));
+    uint8_t x117 = (uint8_t)(x115 >> 8);
+    uint8_t x118 = (uint8_t)(x115 & UINT8_C(0xff));
+    out1[0] = x51;
+    out1[1] = x53;
+    out1[2] = x55;
+    out1[3] = x58;
+    out1[4] = x60;
+    out1[5] = x62;
+    out1[6] = x65;
+    out1[7] = x67;
+    out1[8] = x69;
+    out1[9] = x72;
+    out1[10] = x74;
+    out1[11] = x76;
+    out1[12] = x79;
+    out1[13] = x81;
+    out1[14] = x83;
+    out1[15] = x84;
+    out1[16] = x86;
+    out1[17] = x88;
+    out1[18] = x90;
+    out1[19] = x93;
+    out1[20] = x95;
+    out1[21] = x97;
+    out1[22] = x100;
+    out1[23] = x102;
+    out1[24] = x104;
+    out1[25] = x107;
+    out1[26] = x109;
+    out1[27] = x111;
+    out1[28] = x114;
+    out1[29] = x116;
+    out1[30] = x118;
+    out1[31] = x117;
+}
 
-    u = 0;
-    for (j = 0; j < 31; ++j) {
-        u += 121665 * a[j];
-        out[j] = u & 0xFF;
-        u >>= 8;
-    }
-    u += 121665 * a[31];
-    out[31] = u & 0x7F;
-    u = 19 * (u >> 7);
-    for (j = 0; j < 31; ++j) {
-        u += out[j];
-        out[j] = u & 0xFF;
-        u >>= 8;
-    }
-    u += out[j];
-    out[j] = u;
+static inline void
+fe_tobytes(uint8_t s[32], const fe *f)
+{
+    assert_fe(f->v);
+    fiat_25519_to_bytes(s, f->v);
+}
+
+/* h = f */
+static inline void
+fe_copy(fe *h, const fe *f)
+{
+    memmove(h, f, sizeof(fe));
 }
 
+static inline void
+fe_copy_lt(fe_loose *h, const fe *f)
+{
+    PORT_Assert(sizeof(fe) == sizeof(fe_loose));
+    memmove(h, f, sizeof(fe));
+}
+
+/*
+ * h = 0
+ */
+static inline void
+fe_0(fe *h)
+{
+    memset(h, 0, sizeof(fe));
+}
+
+/*
+ * h = 1
+ */
+static inline void
+fe_1(fe *h)
+{
+    memset(h, 0, sizeof(fe));
+    h->v[0] = 1;
+}
 /*
- * Square a and squeeze the result.
- * out = a * a
+ * The function fiat_25519_add adds two field elements.
+ * Postconditions:
+ *   eval out1 mod m = (eval arg1 + eval arg2) mod m
+ *
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
+ *   arg2: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999]]
  */
 static void
-square(elem out, const elem a)
-{
-    uint32_t i;
-    uint32_t j;
-    uint32_t u;
-
-    for (i = 0; i < 32; ++i) {
-        u = 0;
-        for (j = 0; j < i - j; ++j) {
-            u += a[j] * a[i - j];
-        }
-        for (j = i + 1; j < i + 32 - j; ++j) {
-            u += 38 * a[j] * a[i + 32 - j];
-        }
-        u *= 2;
-        if ((i & 1) == 0) {
-            u += a[i / 2] * a[i / 2];
-            u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
-        }
-        out[i] = u;
-    }
-    squeeze(out);
+fiat_25519_add(uint32_t out1[10], const uint32_t arg1[10], const uint32_t arg2[10])
+{
+    uint32_t x1 = ((arg1[0]) + (arg2[0]));
+    uint32_t x2 = ((arg1[1]) + (arg2[1]));
+    uint32_t x3 = ((arg1[2]) + (arg2[2]));
+    uint32_t x4 = ((arg1[3]) + (arg2[3]));
+    uint32_t x5 = ((arg1[4]) + (arg2[4]));
+    uint32_t x6 = ((arg1[5]) + (arg2[5]));
+    uint32_t x7 = ((arg1[6]) + (arg2[6]));
+    uint32_t x8 = ((arg1[7]) + (arg2[7]));
+    uint32_t x9 = ((arg1[8]) + (arg2[8]));
+    uint32_t x10 = ((arg1[9]) + (arg2[9]));
+    out1[0] = x1;
+    out1[1] = x2;
+    out1[2] = x3;
+    out1[3] = x4;
+    out1[4] = x5;
+    out1[5] = x6;
+    out1[6] = x7;
+    out1[7] = x8;
+    out1[8] = x9;
+    out1[9] = x10;
 }
 
 /*
- * Constant time swap between r and s depending on b
+ * Add two field elements.
+ * h = f + g
+ */
+static inline void
+fe_add(fe_loose *h, const fe *f, const fe *g)
+{
+    assert_fe(f->v);
+    assert_fe(g->v);
+    fiat_25519_add(h->v, f->v, g->v);
+    assert_fe_loose(h->v);
+}
+
+/*
+ * The function fiat_25519_sub subtracts two field elements.
