diff --git a/ext/fiat/LICENSE b/ext/fiat/LICENSE
new file mode 100644
index 0000000..bd46c61
--- /dev/null
+++ b/ext/fiat/LICENSE
@@ -0,0 +1,22 @@
+The MIT License (MIT)
+
+Copyright (c) 2015-2016 the fiat-crypto authors (see
+https://github.com/mit-plv/fiat-crypto/blob/master/AUTHORS).
+
+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.
diff --git a/ext/fiat/METADATA b/ext/fiat/METADATA
new file mode 100644
index 0000000..0e4012f
--- /dev/null
+++ b/ext/fiat/METADATA
@@ -0,0 +1,13 @@
+name: "fiat"
+description: "Fiat-Crypto: Synthesizing Correct-by-Construction Code for Cryptographic Primitives."
+
+third_party {
+  url {
+    type: GIT
+    value: "https://github.com/mit-plv/fiat-crypto"
+  }
+  version: "4441785fb44b88bb6943ddbf639d872c8c903281"
+  last_upgrade_date { year: 2019 month: 1 day: 16 }
+
+  local_modifications: "Fiat-generated code has been integrated into existing BoringSSL code"
+}
diff --git a/ext/fiat/README.chromium b/ext/fiat/README.chromium
new file mode 100644
index 0000000..73c5ba2
--- /dev/null
+++ b/ext/fiat/README.chromium
@@ -0,0 +1,10 @@
+Name: Fiat-Crypto: Synthesizing Correct-by-Construction Code for Cryptographic Primitives
+Short Name: fiat-crypto
+URL: https://github.com/mit-plv/fiat-crypto
+Version: git (see METADATA)
+License: MIT
+License File: LICENSE
+Security Critical: yes
+
+Description:
+See README.md and METADATA.
diff --git a/ext/fiat/README.md b/ext/fiat/README.md
new file mode 100644
index 0000000..cf66900
--- /dev/null
+++ b/ext/fiat/README.md
@@ -0,0 +1,47 @@
+# Fiat
+
+Some of the code in this directory is generated by
+[Fiat](https://github.com/mit-plv/fiat-crypto) and thus these files are
+licensed under the MIT license. (See LICENSE file.)
+
+## Curve25519
+
+To generate the field arithmetic procedures in `curve25519.c` from a fiat-crypto
+checkout (as of `7892c66d5e0e5770c79463ce551193ceef870641`), run
+`make src/Specific/solinas32_2e255m19_10limbs/femul.c` (replacing `femul` with
+the desired field operation). The "source" file specifying the finite field and
+referencing the desired implementation strategy is
+`src/Specific/solinas32_2e255m19_10limbs/CurveParameters.v`, specifying roughly
+"unsaturated arithmetic modulo 2^255-19 using 10 limbs of radix 2^25.5 in 32-bit
+unsigned integers with a single carry chain and two wraparound carries" where
+only the prime is considered normative and everything else is treated as
+"compiler hints".
+
+The 64-bit implementation uses 5 limbs of radix 2^51 with instruction scheduling
+taken from curve25519-donna-c64. It is found in
+`src/Specific/solinas64_2e255m19_5limbs_donna`.
+
+## P256
+
+To generate the field arithmetic procedures in `p256.c` from a fiat-crypto
+checkout, run
+`make src/Specific/montgomery64_2e256m2e224p2e192p2e96m1_4limbs/femul.c`.
+The corresponding "source" file is
+`src/Specific/montgomery64_2e256m2e224p2e192p2e96m1_4limbs/CurveParameters.v`,
+specifying roughly "64-bit saturated word-by-word Montgomery reduction modulo
+2^256 - 2^224 + 2^192 + 2^96 - 1". Again, everything except for the prime is
+untrusted. There is currently a known issue where `fesub.c` for p256 does not
+manage to complete the build (specialization) within a week on Coq 8.7.0.
+<https://github.com/JasonGross/fiat-crypto/tree/3e6851ddecaac70d0feb484a75360d57f6e41244/src/Specific/montgomery64_2e256m2e224p2e192p2e96m1_4limbs>
+does manage to build that file, but the work on that branch was never finished
+(the correctness proofs of implementation templates still apply, but the
+now abandoned prototype specialization facilities there are unverified).
+
+## Working With Fiat Crypto Field Arithmetic
+
+The fiat-crypto readme <https://github.com/mit-plv/fiat-crypto#arithmetic-core>
+contains an overview of the implementation templates followed by a tour of the
+specialization machinery. It may be helpful to first read about the less messy
+parts of the system from chapter 3 of <http://adam.chlipala.net/theses/andreser.pdf>.
+There is work ongoing to replace the entire specialization mechanism with
+something much more principled <https://github.com/mit-plv/fiat-crypto/projects/4>.
diff --git a/ext/fiat/src/curve25519.c b/ext/fiat/src/curve25519.c
new file mode 100644
index 0000000..0215caf
--- /dev/null
+++ b/ext/fiat/src/curve25519.c
@@ -0,0 +1,1104 @@
+// 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.
+
+// Some of this code is taken from the ref10 version of Ed25519 in SUPERCOP
+// 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
+// public domain but parts have been replaced with code generated by Fiat
+// (https://github.com/mit-plv/fiat-crypto), which is MIT licensed.
+//
+// The field functions are shared by Ed25519 and X25519 where possible.
+
+#include <assert.h>
+#include <string.h>
+#include <stdint.h>
+
+#include <mbedtls/platform_util.h>
+#include <mbedtls/sha512.h>
+
+#include "curve25519.h"
+// Various pre-computed constants.
+#include "curve25519_tables.h"
+
+#define SHA512_DIGEST_LENGTH 64
+
+// Low-level intrinsic operations
+
+static uint64_t load_3(const uint8_t *in) {
+  uint64_t result;
+  result = (uint64_t)in[0];
+  result |= ((uint64_t)in[1]) << 8;
+  result |= ((uint64_t)in[2]) << 16;
+  return result;
+}
+
+static uint64_t load_4(const uint8_t *in) {
+  uint64_t result;
+  result = (uint64_t)in[0];
+  result |= ((uint64_t)in[1]) << 8;
+  result |= ((uint64_t)in[2]) << 16;
+  result |= ((uint64_t)in[3]) << 24;
+  return result;
+}
+
+
+// Field operations.
+
+typedef uint32_t fe_limb_t;
+#define FE_NUM_LIMBS 10
+
+// assert_fe asserts that |f| satisfies bounds:
+//
+//  [[0x0 ~> 0x4666666], [0x0 ~> 0x2333333],
+//   [0x0 ~> 0x4666666], [0x0 ~> 0x2333333],
+//   [0x0 ~> 0x4666666], [0x0 ~> 0x2333333],
+//   [0x0 ~> 0x4666666], [0x0 ~> 0x2333333],
+//   [0x0 ~> 0x4666666], [0x0 ~> 0x2333333]]
+//
+// See comments in curve25519_32.h for which functions use these bounds for
+// inputs or outputs.
+#define assert_fe(f)                                                     \
+  do {                                                                   \
+    for (unsigned _assert_fe_i = 0; _assert_fe_i < 10; _assert_fe_i++) { \
+      assert(f[_assert_fe_i] <=                                          \
+             ((_assert_fe_i & 1) ? 0x2333333u : 0x4666666u));            \
+    }                                                                    \
+  } while (0)
+
+// assert_fe_loose asserts that |f| satisfies bounds:
+//
+//  [[0x0 ~> 0xd333332], [0x0 ~> 0x6999999],
+//   [0x0 ~> 0xd333332], [0x0 ~> 0x6999999],
+//   [0x0 ~> 0xd333332], [0x0 ~> 0x6999999],
+//   [0x0 ~> 0xd333332], [0x0 ~> 0x6999999],
+//   [0x0 ~> 0xd333332], [0x0 ~> 0x6999999]]
+//
+// See comments in curve25519_32.h for which functions use these bounds for
+// inputs or outputs.