+ * Postconditions:
+ *   eval out1 mod m = (eval arg1 - eval arg2) mod m
+ *
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
+ *   arg2: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999]]
  */
 static void
-cswap(uint32_t p[64], uint32_t q[64], uint32_t b)
+fiat_25519_sub(uint32_t out1[10], const uint32_t arg1[10], const uint32_t arg2[10])
 {
-    uint32_t j;
-    uint32_t swap = 1 + ~b;
+    uint32_t x1 = ((UINT32_C(0x7ffffda) + (arg1[0])) - (arg2[0]));
+    uint32_t x2 = ((UINT32_C(0x3fffffe) + (arg1[1])) - (arg2[1]));
+    uint32_t x3 = ((UINT32_C(0x7fffffe) + (arg1[2])) - (arg2[2]));
+    uint32_t x4 = ((UINT32_C(0x3fffffe) + (arg1[3])) - (arg2[3]));
+    uint32_t x5 = ((UINT32_C(0x7fffffe) + (arg1[4])) - (arg2[4]));
+    uint32_t x6 = ((UINT32_C(0x3fffffe) + (arg1[5])) - (arg2[5]));
+    uint32_t x7 = ((UINT32_C(0x7fffffe) + (arg1[6])) - (arg2[6]));
+    uint32_t x8 = ((UINT32_C(0x3fffffe) + (arg1[7])) - (arg2[7]));
+    uint32_t x9 = ((UINT32_C(0x7fffffe) + (arg1[8])) - (arg2[8]));
+    uint32_t x10 = ((UINT32_C(0x3fffffe) + (arg1[9])) - (arg2[9]));
+    out1[0] = x1;
+    out1[1] = x2;
+    out1[2] = x3;
+    out1[3] = x4;
+    out1[4] = x5;
+    out1[5] = x6;
+    out1[6] = x7;
+    out1[7] = x8;
+    out1[8] = x9;
+    out1[9] = x10;
+}
 
-    for (j = 0; j < 64; ++j) {
-        const uint32_t t = swap & (p[j] ^ q[j]);
-        p[j] ^= t;
-        q[j] ^= t;
-    }
+/*
+ * Subtract two field elements.
+ * h = f - g
+ */
+static void
+fe_sub(fe_loose *h, const fe *f, const fe *g)
+{
+    assert_fe(f->v);
+    assert_fe(g->v);
+    fiat_25519_sub(h->v, f->v, g->v);
+    assert_fe_loose(h->v);
 }
 
 /*
- * Montgomery ladder
+ * The function fiat_25519_carry_mul multiplies two field elements and reduces the result.
+ * Postconditions:
+ *   eval out1 mod m = (eval arg1 * eval arg2) mod m
+ *
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999]]
+ *   arg2: [[0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333], [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
  */
 static void
-monty(elem x_2_out, elem z_2_out,
-      const elem point, const elem scalar)
-{
-    uint32_t x_3[64] = { 0 };
-    uint32_t x_2[64] = { 0 };
-    uint32_t a0[64];
-    uint32_t a1[64];
-    uint32_t b0[64];
-    uint32_t b1[64];
-    uint32_t c1[64];
-    uint32_t r[32];
-    uint32_t s[32];
-    uint32_t t[32];
-    uint32_t u[32];
-    uint32_t swap = 0;
-    uint32_t k_t = 0;
-    int j;
-
-    for (j = 0; j < 32; ++j) {
-        x_3[j] = point[j];
-    }
-    x_3[32] = 1;
-    x_2[0] = 1;
-
-    for (j = 254; j >= 0; --j) {
-        k_t = (scalar[j >> 3] >> (j & 7)) & 1;
-        swap ^= k_t;
-        cswap(x_2, x_3, swap);
-        swap = k_t;
-        add(a0, x_2, x_2 + 32);
-        sub(a0 + 32, x_2, x_2 + 32);
-        add(a1, x_3, x_3 + 32);
-        sub(a1 + 32, x_3, x_3 + 32);
-        square(b0, a0);
-        square(b0 + 32, a0 + 32);
-        mult(b1, a1, a0 + 32);
-        mult(b1 + 32, a1 + 32, a0);
-        add(c1, b1, b1 + 32);
-        sub(c1 + 32, b1, b1 + 32);
-        square(r, c1 + 32);
-        sub(s, b0, b0 + 32);
-        mult121665(t, s);
-        add(u, t, b0);
-        mult(x_2, b0, b0 + 32);
-        mult(x_2 + 32, s, u);
-        square(x_3, c1);
-        mult(x_3 + 32, r, point);
-    }
+fiat_25519_carry_mul(uint32_t out1[10], const uint32_t arg1[10], const uint32_t arg2[10])
+{
+    uint64_t x1 = ((uint64_t)(arg1[9]) * ((arg2[9]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x2 = ((uint64_t)(arg1[9]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x3 = ((uint64_t)(arg1[9]) * ((arg2[7]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x4 = ((uint64_t)(arg1[9]) * ((arg2[6]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x5 = ((uint64_t)(arg1[9]) * ((arg2[5]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x6 = ((uint64_t)(arg1[9]) * ((arg2[4]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x7 = ((uint64_t)(arg1[9]) * ((arg2[3]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x8 = ((uint64_t)(arg1[9]) * ((arg2[2]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x9 = ((uint64_t)(arg1[9]) * ((arg2[1]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x10 = ((uint64_t)(arg1[8]) * ((arg2[9]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x11 = ((uint64_t)(arg1[8]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x12 = ((uint64_t)(arg1[8]) * ((arg2[7]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x13 = ((uint64_t)(arg1[8]) * ((arg2[6]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x14 = ((uint64_t)(arg1[8]) * ((arg2[5]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x15 = ((uint64_t)(arg1[8]) * ((arg2[4]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x16 = ((uint64_t)(arg1[8]) * ((arg2[3]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x17 = ((uint64_t)(arg1[8]) * ((arg2[2]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x18 = ((uint64_t)(arg1[7]) * ((arg2[9]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x19 = ((uint64_t)(arg1[7]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x20 = ((uint64_t)(arg1[7]) * ((arg2[7]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x21 = ((uint64_t)(arg1[7]) * ((arg2[6]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x22 = ((uint64_t)(arg1[7]) * ((arg2[5]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x23 = ((uint64_t)(arg1[7]) * ((arg2[4]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x24 = ((uint64_t)(arg1[7]) * ((arg2[3]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x25 = ((uint64_t)(arg1[6]) * ((arg2[9]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x26 = ((uint64_t)(arg1[6]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x27 = ((uint64_t)(arg1[6]) * ((arg2[7]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x28 = ((uint64_t)(arg1[6]) * ((arg2[6]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x29 = ((uint64_t)(arg1[6]) * ((arg2[5]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x30 = ((uint64_t)(arg1[6]) * ((arg2[4]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x31 = ((uint64_t)(arg1[5]) * ((arg2[9]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x32 = ((uint64_t)(arg1[5]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x33 = ((uint64_t)(arg1[5]) * ((arg2[7]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x34 = ((uint64_t)(arg1[5]) * ((arg2[6]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x35 = ((uint64_t)(arg1[5]) * ((arg2[5]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x36 = ((uint64_t)(arg1[4]) * ((arg2[9]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x37 = ((uint64_t)(arg1[4]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x38 = ((uint64_t)(arg1[4]) * ((arg2[7]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x39 = ((uint64_t)(arg1[4]) * ((arg2[6]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x40 = ((uint64_t)(arg1[3]) * ((arg2[9]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x41 = ((uint64_t)(arg1[3]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x42 = ((uint64_t)(arg1[3]) * ((arg2[7]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x43 = ((uint64_t)(arg1[2]) * ((arg2[9]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x44 = ((uint64_t)(arg1[2]) * ((arg2[8]) * (uint32_t)UINT8_C(0x13)));
+    uint64_t x45 = ((uint64_t)(arg1[1]) * ((arg2[9]) * ((uint32_t)0x2 * UINT8_C(0x13))));
+    uint64_t x46 = ((uint64_t)(arg1[9]) * (arg2[0]));
+    uint64_t x47 = ((uint64_t)(arg1[8]) * (arg2[1]));
+    uint64_t x48 = ((uint64_t)(arg1[8]) * (arg2[0]));
+    uint64_t x49 = ((uint64_t)(arg1[7]) * (arg2[2]));
+    uint64_t x50 = ((uint64_t)(arg1[7]) * ((arg2[1]) * (uint32_t)0x2));
+    uint64_t x51 = ((uint64_t)(arg1[7]) * (arg2[0]));
+    uint64_t x52 = ((uint64_t)(arg1[6]) * (arg2[3]));
+    uint64_t x53 = ((uint64_t)(arg1[6]) * (arg2[2]));
+    uint64_t x54 = ((uint64_t)(arg1[6]) * (arg2[1]));
+    uint64_t x55 = ((uint64_t)(arg1[6]) * (arg2[0]));
+    uint64_t x56 = ((uint64_t)(arg1[5]) * (arg2[4]));
+    uint64_t x57 = ((uint64_t)(arg1[5]) * ((arg2[3]) * (uint32_t)0x2));
+    uint64_t x58 = ((uint64_t)(arg1[5]) * (arg2[2]));
+    uint64_t x59 = ((uint64_t)(arg1[5]) * ((arg2[1]) * (uint32_t)0x2));
+    uint64_t x60 = ((uint64_t)(arg1[5]) * (arg2[0]));
+    uint64_t x61 = ((uint64_t)(arg1[4]) * (arg2[5]));
+    uint64_t x62 = ((uint64_t)(arg1[4]) * (arg2[4]));
+    uint64_t x63 = ((uint64_t)(arg1[4]) * (arg2[3]));
+    uint64_t x64 = ((uint64_t)(arg1[4]) * (arg2[2]));
+    uint64_t x65 = ((uint64_t)(arg1[4]) * (arg2[1]));