+#define assert_fe_loose(f)                                               \
+  do {                                                                   \
+    for (unsigned _assert_fe_i = 0; _assert_fe_i < 10; _assert_fe_i++) { \
+      assert(f[_assert_fe_i] <=                                          \
+             ((_assert_fe_i & 1) ? 0x6999999u : 0xd333332u));            \
+    }                                                                    \
+  } while (0)
+
+//FIXME: use Zephyr macro
+_Static_assert(sizeof(fe) == sizeof(fe_limb_t) * FE_NUM_LIMBS,
+               "fe_limb_t[FE_NUM_LIMBS] is inconsistent with fe");
+
+static void fe_frombytes_strict(fe *h, const uint8_t s[32]) {
+  // |fiat_25519_from_bytes| requires the top-most bit be clear.
+  assert((s[31] & 0x80) == 0);
+  fiat_25519_from_bytes(h->v, s);
+  assert_fe(h->v);
+}
+
+static void fe_frombytes(fe *h, const uint8_t s[32]) {
+  uint8_t s_copy[32];
+  memcpy(s_copy, s, 32);
+  s_copy[31] &= 0x7f;
+  fe_frombytes_strict(h, s_copy);
+}
+
+static void fe_tobytes(uint8_t s[32], const fe *f) {
+  assert_fe(f->v);
+  fiat_25519_to_bytes(s, f->v);
+}
+
+// h = 0
+static void fe_0(fe *h) {
+  mbedtls_platform_zeroize(h, sizeof(fe));
+}
+
+// h = 1
+static void fe_1(fe *h) {
+  mbedtls_platform_zeroize(h, sizeof(fe));
+  h->v[0] = 1;
+}
+
+// h = f + g
+// Can overlap h with f or g.
+static 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);
+}
+
+// h = f - g
+// Can overlap h with f or 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);
+}
+
+static void fe_carry(fe *h, const fe_loose* f) {
+  assert_fe_loose(f->v);
+  fiat_25519_carry(h->v, f->v);
+  assert_fe(h->v);
+}
+
+static void fe_mul_impl(fe_limb_t out[FE_NUM_LIMBS],
+                        const fe_limb_t in1[FE_NUM_LIMBS],
+                        const fe_limb_t in2[FE_NUM_LIMBS]) {
+  assert_fe_loose(in1);
+  assert_fe_loose(in2);
+  fiat_25519_carry_mul(out, in1, in2);
+  assert_fe(out);
+}
+
+static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
+  fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_ttt(fe *h, const fe *f, const fe *g) {
+  fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) {
+  fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) {
+  fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) {
+  fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_sq_tl(fe *h, const fe_loose *f) {
+  assert_fe_loose(f->v);
+  fiat_25519_carry_square(h->v, f->v);
+  assert_fe(h->v);
+}
+
+static void fe_sq_tt(fe *h, const fe *f) {
+  assert_fe_loose(f->v);
+  fiat_25519_carry_square(h->v, f->v);
+  assert_fe(h->v);
+}
+
+// h = -f
+static void fe_neg(fe_loose *h, const fe *f) {
+  assert_fe(f->v);
+  fiat_25519_opp(h->v, f->v);
+  assert_fe_loose(h->v);
+}
+
+// h = f
+static void fe_copy(fe *h, const fe *f) {
+  memmove(h, f, sizeof(fe));
+}
+
+static void fe_copy_lt(fe_loose *h, const fe *f) {
+  //FIXME: use Zephyr macro
+  _Static_assert(sizeof(fe_loose) == sizeof(fe), "fe and fe_loose mismatch");
+  memmove(h, f, sizeof(fe));
+}
+
+static void fe_loose_invert(fe *out, const fe_loose *z) {
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+  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);
+  }
+  fe_mul_ttt(&t2, &t3, &t2);
+  fe_sq_tt(&t2, &t2);
+  for (i = 1; i < 10; ++i) {
+    fe_sq_tt(&t2, &t2);
+  }
+  fe_mul_ttt(&t1, &t2, &t1);
+  fe_sq_tt(&t2, &t1);
+  for (i = 1; i < 50; ++i) {
+    fe_sq_tt(&t2, &t2);
+  }
+  fe_mul_ttt(&t2, &t2, &t1);
+  fe_sq_tt(&t3, &t2);
+  for (i = 1; i < 100; ++i) {
+    fe_sq_tt(&t3, &t3);
+  }
+  fe_mul_ttt(&t2, &t3, &t2);
+  fe_sq_tt(&t2, &t2);
+  for (i = 1; i < 50; ++i) {
+    fe_sq_tt(&t2, &t2);
+  }
+  fe_mul_ttt(&t1, &t2, &t1);
+  fe_sq_tt(&t1, &t1);
+  for (i = 1; i < 5; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(out, &t1, &t0);
+}
+
+static void fe_invert(fe *out, const fe *z) {
+  fe_loose l;
+  fe_copy_lt(&l, z);
+  fe_loose_invert(out, &l);
+}
+
+static int CRYPTO_memcmp(const void *in_a, const void *in_b, size_t len) {
+  const uint8_t *a = in_a;
+  const uint8_t *b = in_b;
+  uint8_t x = 0;
+
+  for (size_t i = 0; i < len; i++) {
+    x |= a[i] ^ b[i];
+  }
+
+  return x;
+}
+
+// return 0 if f == 0
+// return 1 if f != 0
+static int fe_isnonzero(const fe_loose *f) {
+  fe tight;
+  fe_carry(&tight, f);
+  uint8_t s[32];
+  fe_tobytes(s, &tight);
+
+  static const uint8_t zero[32] = {0};
+  return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
+}
+
+// return 1 if f is in {1,3,5,...,q-2}
+// return 0 if f is in {0,2,4,...,q-1}
+static int fe_isnegative(const fe *f) {
+  uint8_t s[32];
+  fe_tobytes(s, f);
+  return s[0] & 1;
+}
+
+static void fe_sq2_tt(fe *h, const fe *f) {
+  // h = f^2
+  fe_sq_tt(h, f);
+
+  // h = h + h
+  fe_loose tmp;
+  fe_add(&tmp, h, h);
+  fe_carry(h, &tmp);
+}
+
+static void fe_pow22523(fe *out, const fe *z) {
+  fe t0;
+  fe t1;
+  fe t2;
+  int i;
+
+  fe_sq_tt(&t0, z);
+  fe_sq_tt(&t1, &t0);
+  for (i = 1; i < 2; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(&t1, z, &t1);
+  fe_mul_ttt(&t0, &t0, &t1);
+  fe_sq_tt(&t0, &t0);
+  fe_mul_ttt(&t0, &t1, &t0);
+  fe_sq_tt(&t1, &t0);
+  for (i = 1; i < 5; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(&t0, &t1, &t0);
+  fe_sq_tt(&t1, &t0);
+  for (i = 1; i < 10; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(&t1, &t1, &t0);
+  fe_sq_tt(&t2, &t1);
+  for (i = 1; i < 20; ++i) {
+    fe_sq_tt(&t2, &t2);
+  }
+  fe_mul_ttt(&t1, &t2, &t1);
+  fe_sq_tt(&t1, &t1);
+  for (i = 1; i < 10; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(&t0, &t1, &t0);
+  fe_sq_tt(&t1, &t0);
+  for (i = 1; i < 50; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(&t1, &t1, &t0);
+  fe_sq_tt(&t2, &t1);
+  for (i = 1; i < 100; ++i) {
+    fe_sq_tt(&t2, &t2);
+  }
+  fe_mul_ttt(&t1, &t2, &t1);
+  fe_sq_tt(&t1, &t1);
+  for (i = 1; i < 50; ++i) {
+    fe_sq_tt(&t1, &t1);
+  }
+  fe_mul_ttt(&t0, &t1, &t0);
+  fe_sq_tt(&t0, &t0);
+  for (i = 1; i < 2; ++i) {
+    fe_sq_tt(&t0, &t0);
+  }
+  fe_mul_ttt(out, &t0, z);
+}
+
+
+// Group operations.