+    uint64_t x66 = ((uint64_t)(arg1[4]) * (arg2[0]));
+    uint64_t x67 = ((uint64_t)(arg1[3]) * (arg2[6]));
+    uint64_t x68 = ((uint64_t)(arg1[3]) * ((arg2[5]) * (uint32_t)0x2));
+    uint64_t x69 = ((uint64_t)(arg1[3]) * (arg2[4]));
+    uint64_t x70 = ((uint64_t)(arg1[3]) * ((arg2[3]) * (uint32_t)0x2));
+    uint64_t x71 = ((uint64_t)(arg1[3]) * (arg2[2]));
+    uint64_t x72 = ((uint64_t)(arg1[3]) * ((arg2[1]) * (uint32_t)0x2));
+    uint64_t x73 = ((uint64_t)(arg1[3]) * (arg2[0]));
+    uint64_t x74 = ((uint64_t)(arg1[2]) * (arg2[7]));
+    uint64_t x75 = ((uint64_t)(arg1[2]) * (arg2[6]));
+    uint64_t x76 = ((uint64_t)(arg1[2]) * (arg2[5]));
+    uint64_t x77 = ((uint64_t)(arg1[2]) * (arg2[4]));
+    uint64_t x78 = ((uint64_t)(arg1[2]) * (arg2[3]));
+    uint64_t x79 = ((uint64_t)(arg1[2]) * (arg2[2]));
+    uint64_t x80 = ((uint64_t)(arg1[2]) * (arg2[1]));
+    uint64_t x81 = ((uint64_t)(arg1[2]) * (arg2[0]));
+    uint64_t x82 = ((uint64_t)(arg1[1]) * (arg2[8]));
+    uint64_t x83 = ((uint64_t)(arg1[1]) * ((arg2[7]) * (uint32_t)0x2));
+    uint64_t x84 = ((uint64_t)(arg1[1]) * (arg2[6]));
+    uint64_t x85 = ((uint64_t)(arg1[1]) * ((arg2[5]) * (uint32_t)0x2));
+    uint64_t x86 = ((uint64_t)(arg1[1]) * (arg2[4]));
+    uint64_t x87 = ((uint64_t)(arg1[1]) * ((arg2[3]) * (uint32_t)0x2));
+    uint64_t x88 = ((uint64_t)(arg1[1]) * (arg2[2]));
+    uint64_t x89 = ((uint64_t)(arg1[1]) * ((arg2[1]) * (uint32_t)0x2));
+    uint64_t x90 = ((uint64_t)(arg1[1]) * (arg2[0]));
+    uint64_t x91 = ((uint64_t)(arg1[0]) * (arg2[9]));
+    uint64_t x92 = ((uint64_t)(arg1[0]) * (arg2[8]));
+    uint64_t x93 = ((uint64_t)(arg1[0]) * (arg2[7]));
+    uint64_t x94 = ((uint64_t)(arg1[0]) * (arg2[6]));
+    uint64_t x95 = ((uint64_t)(arg1[0]) * (arg2[5]));
+    uint64_t x96 = ((uint64_t)(arg1[0]) * (arg2[4]));
+    uint64_t x97 = ((uint64_t)(arg1[0]) * (arg2[3]));
+    uint64_t x98 = ((uint64_t)(arg1[0]) * (arg2[2]));
+    uint64_t x99 = ((uint64_t)(arg1[0]) * (arg2[1]));
+    uint64_t x100 = ((uint64_t)(arg1[0]) * (arg2[0]));
+    uint64_t x101 = (x100 + (x45 + (x44 + (x42 + (x39 + (x35 + (x30 + (x24 + (x17 + x9)))))))));
+    uint64_t x102 = (x101 >> 26);
+    uint32_t x103 = (uint32_t)(x101 & UINT32_C(0x3ffffff));
+    uint64_t x104 = (x91 + (x82 + (x74 + (x67 + (x61 + (x56 + (x52 + (x49 + (x47 + x46)))))))));
+    uint64_t x105 = (x92 + (x83 + (x75 + (x68 + (x62 + (x57 + (x53 + (x50 + (x48 + x1)))))))));
+    uint64_t x106 = (x93 + (x84 + (x76 + (x69 + (x63 + (x58 + (x54 + (x51 + (x10 + x2)))))))));
+    uint64_t x107 = (x94 + (x85 + (x77 + (x70 + (x64 + (x59 + (x55 + (x18 + (x11 + x3)))))))));
+    uint64_t x108 = (x95 + (x86 + (x78 + (x71 + (x65 + (x60 + (x25 + (x19 + (x12 + x4)))))))));
+    uint64_t x109 = (x96 + (x87 + (x79 + (x72 + (x66 + (x31 + (x26 + (x20 + (x13 + x5)))))))));
+    uint64_t x110 = (x97 + (x88 + (x80 + (x73 + (x36 + (x32 + (x27 + (x21 + (x14 + x6)))))))));
+    uint64_t x111 = (x98 + (x89 + (x81 + (x40 + (x37 + (x33 + (x28 + (x22 + (x15 + x7)))))))));
+    uint64_t x112 = (x99 + (x90 + (x43 + (x41 + (x38 + (x34 + (x29 + (x23 + (x16 + x8)))))))));
+    uint64_t x113 = (x102 + x112);
+    uint64_t x114 = (x113 >> 25);
+    uint32_t x115 = (uint32_t)(x113 & UINT32_C(0x1ffffff));
+    uint64_t x116 = (x114 + x111);
+    uint64_t x117 = (x116 >> 26);
+    uint32_t x118 = (uint32_t)(x116 & UINT32_C(0x3ffffff));
+    uint64_t x119 = (x117 + x110);
+    uint64_t x120 = (x119 >> 25);
+    uint32_t x121 = (uint32_t)(x119 & UINT32_C(0x1ffffff));
+    uint64_t x122 = (x120 + x109);
+    uint64_t x123 = (x122 >> 26);
+    uint32_t x124 = (uint32_t)(x122 & UINT32_C(0x3ffffff));
+    uint64_t x125 = (x123 + x108);
+    uint64_t x126 = (x125 >> 25);
+    uint32_t x127 = (uint32_t)(x125 & UINT32_C(0x1ffffff));
+    uint64_t x128 = (x126 + x107);
+    uint64_t x129 = (x128 >> 26);
+    uint32_t x130 = (uint32_t)(x128 & UINT32_C(0x3ffffff));
+    uint64_t x131 = (x129 + x106);
+    uint64_t x132 = (x131 >> 25);
+    uint32_t x133 = (uint32_t)(x131 & UINT32_C(0x1ffffff));
+    uint64_t x134 = (x132 + x105);
+    uint64_t x135 = (x134 >> 26);
+    uint32_t x136 = (uint32_t)(x134 & UINT32_C(0x3ffffff));
+    uint64_t x137 = (x135 + x104);
+    uint64_t x138 = (x137 >> 25);
+    uint32_t x139 = (uint32_t)(x137 & UINT32_C(0x1ffffff));