+
+void x25519_ge_tobytes(uint8_t s[32], const ge_p2 *h) {
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(&recip, &h->Z);
+  fe_mul_ttt(&x, &h->X, &recip);
+  fe_mul_ttt(&y, &h->Y, &recip);
+  fe_tobytes(s, &y);
+  s[31] ^= fe_isnegative(&x) << 7;
+}
+
+int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t s[32]) {
+  fe u;
+  fe_loose v;
+  fe v3;
+  fe vxx;
+  fe_loose check;
+
+  fe_frombytes(&h->Y, s);
+  fe_1(&h->Z);
+  fe_sq_tt(&v3, &h->Y);
+  fe_mul_ttt(&vxx, &v3, &d);
+  fe_sub(&v, &v3, &h->Z);  // u = y^2-1
+  fe_carry(&u, &v);
+  fe_add(&v, &vxx, &h->Z);  // v = dy^2+1
+
+  fe_sq_tl(&v3, &v);
+  fe_mul_ttl(&v3, &v3, &v);  // v3 = v^3
+  fe_sq_tt(&h->X, &v3);
+  fe_mul_ttl(&h->X, &h->X, &v);
+  fe_mul_ttt(&h->X, &h->X, &u);  // x = uv^7
+
+  fe_pow22523(&h->X, &h->X);  // x = (uv^7)^((q-5)/8)
+  fe_mul_ttt(&h->X, &h->X, &v3);
+  fe_mul_ttt(&h->X, &h->X, &u);  // x = uv^3(uv^7)^((q-5)/8)
+
+  fe_sq_tt(&vxx, &h->X);
+  fe_mul_ttl(&vxx, &vxx, &v);
+  fe_sub(&check, &vxx, &u);
+  if (fe_isnonzero(&check)) {
+    fe_add(&check, &vxx, &u);
+    if (fe_isnonzero(&check)) {
+      return 0;
+    }
+    fe_mul_ttt(&h->X, &h->X, &sqrtm1);
+  }
+
+  if (fe_isnegative(&h->X) != (s[31] >> 7)) {
+    fe_loose t;
+    fe_neg(&t, &h->X);
+    fe_carry(&h->X, &t);
+  }
+
+  fe_mul_ttt(&h->T, &h->X, &h->Y);
+  return 1;
+}
+
+static void ge_p2_0(ge_p2 *h) {
+  fe_0(&h->X);
+  fe_1(&h->Y);
+  fe_1(&h->Z);
+}
+
+// r = p
+static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+  fe_copy(&r->X, &p->X);
+  fe_copy(&r->Y, &p->Y);
+  fe_copy(&r->Z, &p->Z);
+}
+
+// r = p
+void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+  fe_add(&r->YplusX, &p->Y, &p->X);
+  fe_sub(&r->YminusX, &p->Y, &p->X);
+  fe_copy_lt(&r->Z, &p->Z);
+  fe_mul_ltt(&r->T2d, &p->T, &d2);
+}
+
+// r = p
+void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+  fe_mul_tll(&r->X, &p->X, &p->T);
+  fe_mul_tll(&r->Y, &p->Y, &p->Z);
+  fe_mul_tll(&r->Z, &p->Z, &p->T);
+}
+
+// r = p
+void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+  fe_mul_tll(&r->X, &p->X, &p->T);
+  fe_mul_tll(&r->Y, &p->Y, &p->Z);
+  fe_mul_tll(&r->Z, &p->Z, &p->T);
+  fe_mul_tll(&r->T, &p->X, &p->Y);
+}
+
+// r = 2 * p
+static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+  fe trX, trZ, trT;
+  fe t0;
+
+  fe_sq_tt(&trX, &p->X);
+  fe_sq_tt(&trZ, &p->Y);
+  fe_sq2_tt(&trT, &p->Z);
+  fe_add(&r->Y, &p->X, &p->Y);
+  fe_sq_tl(&t0, &r->Y);
+
+  fe_add(&r->Y, &trZ, &trX);
+  fe_sub(&r->Z, &trZ, &trX);
+  fe_carry(&trZ, &r->Y);
+  fe_sub(&r->X, &t0, &trZ);
+  fe_carry(&trZ, &r->Z);
+  fe_sub(&r->T, &trT, &trZ);
+}
+
+// r = 2 * p
+static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+  ge_p2 q;
+  ge_p3_to_p2(&q, p);
+  ge_p2_dbl(r, &q);
+}
+
+// r = p + q
+static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+  fe trY, trZ, trT;
+
+  fe_add(&r->X, &p->Y, &p->X);
+  fe_sub(&r->Y, &p->Y, &p->X);
+  fe_mul_tll(&trZ, &r->X, &q->yplusx);
+  fe_mul_tll(&trY, &r->Y, &q->yminusx);
+  fe_mul_tlt(&trT, &q->xy2d, &p->T);
+  fe_add(&r->T, &p->Z, &p->Z);
+  fe_sub(&r->X, &trZ, &trY);
+  fe_add(&r->Y, &trZ, &trY);
+  fe_carry(&trZ, &r->T);
+  fe_add(&r->Z, &trZ, &trT);
+  fe_sub(&r->T, &trZ, &trT);
+}
+
+// r = p - q
+static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+  fe trY, trZ, trT;
+
+  fe_add(&r->X, &p->Y, &p->X);
+  fe_sub(&r->Y, &p->Y, &p->X);
+  fe_mul_tll(&trZ, &r->X, &q->yminusx);
+  fe_mul_tll(&trY, &r->Y, &q->yplusx);
+  fe_mul_tlt(&trT, &q->xy2d, &p->T);
+  fe_add(&r->T, &p->Z, &p->Z);
+  fe_sub(&r->X, &trZ, &trY);
+  fe_add(&r->Y, &trZ, &trY);
+  fe_carry(&trZ, &r->T);
+  fe_sub(&r->Z, &trZ, &trT);
+  fe_add(&r->T, &trZ, &trT);
+}
+
+// r = p + q
+void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+  fe trX, trY, trZ, trT;
+
+  fe_add(&r->X, &p->Y, &p->X);
+  fe_sub(&r->Y, &p->Y, &p->X);
+  fe_mul_tll(&trZ, &r->X, &q->YplusX);
+  fe_mul_tll(&trY, &r->Y, &q->YminusX);
+  fe_mul_tlt(&trT, &q->T2d, &p->T);
+  fe_mul_ttl(&trX, &p->Z, &q->Z);
+  fe_add(&r->T, &trX, &trX);
+  fe_sub(&r->X, &trZ, &trY);
+  fe_add(&r->Y, &trZ, &trY);
+  fe_carry(&trZ, &r->T);
+  fe_add(&r->Z, &trZ, &trT);
+  fe_sub(&r->T, &trZ, &trT);
+}
+
+// r = p - q
+void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+  fe trX, trY, trZ, trT;
+
+  fe_add(&r->X, &p->Y, &p->X);
+  fe_sub(&r->Y, &p->Y, &p->X);
+  fe_mul_tll(&trZ, &r->X, &q->YminusX);
+  fe_mul_tll(&trY, &r->Y, &q->YplusX);
+  fe_mul_tlt(&trT, &q->T2d, &p->T);
+  fe_mul_ttl(&trX, &p->Z, &q->Z);
+  fe_add(&r->T, &trX, &trX);
+  fe_sub(&r->X, &trZ, &trY);
+  fe_add(&r->Y, &trZ, &trY);
+  fe_carry(&trZ, &r->T);
+  fe_sub(&r->Z, &trZ, &trT);
+  fe_add(&r->T, &trZ, &trT);
+}
+
+static void slide(signed char *r, const uint8_t *a) {
+  int i;
+  int b;
+  int k;
+
+  for (i = 0; i < 256; ++i) {
+    r[i] = 1 & (a[i >> 3] >> (i & 7));
+  }
+
+  for (i = 0; i < 256; ++i) {
+    if (r[i]) {
+      for (b = 1; b <= 6 && i + b < 256; ++b) {
+        if (r[i + b]) {
+          if (r[i] + (r[i + b] << b) <= 15) {
+            r[i] += r[i + b] << b;
+            r[i + b] = 0;
+          } else if (r[i] - (r[i + b] << b) >= -15) {
+            r[i] -= r[i + b] << b;
+            for (k = i + b; k < 256; ++k) {
+              if (!r[k]) {
+                r[k] = 1;
+                break;
+              }
+              r[k] = 0;
+            }
+          } else {
+            break;
+          }
+        }
+      }
+    }
+  }
+}
+
+// r = a * A + b * B
+// where a = a[0]+256*a[1]+...+256^31 a[31].