+    uint64_t x140 = (x138 * (uint64_t)UINT8_C(0x13));
+    uint64_t x141 = (x103 + x140);
+    uint32_t x142 = (uint32_t)(x141 >> 26);
+    uint32_t x143 = (uint32_t)(x141 & UINT32_C(0x3ffffff));
+    uint32_t x144 = (x142 + x115);
+    uint32_t x145 = (x144 >> 25);
+    uint32_t x146 = (x144 & UINT32_C(0x1ffffff));
+    uint32_t x147 = (x145 + x118);
+    out1[0] = x143;
+    out1[1] = x146;
+    out1[2] = x147;
+    out1[3] = x121;
+    out1[4] = x124;
+    out1[5] = x127;
+    out1[6] = x130;
+    out1[7] = x133;
+    out1[8] = x136;
+    out1[9] = x139;
+}
 
-    cswap(x_2, x_3, swap);
-    for (j = 0; j < 32; ++j) {
-        x_2_out[j] = x_2[j];
-    }
-    for (j = 0; j < 32; ++j) {
-        z_2_out[j] = x_2[j + 32];
-    }
+static void
+fe_mul(uint32_t out1[10], const uint32_t arg1[10], const uint32_t arg2[10])
+{
+    assert_fe_loose(arg1);
+    assert_fe_loose(arg2);
+    fiat_25519_carry_mul(out1, arg1, arg2);
+    assert_fe(out1);
+}
+
+static void
+fe_mul_ttt(fe *h, const fe *f, const fe *g)
+{
+    fe_mul(h->v, f->v, g->v);
+}
+
+static void
+fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
+{
+    fe_mul(h->v, f->v, g->v);
+}
+
+static void
+fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
+{
+    fe_mul(h->v, f->v, g->v);
+}
+
+static void
+fe_sq(uint32_t out[10], const uint32_t in1[10])
+{
+    const uint32_t x17 = in1[9];
+    const uint32_t x18 = in1[8];
+    const uint32_t x16 = in1[7];
+    const uint32_t x14 = in1[6];
+    const uint32_t x12 = in1[5];
+    const uint32_t x10 = in1[4];
+    const uint32_t x8 = in1[3];
+    const uint32_t x6 = in1[2];
+    const uint32_t x4 = in1[1];
+    const uint32_t x2 = in1[0];
+    uint64_t x19 = ((uint64_t)x2 * x2);
+    uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
+    uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
+    uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
+    uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
+    uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
+    uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
+    uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
+    uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
+    uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
+    uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
+    uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
+    uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
+    uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
+    uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
+    uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
+    uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
+    uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
+    uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
+    uint64_t x38 = (x27 + (x37 << 0x4));
+    uint64_t x39 = (x38 + (x37 << 0x1));
+    uint64_t x40 = (x39 + x37);
+    uint64_t x41 = (x26 + (x36 << 0x4));
+    uint64_t x42 = (x41 + (x36 << 0x1));
+    uint64_t x43 = (x42 + x36);
+    uint64_t x44 = (x25 + (x35 << 0x4));
+    uint64_t x45 = (x44 + (x35 << 0x1));
+    uint64_t x46 = (x45 + x35);
+    uint64_t x47 = (x24 + (x34 << 0x4));
+    uint64_t x48 = (x47 + (x34 << 0x1));
+    uint64_t x49 = (x48 + x34);
+    uint64_t x50 = (x23 + (x33 << 0x4));
+    uint64_t x51 = (x50 + (x33 << 0x1));
+    uint64_t x52 = (x51 + x33);
+    uint64_t x53 = (x22 + (x32 << 0x4));
+    uint64_t x54 = (x53 + (x32 << 0x1));
+    uint64_t x55 = (x54 + x32);
+    uint64_t x56 = (x21 + (x31 << 0x4));
+    uint64_t x57 = (x56 + (x31 << 0x1));
+    uint64_t x58 = (x57 + x31);
+    uint64_t x59 = (x20 + (x30 << 0x4));
+    uint64_t x60 = (x59 + (x30 << 0x1));
+    uint64_t x61 = (x60 + x30);
+    uint64_t x62 = (x19 + (x29 << 0x4));
+    uint64_t x63 = (x62 + (x29 << 0x1));
+    uint64_t x64 = (x63 + x29);
+    uint64_t x65 = (x64 >> 0x1a);
+    uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
+    uint64_t x67 = (x65 + x61);
+    uint64_t x68 = (x67 >> 0x19);
+    uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
+    uint64_t x70 = (x68 + x58);
+    uint64_t x71 = (x70 >> 0x1a);
+    uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
+    uint64_t x73 = (x71 + x55);
+    uint64_t x74 = (x73 >> 0x19);
+    uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
+    uint64_t x76 = (x74 + x52);
+    uint64_t x77 = (x76 >> 0x1a);
+    uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
+    uint64_t x79 = (x77 + x49);
+    uint64_t x80 = (x79 >> 0x19);
+    uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
+    uint64_t x82 = (x80 + x46);
+    uint64_t x83 = (x82 >> 0x1a);
+    uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
+    uint64_t x85 = (x83 + x43);
+    uint64_t x86 = (x85 >> 0x19);
+    uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
+    uint64_t x88 = (x86 + x40);
+    uint64_t x89 = (x88 >> 0x1a);
+    uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
+    uint64_t x91 = (x89 + x28);
+    uint64_t x92 = (x91 >> 0x19);
+    uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
+    uint64_t x94 = (x66 + (0x13 * x92));
+    uint32_t x95 = (uint32_t)(x94 >> 0x1a);
+    uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
+    uint32_t x97 = (x95 + x69);
+    uint32_t x98 = (x97 >> 0x19);
+    uint32_t x99 = (x97 & 0x1ffffff);
+    out[0] = x96;
+    out[1] = x99;
+    out[2] = (x98 + x72);
+    out[3] = x75;
+    out[4] = x78;
+    out[5] = x81;
+    out[6] = x84;
+    out[7] = x87;
+    out[8] = x90;
+    out[9] = x93;
+}
+
+static void
+fe_sq_tl(fe *h, const fe_loose *f)
+{
+    fe_sq(h->v, f->v);
 }
 
 static void
-recip(elem out, const elem z)
-{
-    elem z2;
-    elem z9;
-    elem z11;
-    elem z2_5_0;
-    elem z2_10_0;
-    elem z2_20_0;
-    elem z2_50_0;
-    elem z2_100_0;
-    elem t0;
-    elem t1;
+fe_sq_tt(fe *h, const fe *f)
+{
+    fe_sq(h->v, f->v);
+}
+
+static inline void
+fe_loose_invert(fe *out, const fe_loose *z)
+{
+    fe t0, t1, t2, t3;
     int i;
 
-    /* 2 */ square(z2, z);
-    /* 4 */ square(t1, z2);
-    /* 8 */ square(t0, t1);
-    /* 9 */ mult(z9, t0, z);
-    /* 11 */ mult(z11, z9, z2);
-    /* 22 */ square(t0, z11);
-    /* 2^5 - 2^0 = 31 */ mult(z2_5_0, t0, z9);
-
-    /* 2^6 - 2^1 */ square(t0, z2_5_0);
-    /* 2^7 - 2^2 */ square(t1, t0);
-    /* 2^8 - 2^3 */ square(t0, t1);
-    /* 2^9 - 2^4 */ square(t1, t0);
-    /* 2^10 - 2^5 */ square(t0, t1);
-    /* 2^10 - 2^0 */ mult(z2_10_0, t0, z2_5_0);
-
-    /* 2^11 - 2^1 */ square(t0, z2_10_0);
-    /* 2^12 - 2^2 */ square(t1, t0);
-    /* 2^20 - 2^10 */
-    for (i = 2; i < 10; i += 2) {
-        square(t0, t1);
-        square(t1, t0);
+    fe_sq_tl(&t0, z);
+    fe_sq_tt(&t1, &t0);
+    for (i = 1; i < 2; ++i) {
+        fe_sq_tt(&t1, &t1);
+    }
+    fe_mul_tlt(&t1, z, &t1);
+    fe_mul_ttt(&t0, &t0, &t1);
+    fe_sq_tt(&t2, &t0);
+    fe_mul_ttt(&t1, &t1, &t2);
+    fe_sq_tt(&t2, &t1);
+    for (i = 1; i < 5; ++i) {
+        fe_sq_tt(&t2, &t2);
+    }
+    fe_mul_ttt(&t1, &t2, &t1);
+    fe_sq_tt(&t2, &t1);
+    for (i = 1; i < 10; ++i) {
+        fe_sq_tt(&t2, &t2);
+    }
+    fe_mul_ttt(&t2, &t2, &t1);
+    fe_sq_tt(&t3, &t2);
+    for (i = 1; i < 20; ++i) {
+        fe_sq_tt(&t3, &t3);
     }
-    /* 2^20 - 2^0 */ mult(z2_20_0, t1, z2_10_0);
-
-    /* 2^21 - 2^1 */ square(t0, z2_20_0);
-    /* 2^22 - 2^2 */ square(t1, t0);
-    /* 2^40 - 2^20 */
-    for (i = 2; i < 20; i += 2) {
-        square(t0, t1);
-        square(t1, t0);
+    fe_mul_ttt(&t2, &t3, &t2);
+    fe_sq_tt(&t2, &t2);
+    for (i = 1; i < 10; ++i) {
+        fe_sq_tt(&t2, &t2);
     }
-    /* 2^40 - 2^0 */ mult(t0, t1, z2_20_0);
-
-    /* 2^41 - 2^1 */ square(t1, t0);
-    /* 2^42 - 2^2 */ square(t0, t1);
-    /* 2^50 - 2^10 */
-    for (i = 2; i < 10; i += 2) {
-        square(t1, t0);
-        square(t0, t1);
+    fe_mul_ttt(&t1, &t2, &t1);
+    fe_sq_tt(&t2, &t1);
+    for (i = 1; i < 50; ++i) {
+        fe_sq_tt(&t2, &t2);
     }
-    /* 2^50 - 2^0 */ mult(z2_50_0, t0, z2_10_0);
-
-    /* 2^51 - 2^1 */ square(t0, z2_50_0);
-    /* 2^52 - 2^2 */ square(t1, t0);
-    /* 2^100 - 2^50 */
-    for (i = 2; i < 50; i += 2) {
-        square(t0, t1);
-        square(t1, t0);
+    fe_mul_ttt(&t2, &t2, &t1);
+    fe_sq_tt(&t3, &t2);
+    for (i = 1; i < 100; ++i) {
+        fe_sq_tt(&t3, &t3);
     }
-    /* 2^100 - 2^0 */ mult(z2_100_0, t1, z2_50_0);
-
-    /* 2^101 - 2^1 */ square(t1, z2_100_0);
-    /* 2^102 - 2^2 */ square(t0, t1);
-    /* 2^200 - 2^100 */