+// and b = b[0]+256*b[1]+...+256^31 b[31].
+// B is the Ed25519 base point (x,4/5) with x positive.
+static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
+                                         const ge_p3 *A, const uint8_t *b) {
+  signed char aslide[256];
+  signed char bslide[256];
+  ge_cached Ai[8];  // A,3A,5A,7A,9A,11A,13A,15A
+  ge_p1p1 t;
+  ge_p3 u;
+  ge_p3 A2;
+  int i;
+
+  slide(aslide, a);
+  slide(bslide, b);
+
+  x25519_ge_p3_to_cached(&Ai[0], A);
+  ge_p3_dbl(&t, A);
+  x25519_ge_p1p1_to_p3(&A2, &t);
+  x25519_ge_add(&t, &A2, &Ai[0]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[1], &u);
+  x25519_ge_add(&t, &A2, &Ai[1]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[2], &u);
+  x25519_ge_add(&t, &A2, &Ai[2]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[3], &u);
+  x25519_ge_add(&t, &A2, &Ai[3]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[4], &u);
+  x25519_ge_add(&t, &A2, &Ai[4]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[5], &u);
+  x25519_ge_add(&t, &A2, &Ai[5]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[6], &u);
+  x25519_ge_add(&t, &A2, &Ai[6]);
+  x25519_ge_p1p1_to_p3(&u, &t);
+  x25519_ge_p3_to_cached(&Ai[7], &u);
+
+  ge_p2_0(r);
+
+  for (i = 255; i >= 0; --i) {
+    if (aslide[i] || bslide[i]) {
+      break;
+    }
+  }
+
+  for (; i >= 0; --i) {
+    ge_p2_dbl(&t, r);
+
+    if (aslide[i] > 0) {
+      x25519_ge_p1p1_to_p3(&u, &t);
+      x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
+    } else if (aslide[i] < 0) {
+      x25519_ge_p1p1_to_p3(&u, &t);
+      x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+    }
+
+    if (bslide[i] > 0) {
+      x25519_ge_p1p1_to_p3(&u, &t);
+      ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+    } else if (bslide[i] < 0) {
+      x25519_ge_p1p1_to_p3(&u, &t);
+      ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+    }
+
+    x25519_ge_p1p1_to_p2(r, &t);
+  }
+}
+
+// int64_lshift21 returns |a << 21| but is defined when shifting bits into the
+// sign bit. This works around a language flaw in C.
+static inline int64_t int64_lshift21(int64_t a) {
+  return (int64_t)((uint64_t)a << 21);
+}
+
+// The set of scalars is \Z/l
+// where l = 2^252 + 27742317777372353535851937790883648493.
+
+// Input:
+//   s[0]+256*s[1]+...+256^63*s[63] = s
+//
+// Output:
+//   s[0]+256*s[1]+...+256^31*s[31] = s mod l
+//   where l = 2^252 + 27742317777372353535851937790883648493.
+//   Overwrites s in place.
+void x25519_sc_reduce(uint8_t s[64]) {
+  int64_t s0 = 2097151 & load_3(s);
+  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+  int64_t s8 = 2097151 & load_3(s + 21);
+  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+  int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+  int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+  int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+  int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+  int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+  int64_t s16 = 2097151 & load_3(s + 42);
+  int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+  int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+  int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+  int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+  int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+  int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+  int64_t s23 = (load_4(s + 60) >> 3);
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+  int64_t carry12;
+  int64_t carry13;
+  int64_t carry14;
+  int64_t carry15;
+  int64_t carry16;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  s23 = 0;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+  s22 = 0;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+  s21 = 0;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+  s20 = 0;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+  s19 = 0;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+  s18 = 0;
+
+  carry6 = (s6 + (1 << 20)) >> 21;
+  s7 += carry6;
+  s6 -= int64_lshift21(carry6);
+  carry8 = (s8 + (1 << 20)) >> 21;
+  s9 += carry8;
+  s8 -= int64_lshift21(carry8);
+  carry10 = (s10 + (1 << 20)) >> 21;
+  s11 += carry10;
+  s10 -= int64_lshift21(carry10);
+  carry12 = (s12 + (1 << 20)) >> 21;
+  s13 += carry12;
+  s12 -= int64_lshift21(carry12);
+  carry14 = (s14 + (1 << 20)) >> 21;
+  s15 += carry14;
+  s14 -= int64_lshift21(carry14);
+  carry16 = (s16 + (1 << 20)) >> 21;
+  s17 += carry16;
+  s16 -= int64_lshift21(carry16);
+
+  carry7 = (s7 + (1 << 20)) >> 21;
+  s8 += carry7;
+  s7 -= int64_lshift21(carry7);
+  carry9 = (s9 + (1 << 20)) >> 21;
+  s10 += carry9;
+  s9 -= int64_lshift21(carry9);
+  carry11 = (s11 + (1 << 20)) >> 21;
+  s12 += carry11;
+  s11 -= int64_lshift21(carry11);
+  carry13 = (s13 + (1 << 20)) >> 21;
+  s14 += carry13;
+  s13 -= int64_lshift21(carry13);
+  carry15 = (s15 + (1 << 20)) >> 21;
+  s16 += carry15;
+  s15 -= int64_lshift21(carry15);
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+  s17 = 0;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+  s16 = 0;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+  s15 = 0;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+  s14 = 0;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+  s13 = 0;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1 << 20)) >> 21;
+  s1 += carry0;
+  s0 -= int64_lshift21(carry0);
+  carry2 = (s2 + (1 << 20)) >> 21;
+  s3 += carry2;
+  s2 -= int64_lshift21(carry2);
+  carry4 = (s4 + (1 << 20)) >> 21;