-    for (i = 2; i < 100; i += 2) {
-        square(t1, t0);
-        square(t0, t1);
+    fe_mul_ttt(&t2, &t3, &t2);
+    fe_sq_tt(&t2, &t2);
+    for (i = 1; i < 50; ++i) {
+        fe_sq_tt(&t2, &t2);
     }
-    /* 2^200 - 2^0 */ mult(t1, t0, z2_100_0);
-
-    /* 2^201 - 2^1 */ square(t0, t1);
-    /* 2^202 - 2^2 */ square(t1, t0);
-    /* 2^250 - 2^50 */
-    for (i = 2; i < 50; i += 2) {
-        square(t0, t1);
-        square(t1, t0);
+    fe_mul_ttt(&t1, &t2, &t1);
+    fe_sq_tt(&t1, &t1);
+    for (i = 1; i < 5; ++i) {
+        fe_sq_tt(&t1, &t1);
     }
-    /* 2^250 - 2^0 */ mult(t0, t1, z2_50_0);
+    fe_mul_ttt(out, &t1, &t0);
+}
 
-    /* 2^251 - 2^1 */ square(t1, t0);
-    /* 2^252 - 2^2 */ square(t0, t1);
-    /* 2^253 - 2^3 */ square(t1, t0);
-    /* 2^254 - 2^4 */ square(t0, t1);
-    /* 2^255 - 2^5 */ square(t1, t0);
-    /* 2^255 - 21 */ mult(out, t1, z11);
+static inline void
+fe_invert(fe *out, const fe *z)
+{
+    fe_loose l;
+    fe_copy_lt(&l, z);
+    fe_loose_invert(out, &l);
 }
 
-/*
- * Computes q = Curve25519(p, s)
+/* Replace (f,g) with (g,f) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
+ *
+ * Preconditions: b in {0,1}
  */
-SECStatus
-ec_Curve25519_mul(PRUint8 *q, const PRUint8 *s, const PRUint8 *p)
-{
-    elem point = { 0 };
-    elem x_2 = { 0 };
-    elem z_2 = { 0 };
-    elem X = { 0 };
-    elem scalar = { 0 };
-    uint32_t i;
-
-    /* read and mask scalar */
-    for (i = 0; i < 32; ++i) {
-        scalar[i] = s[i];
+static inline void
+fe_cswap(fe *f, fe *g, unsigned int b)
+{
+    PORT_Assert(b < 2);
+    unsigned int i;
+    b = 0 - b;
+    for (i = 0; i < 10; i++) {
+        uint32_t x = f->v[i] ^ g->v[i];
+        x &= b;
+        f->v[i] ^= x;
+        g->v[i] ^= x;
     }
-    scalar[0] &= 0xF8;
-    scalar[31] &= 0x7F;
-    scalar[31] |= 64;
+}
 
-    /* read and mask point */
-    for (i = 0; i < 32; ++i) {
-        point[i] = p[i];
-    }
-    point[31] &= 0x7F;
-
-    monty(x_2, z_2, point, scalar);
-    recip(z_2, z_2);
-    mult(X, x_2, z_2);
-    reduce(X);
-    for (i = 0; i < 32; ++i) {
-        q[i] = X[i];
+/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
+static inline void
+fe_mul_121666(uint32_t out[10], const uint32_t in1[10])
+{
+    const uint32_t x20 = in1[9];
+    const uint32_t x21 = in1[8];
+    const uint32_t x19 = in1[7];
+    const uint32_t x17 = in1[6];
+    const uint32_t x15 = in1[5];
+    const uint32_t x13 = in1[4];
+    const uint32_t x11 = in1[3];
+    const uint32_t x9 = in1[2];
+    const uint32_t x7 = in1[1];
+    const uint32_t x5 = in1[0];
+    const uint32_t x38 = 0;
+    const uint32_t x39 = 0;
+    const uint32_t x37 = 0;
+    const uint32_t x35 = 0;
+    const uint32_t x33 = 0;
+    const uint32_t x31 = 0;
+    const uint32_t x29 = 0;
+    const uint32_t x27 = 0;
+    const uint32_t x25 = 0;
+    const uint32_t x23 = 121666;
+    uint64_t x40 = ((uint64_t)x23 * x5);
+    uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+    uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+    uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+    uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+    uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+    uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+    uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+    uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+    uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+    uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+    uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+    uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+    uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+    uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+    uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+    uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+    uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+    uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+    uint64_t x59 = (x48 + (x58 << 0x4));
+    uint64_t x60 = (x59 + (x58 << 0x1));
+    uint64_t x61 = (x60 + x58);
+    uint64_t x62 = (x47 + (x57 << 0x4));
+    uint64_t x63 = (x62 + (x57 << 0x1));
+    uint64_t x64 = (x63 + x57);
+    uint64_t x65 = (x46 + (x56 << 0x4));
+    uint64_t x66 = (x65 + (x56 << 0x1));
+    uint64_t x67 = (x66 + x56);
+    uint64_t x68 = (x45 + (x55 << 0x4));
+    uint64_t x69 = (x68 + (x55 << 0x1));
+    uint64_t x70 = (x69 + x55);
+    uint64_t x71 = (x44 + (x54 << 0x4));
+    uint64_t x72 = (x71 + (x54 << 0x1));
+    uint64_t x73 = (x72 + x54);
+    uint64_t x74 = (x43 + (x53 << 0x4));
+    uint64_t x75 = (x74 + (x53 << 0x1));
+    uint64_t x76 = (x75 + x53);
+    uint64_t x77 = (x42 + (x52 << 0x4));
+    uint64_t x78 = (x77 + (x52 << 0x1));
+    uint64_t x79 = (x78 + x52);
+    uint64_t x80 = (x41 + (x51 << 0x4));
+    uint64_t x81 = (x80 + (x51 << 0x1));
+    uint64_t x82 = (x81 + x51);
+    uint64_t x83 = (x40 + (x50 << 0x4));
+    uint64_t x84 = (x83 + (x50 << 0x1));
+    uint64_t x85 = (x84 + x50);
+    uint64_t x86 = (x85 >> 0x1a);
+    uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+    uint64_t x88 = (x86 + x82);
+    uint64_t x89 = (x88 >> 0x19);
+    uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+    uint64_t x91 = (x89 + x79);
+    uint64_t x92 = (x91 >> 0x1a);
+    uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+    uint64_t x94 = (x92 + x76);
+    uint64_t x95 = (x94 >> 0x19);
+    uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+    uint64_t x97 = (x95 + x73);
+    uint64_t x98 = (x97 >> 0x1a);
+    uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+    uint64_t x100 = (x98 + x70);
+    uint64_t x101 = (x100 >> 0x19);
+    uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+    uint64_t x103 = (x101 + x67);
+    uint64_t x104 = (x103 >> 0x1a);
+    uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+    uint64_t x106 = (x104 + x64);
+    uint64_t x107 = (x106 >> 0x19);
+    uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+    uint64_t x109 = (x107 + x61);
+    uint64_t x110 = (x109 >> 0x1a);
+    uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+    uint64_t x112 = (x110 + x49);
+    uint64_t x113 = (x112 >> 0x19);
+    uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+    uint64_t x115 = (x87 + (0x13 * x113));
+    uint32_t x116 = (uint32_t)(x115 >> 0x1a);
+    uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+    uint32_t x118 = (x116 + x90);
+    uint32_t x119 = (x118 >> 0x19);
+    uint32_t x120 = (x118 & 0x1ffffff);
+    out[0] = x117;
+    out[1] = x120;
+    out[2] = (x119 + x93);
+    out[3] = x96;
+    out[4] = x99;
+    out[5] = x102;
+    out[6] = x105;
+    out[7] = x108;
+    out[8] = x111;
+    out[9] = x114;
+}
+
+static void
+fe_mul_121666_tl(fe *h, const fe_loose *f)
+{
+    assert_fe_loose(f->v);
+    fe_mul_121666(h->v, f->v);
+    assert_fe(h->v);
+}
+
+SECStatus
+ec_Curve25519_mul(PRUint8 *out, const PRUint8 *scalar, const PRUint8 *point)
+{
+    fe x1, x2, z2, x3, z3, tmp0, tmp1;
+    fe_loose x2l, z2l, x3l, tmp0l, tmp1l;
+    unsigned int swap = 0;
+    unsigned int b;
+    int pos;
+    uint8_t e[32];
+
+    memcpy(e, scalar, 32);
+    e[0] &= 0xF8;
+    e[31] &= 0x7F;
+    e[31] |= 0x40;
+
+    fe_frombytes(&x1, point);
+    fe_1(&x2);
+    fe_0(&z2);
+    fe_copy(&x3, &x1);
+    fe_1(&z3);
+
+    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;
+        fe_sub(&tmp0l, &x3, &z3);
+        fe_sub(&tmp1l, &x2, &z2);
+        fe_add(&x2l, &x2, &z2);
+        fe_add(&z2l, &x3, &z3);
+        fe_mul_tll(&z3, &tmp0l, &x2l);
+        fe_mul_tll(&z2, &z2l, &tmp1l);
+        fe_sq_tl(&tmp0, &tmp1l);
+        fe_sq_tl(&tmp1, &x2l);
+        fe_add(&x3l, &z3, &z2);
+        fe_sub(&z2l, &z3, &z2);
+        fe_mul_ttt(&x2, &tmp1, &tmp0);
+        fe_sub(&tmp1l, &tmp1, &tmp0);
+        fe_sq_tl(&z2, &z2l);
+        fe_mul_121666_tl(&z3, &tmp1l);
+        fe_sq_tl(&x3, &x3l);
+        fe_add(&tmp0l, &tmp0, &z3);
+        fe_mul_ttt(&z3, &x1, &z2);
+        fe_mul_tll(&z2, &tmp1l, &tmp0l);
     }
+
+    fe_cswap(&x2, &x3, swap);
+    fe_cswap(&z2, &z3, swap);
+
+    fe_invert(&z2, &z2);
+    fe_mul_ttt(&x2, &x2, &z2);
+    fe_tobytes(out, &x2);
+
+    memset(x1.v, 0, sizeof(x1));
+    memset(x2.v, 0, sizeof(x2));
+    memset(z2.v, 0, sizeof(z2));
+    memset(x3.v, 0, sizeof(x3));
+    memset(z3.v, 0, sizeof(z3));
+    memset(x2l.v, 0, sizeof(x2l));
+    memset(z2l.v, 0, sizeof(z2l));
+    memset(x3l.v, 0, sizeof(x3l));
+    memset(e, 0, sizeof(e));
     return 0;
 }