+  s5 += carry4;
+  s4 -= int64_lshift21(carry4);
+  carry6 = (s6 + (1 << 20)) >> 21;
+  s7 += carry6;
+  s6 -= int64_lshift21(carry6);
+  carry8 = (s8 + (1 << 20)) >> 21;
+  s9 += carry8;
+  s8 -= int64_lshift21(carry8);
+  carry10 = (s10 + (1 << 20)) >> 21;
+  s11 += carry10;
+  s10 -= int64_lshift21(carry10);
+
+  carry1 = (s1 + (1 << 20)) >> 21;
+  s2 += carry1;
+  s1 -= int64_lshift21(carry1);
+  carry3 = (s3 + (1 << 20)) >> 21;
+  s4 += carry3;
+  s3 -= int64_lshift21(carry3);
+  carry5 = (s5 + (1 << 20)) >> 21;
+  s6 += carry5;
+  s5 -= int64_lshift21(carry5);
+  carry7 = (s7 + (1 << 20)) >> 21;
+  s8 += carry7;
+  s7 -= int64_lshift21(carry7);
+  carry9 = (s9 + (1 << 20)) >> 21;
+  s10 += carry9;
+  s9 -= int64_lshift21(carry9);
+  carry11 = (s11 + (1 << 20)) >> 21;
+  s12 += carry11;
+  s11 -= int64_lshift21(carry11);
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21;
+  s1 += carry0;
+  s0 -= int64_lshift21(carry0);
+  carry1 = s1 >> 21;
+  s2 += carry1;
+  s1 -= int64_lshift21(carry1);
+  carry2 = s2 >> 21;
+  s3 += carry2;
+  s2 -= int64_lshift21(carry2);
+  carry3 = s3 >> 21;
+  s4 += carry3;
+  s3 -= int64_lshift21(carry3);
+  carry4 = s4 >> 21;
+  s5 += carry4;
+  s4 -= int64_lshift21(carry4);
+  carry5 = s5 >> 21;
+  s6 += carry5;
+  s5 -= int64_lshift21(carry5);
+  carry6 = s6 >> 21;
+  s7 += carry6;
+  s6 -= int64_lshift21(carry6);
+  carry7 = s7 >> 21;
+  s8 += carry7;
+  s7 -= int64_lshift21(carry7);
+  carry8 = s8 >> 21;
+  s9 += carry8;
+  s8 -= int64_lshift21(carry8);
+  carry9 = s9 >> 21;
+  s10 += carry9;
+  s9 -= int64_lshift21(carry9);
+  carry10 = s10 >> 21;
+  s11 += carry10;
+  s10 -= int64_lshift21(carry10);
+  carry11 = s11 >> 21;
+  s12 += carry11;
+  s11 -= int64_lshift21(carry11);
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21;
+  s1 += carry0;
+  s0 -= int64_lshift21(carry0);
+  carry1 = s1 >> 21;
+  s2 += carry1;
+  s1 -= int64_lshift21(carry1);
+  carry2 = s2 >> 21;
+  s3 += carry2;
+  s2 -= int64_lshift21(carry2);
+  carry3 = s3 >> 21;
+  s4 += carry3;
+  s3 -= int64_lshift21(carry3);
+  carry4 = s4 >> 21;
+  s5 += carry4;
+  s4 -= int64_lshift21(carry4);
+  carry5 = s5 >> 21;
+  s6 += carry5;
+  s5 -= int64_lshift21(carry5);
+  carry6 = s6 >> 21;
+  s7 += carry6;
+  s6 -= int64_lshift21(carry6);
+  carry7 = s7 >> 21;
+  s8 += carry7;
+  s7 -= int64_lshift21(carry7);
+  carry8 = s8 >> 21;
+  s9 += carry8;
+  s8 -= int64_lshift21(carry8);
+  carry9 = s9 >> 21;
+  s10 += carry9;
+  s9 -= int64_lshift21(carry9);
+  carry10 = s10 >> 21;
+  s11 += carry10;
+  s10 -= int64_lshift21(carry10);
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}
+
+int ED25519_verify(const uint8_t *message, size_t message_len,
+                   const uint8_t signature[64], const uint8_t public_key[32]) {
+  ge_p3 A;
+  if ((signature[63] & 224) != 0 ||
+      !x25519_ge_frombytes_vartime(&A, public_key)) {
+    return 0;
+  }
+
+  fe_loose t;
+  fe_neg(&t, &A.X);
+  fe_carry(&A.X, &t);
+  fe_neg(&t, &A.T);
+  fe_carry(&A.T, &t);
+
+  uint8_t pkcopy[32];
+  memcpy(pkcopy, public_key, 32);
+  uint8_t rcopy[32];
+  memcpy(rcopy, signature, 32);
+  union {
+    uint64_t u64[4];
+    uint8_t u8[32];
+  } scopy;
+  memcpy(&scopy.u8[0], signature + 32, 32);
+
+  // https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that s be in
+  // the range [0, order) in order to prevent signature malleability.
+
+  // kOrder is the order of Curve25519 in little-endian form.
+  static const uint64_t kOrder[4] = {
+    UINT64_C(0x5812631a5cf5d3ed),
+    UINT64_C(0x14def9dea2f79cd6),
+    0,
+    UINT64_C(0x1000000000000000),
+  };
+  for (size_t i = 3;; i--) {
+    if (scopy.u64[i] > kOrder[i]) {
+      return 0;
+    } else if (scopy.u64[i] < kOrder[i]) {
+      break;
+    } else if (i == 0) {
+      return 0;
+    }
+  }
+
+  mbedtls_sha512_context ctx;
+  mbedtls_sha512_init(&ctx);
+  int ret;
+  ret = mbedtls_sha512_starts_ret(&ctx, 0);
+  assert(ret == 0);
+
+  ret = mbedtls_sha512_update_ret(&ctx, signature, 32);
+  assert(ret == 0);
+  ret = mbedtls_sha512_update_ret(&ctx, public_key, 32);
+  assert(ret == 0);
+  ret = mbedtls_sha512_update_ret(&ctx, message, message_len);
+  assert(ret == 0);
+
+  uint8_t h[SHA512_DIGEST_LENGTH];
+  ret = mbedtls_sha512_finish_ret(&ctx, h);
+  assert(ret == 0);
+  mbedtls_sha512_free(&ctx);
+
+  x25519_sc_reduce(h);
+
+  ge_p2 R;
+  ge_double_scalarmult_vartime(&R, h, &A, scopy.u8);
+
+  uint8_t rcheck[32];
+  x25519_ge_tobytes(rcheck, &R);
+
+  return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
+}
diff --git a/ext/fiat/src/curve25519.h b/ext/fiat/src/curve25519.h
new file mode 100644
index 0000000..55c281b
--- /dev/null
+++ b/ext/fiat/src/curve25519.h
@@ -0,0 +1,864 @@
+/* Autogenerated */
+/* curve description: 25519 */
+/* requested operations: carry_mul, carry_square, carry_scmul121666, carry, add, sub, opp, selectznz, to_bytes, from_bytes */
+/* n = 10 (from "10") */
+/* s = 0x8000000000000000000000000000000000000000000000000000000000000000 (from "2^255") */
+/* c = [(1, 19)] (from "1,19") */
+/* machine_wordsize = 32 (from "32") */
+
+#include <stdint.h>
+
+#ifndef UINT64_C
+#define UINT64_C(x) x##ULL
+#endif
+#ifndef UINT32_C
+#define UINT32_C(x) x##UL
+#endif
+#ifndef UINT8_C
+#define UINT8_C(x) (x)
+#endif
+
+// 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;
+
+// ge means group element.
+//
+// Here the group is the set of pairs (x,y) of field elements (see fe.h)
+// satisfying -x^2 + y^2 = 1 + d x^2y^2
+// where d = -121665/121666.
+//
+// Representations:
+//   ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+//   ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+//   ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+//   ge_precomp (Duif): (y+x,y-x,2dxy)
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe_loose X;
+  fe_loose Y;
+  fe_loose Z;
+  fe_loose T;
+} ge_p1p1;
+
+typedef struct {
+  fe_loose yplusx;
+  fe_loose yminusx;
+  fe_loose xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe_loose YplusX;
+  fe_loose YminusX;
+  fe_loose Z;
+  fe_loose T2d;
+} ge_cached;
+
+typedef unsigned char fiat_25519_uint1;
+typedef signed char fiat_25519_int1;
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x3ffffff]
+ *   arg3: [0x0 ~> 0x3ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x3ffffff]
+ *   out2: [0x0 ~> 0x1]
+ */
+static void fiat_25519_addcarryx_u26(uint32_t* out1, fiat_25519_uint1* out2, fiat_25519_uint1 arg1, uint32_t arg2, uint32_t arg3) {
+  uint32_t x1 = ((arg1 + arg2) + arg3);
+  uint32_t x2 = (x1 & UINT32_C(0x3ffffff));
+  fiat_25519_uint1 x3 = (fiat_25519_uint1)(x1 >> 26);
+  *out1 = x2;
+  *out2 = x3;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x3ffffff]
+ *   arg3: [0x0 ~> 0x3ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x3ffffff]
+ *   out2: [0x0 ~> 0x1]
+ */
+static void fiat_25519_subborrowx_u26(uint32_t* out1, fiat_25519_uint1* out2, fiat_25519_uint1 arg1, uint32_t arg2, uint32_t arg3) {
+  int32_t x1 = ((int32_t)(arg2 - arg1) - (int32_t)arg3);
+  fiat_25519_int1 x2 = (fiat_25519_int1)(x1 >> 26);
+  uint32_t x3 = (x1 & UINT32_C(0x3ffffff));
+  *out1 = x3;
+  *out2 = (fiat_25519_uint1)(0x0 - x2);
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x1ffffff]
+ *   arg3: [0x0 ~> 0x1ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x1ffffff]
+ *   out2: [0x0 ~> 0x1]
+ */
+static void fiat_25519_addcarryx_u25(uint32_t* out1, fiat_25519_uint1* out2, fiat_25519_uint1 arg1, uint32_t arg2, uint32_t arg3) {
+  uint32_t x1 = ((arg1 + arg2) + arg3);
+  uint32_t x2 = (x1 & UINT32_C(0x1ffffff));
+  fiat_25519_uint1 x3 = (fiat_25519_uint1)(x1 >> 25);
+  *out1 = x2;
+  *out2 = x3;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0x1ffffff]
+ *   arg3: [0x0 ~> 0x1ffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0x1ffffff]
+ *   out2: [0x0 ~> 0x1]
+ */
+static void fiat_25519_subborrowx_u25(uint32_t* out1, fiat_25519_uint1* out2, fiat_25519_uint1 arg1, uint32_t arg2, uint32_t arg3) {
+  int32_t x1 = ((int32_t)(arg2 - arg1) - (int32_t)arg3);
+  fiat_25519_int1 x2 = (fiat_25519_int1)(x1 >> 25);
+  uint32_t x3 = (x1 & UINT32_C(0x1ffffff));
+  *out1 = x3;
+  *out2 = (fiat_25519_uint1)(0x0 - x2);
+}
+
+/*
+ * 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, fiat_25519_uint1 arg1, uint32_t arg2, uint32_t arg3) {
+  fiat_25519_uint1 x1 = (!(!arg1));
+  uint32_t x2 = ((fiat_25519_int1)(0x0 - x1) & UINT32_C(0xffffffff));
+  uint32_t x3 = ((x2 & arg3) | ((~x2) & arg2));
+  *out1 = x3;
+}
+
+/*
+ * 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 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;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[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 fiat_25519_carry_square(uint32_t out1[10], const uint32_t arg1[10]) {
+  uint32_t x1 = ((arg1[9]) * (uint32_t)UINT8_C(0x13));
+  uint32_t x2 = (x1 * (uint32_t)0x2);
+  uint32_t x3 = ((arg1[9]) * (uint32_t)0x2);
+  uint32_t x4 = ((arg1[8]) * (uint32_t)UINT8_C(0x13));
+  uint64_t x5 = (x4 * (uint64_t)0x2);
+  uint32_t x6 = ((arg1[8]) * (uint32_t)0x2);
+  uint32_t x7 = ((arg1[7]) * (uint32_t)UINT8_C(0x13));
+  uint32_t x8 = (x7 * (uint32_t)0x2);
+  uint32_t x9 = ((arg1[7]) * (uint32_t)0x2);
+  uint32_t x10 = ((arg1[6]) * (uint32_t)UINT8_C(0x13));
+  uint64_t x11 = (x10 * (uint64_t)0x2);
+  uint32_t x12 = ((arg1[6]) * (uint32_t)0x2);
+  uint32_t x13 = ((arg1[5]) * (uint32_t)UINT8_C(0x13));
+  uint32_t x14 = ((arg1[5]) * (uint32_t)0x2);
+  uint32_t x15 = ((arg1[4]) * (uint32_t)0x2);
+  uint32_t x16 = ((arg1[3]) * (uint32_t)0x2);
+  uint32_t x17 = ((arg1[2]) * (uint32_t)0x2);
+  uint32_t x18 = ((arg1[1]) * (uint32_t)0x2);
+  uint64_t x19 = ((uint64_t)(arg1[9]) * (x1 * (uint32_t)0x2));
+  uint64_t x20 = ((uint64_t)(arg1[8]) * x2);
+  uint64_t x21 = ((uint64_t)(arg1[8]) * x4);
+  uint64_t x22 = ((arg1[7]) * (x2 * (uint64_t)0x2));
+  uint64_t x23 = ((arg1[7]) * x5);
+  uint64_t x24 = ((uint64_t)(arg1[7]) * (x7 * (uint32_t)0x2));
+  uint64_t x25 = ((uint64_t)(arg1[6]) * x2);
+  uint64_t x26 = ((arg1[6]) * x5);
+  uint64_t x27 = ((uint64_t)(arg1[6]) * x8);
+  uint64_t x28 = ((uint64_t)(arg1[6]) * x10);
+  uint64_t x29 = ((arg1[5]) * (x2 * (uint64_t)0x2));
+  uint64_t x30 = ((arg1[5]) * x5);
+  uint64_t x31 = ((arg1[5]) * (x8 * (uint64_t)0x2));
+  uint64_t x32 = ((arg1[5]) * x11);
+  uint64_t x33 = ((uint64_t)(arg1[5]) * (x13 * (uint32_t)0x2));
+  uint64_t x34 = ((uint64_t)(arg1[4]) * x2);
+  uint64_t x35 = ((arg1[4]) * x5);
+  uint64_t x36 = ((uint64_t)(arg1[4]) * x8);
+  uint64_t x37 = ((arg1[4]) * x11);
+  uint64_t x38 = ((uint64_t)(arg1[4]) * x14);
+  uint64_t x39 = ((uint64_t)(arg1[4]) * (arg1[4]));
+  uint64_t x40 = ((arg1[3]) * (x2 * (uint64_t)0x2));
+  uint64_t x41 = ((arg1[3]) * x5);
+  uint64_t x42 = ((arg1[3]) * (x8 * (uint64_t)0x2));
+  uint64_t x43 = ((uint64_t)(arg1[3]) * x12);
+  uint64_t x44 = ((uint64_t)(arg1[3]) * (x14 * (uint32_t)0x2));
+  uint64_t x45 = ((uint64_t)(arg1[3]) * x15);
+  uint64_t x46 = ((uint64_t)(arg1[3]) * ((arg1[3]) * (uint32_t)0x2));
+  uint64_t x47 = ((uint64_t)(arg1[2]) * x2);
+  uint64_t x48 = ((arg1[2]) * x5);
+  uint64_t x49 = ((uint64_t)(arg1[2]) * x9);
+  uint64_t x50 = ((uint64_t)(arg1[2]) * x12);
+  uint64_t x51 = ((uint64_t)(arg1[2]) * x14);
+  uint64_t x52 = ((uint64_t)(arg1[2]) * x15);
+  uint64_t x53 = ((uint64_t)(arg1[2]) * x16);
+  uint64_t x54 = ((uint64_t)(arg1[2]) * (arg1[2]));
+  uint64_t x55 = ((arg1[1]) * (x2 * (uint64_t)0x2));
+  uint64_t x56 = ((uint64_t)(arg1[1]) * x6);
+  uint64_t x57 = ((uint64_t)(arg1[1]) * (x9 * (uint32_t)0x2));
+  uint64_t x58 = ((uint64_t)(arg1[1]) * x12);
+  uint64_t x59 = ((uint64_t)(arg1[1]) * (x14 * (uint32_t)0x2));
+  uint64_t x60 = ((uint64_t)(arg1[1]) * x15);
+  uint64_t x61 = ((uint64_t)(arg1[1]) * (x16 * (uint32_t)0x2));
+  uint64_t x62 = ((uint64_t)(arg1[1]) * x17);
+  uint64_t x63 = ((uint64_t)(arg1[1]) * ((arg1[1]) * (uint32_t)0x2));
+  uint64_t x64 = ((uint64_t)(arg1[0]) * x3);
+  uint64_t x65 = ((uint64_t)(arg1[0]) * x6);
+  uint64_t x66 = ((uint64_t)(arg1[0]) * x9);
+  uint64_t x67 = ((uint64_t)(arg1[0]) * x12);
+  uint64_t x68 = ((uint64_t)(arg1[0]) * x14);
+  uint64_t x69 = ((uint64_t)(arg1[0]) * x15);
+  uint64_t x70 = ((uint64_t)(arg1[0]) * x16);
+  uint64_t x71 = ((uint64_t)(arg1[0]) * x17);
+  uint64_t x72 = ((uint64_t)(arg1[0]) * x18);
+  uint64_t x73 = ((uint64_t)(arg1[0]) * (arg1[0]));
+  uint64_t x74 = (x73 + (x55 + (x48 + (x42 + (x37 + x33)))));
+  uint64_t x75 = (x74 >> 26);
+  uint32_t x76 = (uint32_t)(x74 & UINT32_C(0x3ffffff));
+  uint64_t x77 = (x64 + (x56 + (x49 + (x43 + x38))));
+  uint64_t x78 = (x65 + (x57 + (x50 + (x44 + (x39 + x19)))));
+  uint64_t x79 = (x66 + (x58 + (x51 + (x45 + x20))));
+  uint64_t x80 = (x67 + (x59 + (x52 + (x46 + (x22 + x21)))));
+  uint64_t x81 = (x68 + (x60 + (x53 + (x25 + x23))));
+  uint64_t x82 = (x69 + (x61 + (x54 + (x29 + (x26 + x24)))));
+  uint64_t x83 = (x70 + (x62 + (x34 + (x30 + x27))));
+  uint64_t x84 = (x71 + (x63 + (x40 + (x35 + (x31 + x28)))));
+  uint64_t x85 = (x72 + (x47 + (x41 + (x36 + x32))));
+  uint64_t x86 = (x75 + x85);
+  uint64_t x87 = (x86 >> 25);
+  uint32_t x88 = (uint32_t)(x86 & UINT32_C(0x1ffffff));
+  uint64_t x89 = (x87 + x84);
+  uint64_t x90 = (x89 >> 26);
+  uint32_t x91 = (uint32_t)(x89 & UINT32_C(0x3ffffff));
+  uint64_t x92 = (x90 + x83);
+  uint64_t x93 = (x92 >> 25);
+  uint32_t x94 = (uint32_t)(x92 & UINT32_C(0x1ffffff));
+  uint64_t x95 = (x93 + x82);
+  uint64_t x96 = (x95 >> 26);
+  uint32_t x97 = (uint32_t)(x95 & UINT32_C(0x3ffffff));
+  uint64_t x98 = (x96 + x81);
+  uint64_t x99 = (x98 >> 25);
+  uint32_t x100 = (uint32_t)(x98 & UINT32_C(0x1ffffff));
+  uint64_t x101 = (x99 + x80);
+  uint64_t x102 = (x101 >> 26);
+  uint32_t x103 = (uint32_t)(x101 & UINT32_C(0x3ffffff));
+  uint64_t x104 = (x102 + x79);
+  uint64_t x105 = (x104 >> 25);
+  uint32_t x106 = (uint32_t)(x104 & UINT32_C(0x1ffffff));
+  uint64_t x107 = (x105 + x78);
+  uint64_t x108 = (x107 >> 26);
+  uint32_t x109 = (uint32_t)(x107 & UINT32_C(0x3ffffff));
+  uint64_t x110 = (x108 + x77);
+  uint64_t x111 = (x110 >> 25);
+  uint32_t x112 = (uint32_t)(x110 & UINT32_C(0x1ffffff));
+  uint64_t x113 = (x111 * (uint64_t)UINT8_C(0x13));
+  uint64_t x114 = (x76 + x113);
+  uint32_t x115 = (uint32_t)(x114 >> 26);
+  uint32_t x116 = (uint32_t)(x114 & UINT32_C(0x3ffffff));
+  uint32_t x117 = (x115 + x88);
+  uint32_t x118 = (x117 >> 25);
+  uint32_t x119 = (x117 & UINT32_C(0x1ffffff));
+  uint32_t x120 = (x118 + x91);
+  out1[0] = x116;
+  out1[1] = x119;
+  out1[2] = x120;
+  out1[3] = x94;
+  out1[4] = x97;
+  out1[5] = x100;
+  out1[6] = x103;
+  out1[7] = x106;
+  out1[8] = x109;
+  out1[9] = x112;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[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 fiat_25519_carry(uint32_t out1[10], const uint32_t arg1[10]) {
+  uint32_t x1 = (arg1[0]);
+  uint32_t x2 = ((x1 >> 26) + (arg1[1]));
+  uint32_t x3 = ((x2 >> 25) + (arg1[2]));
+  uint32_t x4 = ((x3 >> 26) + (arg1[3]));
+  uint32_t x5 = ((x4 >> 25) + (arg1[4]));
+  uint32_t x6 = ((x5 >> 26) + (arg1[5]));
+  uint32_t x7 = ((x6 >> 25) + (arg1[6]));
+  uint32_t x8 = ((x7 >> 26) + (arg1[7]));
+  uint32_t x9 = ((x8 >> 25) + (arg1[8]));
+  uint32_t x10 = ((x9 >> 26) + (arg1[9]));
+  uint32_t x11 = ((x1 & UINT32_C(0x3ffffff)) + ((x10 >> 25) * (uint32_t)UINT8_C(0x13)));
+  uint32_t x12 = ((x11 >> 26) + (x2 & UINT32_C(0x1ffffff)));
+  uint32_t x13 = (x11 & UINT32_C(0x3ffffff));
+  uint32_t x14 = (x12 & UINT32_C(0x1ffffff));
+  uint32_t x15 = ((x12 >> 25) + (x3 & UINT32_C(0x3ffffff)));
+  uint32_t x16 = (x4 & UINT32_C(0x1ffffff));
+  uint32_t x17 = (x5 & UINT32_C(0x3ffffff));
+  uint32_t x18 = (x6 & UINT32_C(0x1ffffff));
+  uint32_t x19 = (x7 & UINT32_C(0x3ffffff));
+  uint32_t x20 = (x8 & UINT32_C(0x1ffffff));
+  uint32_t x21 = (x9 & UINT32_C(0x3ffffff));
+  uint32_t x22 = (x10 & UINT32_C(0x1ffffff));
+  out1[0] = x13;
+  out1[1] = x14;
+  out1[2] = x15;
+  out1[3] = x16;
+  out1[4] = x17;
+  out1[5] = x18;
+  out1[6] = x19;
+  out1[7] = x20;
+  out1[8] = x21;
+  out1[9] = x22;
+}
+
+/*
+ * 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 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;
+}
+
+/*
+ * 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 fiat_25519_sub(uint32_t out1[10], const uint32_t arg1[10], const uint32_t arg2[10]) {
+  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;
+}
+
+/*
+ * 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 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999], [0x0 ~> 0xd333332], [0x0 ~> 0x6999999]]
+ */
+static void fiat_25519_opp(uint32_t out1[10], const uint32_t arg1[10]) {
+  uint32_t x1 = (UINT32_C(0x7ffffda) - (arg1[0]));
+  uint32_t x2 = (UINT32_C(0x3fffffe) - (arg1[1]));
+  uint32_t x3 = (UINT32_C(0x7fffffe) - (arg1[2]));
+  uint32_t x4 = (UINT32_C(0x3fffffe) - (arg1[3]));
+  uint32_t x5 = (UINT32_C(0x7fffffe) - (arg1[4]));
+  uint32_t x6 = (UINT32_C(0x3fffffe) - (arg1[5]));
+  uint32_t x7 = (UINT32_C(0x7fffffe) - (arg1[6]));
+  uint32_t x8 = (UINT32_C(0x3fffffe) - (arg1[7]));
+  uint32_t x9 = (UINT32_C(0x7fffffe) - (arg1[8]));
+  uint32_t x10 = (UINT32_C(0x3fffffe) - (arg1[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;
+}
+
+/*
+ * 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 fiat_25519_to_bytes(uint8_t out1[32], const uint32_t arg1[10]) {
+  uint32_t x1;
+  fiat_25519_uint1 x2;
+  fiat_25519_subborrowx_u26(&x1, &x2, 0x0, (arg1[0]), UINT32_C(0x3ffffed));
+  uint32_t x3;
+  fiat_25519_uint1 x4;
+  fiat_25519_subborrowx_u25(&x3, &x4, x2, (arg1[1]), UINT32_C(0x1ffffff));
+  uint32_t x5;
+  fiat_25519_uint1 x6;
+  fiat_25519_subborrowx_u26(&x5, &x6, x4, (arg1[2]), UINT32_C(0x3ffffff));
+  uint32_t x7;
+  fiat_25519_uint1 x8;
+  fiat_25519_subborrowx_u25(&x7, &x8, x6, (arg1[3]), UINT32_C(0x1ffffff));
+  uint32_t x9;
+  fiat_25519_uint1 x10;
+  fiat_25519_subborrowx_u26(&x9, &x10, x8, (arg1[4]), UINT32_C(0x3ffffff));
+  uint32_t x11;
+  fiat_25519_uint1 x12;
+  fiat_25519_subborrowx_u25(&x11, &x12, x10, (arg1[5]), UINT32_C(0x1ffffff));
+  uint32_t x13;
+  fiat_25519_uint1 x14;
+  fiat_25519_subborrowx_u26(&x13, &x14, x12, (arg1[6]), UINT32_C(0x3ffffff));
+  uint32_t x15;
+  fiat_25519_uint1 x16;
+  fiat_25519_subborrowx_u25(&x15, &x16, x14, (arg1[7]), UINT32_C(0x1ffffff));
+  uint32_t x17;
+  fiat_25519_uint1 x18;
+  fiat_25519_subborrowx_u26(&x17, &x18, x16, (arg1[8]), UINT32_C(0x3ffffff));
+  uint32_t x19;
+  fiat_25519_uint1 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;
+  fiat_25519_uint1 x23;
+  fiat_25519_addcarryx_u26(&x22, &x23, 0x0, (x21 & UINT32_C(0x3ffffed)), x1);
+  uint32_t x24;
+  fiat_25519_uint1 x25;
+  fiat_25519_addcarryx_u25(&x24, &x25, x23, (x21 & UINT32_C(0x1ffffff)), x3);
+  uint32_t x26;
+  fiat_25519_uint1 x27;
+  fiat_25519_addcarryx_u26(&x26, &x27, x25, (x21 & UINT32_C(0x3ffffff)), x5);
+  uint32_t x28;
+  fiat_25519_uint1 x29;
+  fiat_25519_addcarryx_u25(&x28, &x29, x27, (x21 & UINT32_C(0x1ffffff)), x7);
+  uint32_t x30;
+  fiat_25519_uint1 x31;
+  fiat_25519_addcarryx_u26(&x30, &x31, x29, (x21 & UINT32_C(0x3ffffff)), x9);
+  uint32_t x32;
+  fiat_25519_uint1 x33;
+  fiat_25519_addcarryx_u25(&x32, &x33, x31, (x21 & UINT32_C(0x1ffffff)), x11);
+  uint32_t x34;
+  fiat_25519_uint1 x35;
+  fiat_25519_addcarryx_u26(&x34, &x35, x33, (x21 & UINT32_C(0x3ffffff)), x13);
+  uint32_t x36;
+  fiat_25519_uint1 x37;
+  fiat_25519_addcarryx_u25(&x36, &x37, x35, (x21 & UINT32_C(0x1ffffff)), x15);
+  uint32_t x38;
+  fiat_25519_uint1 x39;
+  fiat_25519_addcarryx_u26(&x38, &x39, x37, (x21 & UINT32_C(0x3ffffff)), x17);
+  uint32_t x40;
+  fiat_25519_uint1 x41;
+  fiat_25519_addcarryx_u25(&x40, &x41, x39, (x21 & UINT32_C(0x1ffffff)), x19);
+  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));
+  fiat_25519_uint1 x89 = (fiat_25519_uint1)(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;
+}
+
+/*
+ * 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 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;
+}
+
diff --git a/ext/fiat/src/curve25519_tables.h b/ext/fiat/src/curve25519_tables.h
new file mode 100644
index 0000000..bfefc1c
--- /dev/null
+++ b/ext/fiat/src/curve25519_tables.h
@@ -0,0 +1,107 @@
+// 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.
+
+// This file is generated from
+//    ./make_curve25519_tables.py > curve25519_tables.h
+
+static const fe d = {{
+    56195235, 13857412, 51736253, 6949390, 114729, 24766616,
+    60832955, 30306712, 48412415, 21499315
+}};
+
+static const fe sqrtm1 = {{
+    34513072, 25610706, 9377949, 3500415, 12389472,
+    33281959, 41962654, 31548777, 326685, 11406482
+}};
+
+static const fe d2 = {{
+    45281625, 27714825, 36363642, 13898781, 229458, 15978800,
+    54557047, 27058993, 29715967, 9444199
+}};
+
+// Bi[i] = (2*i+1)*B
+static const ge_precomp Bi[8] = {
+    {
+        {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786, 27544626,
+          21800161, 61029707, 2047604}},
+        {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
+          5043384, 19500929, 18085054}},
+        {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918,
+          11864899, 42594502, 29115885}},
+    },
+    {
+        {{15636272, 23865875, 24204772, 25642034, 616976, 16869170, 27787599,
+          18782243, 28944399, 32004408}},
+        {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576,
+          21778470, 7689661, 11199574}},
+        {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774,
+          10017326, 49359771, 23634074}},
+    },
+    {
+        {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860, 32867885,
+          14515107, 51670560, 10819379}},
+        {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
+          12483687, 54440373, 5581305}},
+        {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349,
+          13850243, 43430843, 17738489}},
+    },
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