if_wg: import latest fixup work from the wireguard-freebsd project

This is the culmination of about a week of work from three developers to
fix a number of functional and security issues.  This patch consists of
work done by the following folks:

- Jason A. Donenfeld <Jason@zx2c4.com>
- Matt Dunwoodie <ncon@noconroy.net>
- Kyle Evans <kevans@FreeBSD.org>

Notable changes include:
- Packets are now correctly staged for processing once the handshake has
  completed, resulting in less packet loss in the interim.
- Various race conditions have been resolved, particularly w.r.t. socket
  and packet lifetime (panics)
- Various tests have been added to assure correct functionality and
  tooling conformance
- Many security issues have been addressed
- if_wg now maintains jail-friendly semantics: sockets are created in
  the interface's home vnet so that it can act as the sole network
  connection for a jail
- if_wg no longer fails to remove peer allowed-ips of 0.0.0.0/0
- if_wg now exports via ioctl a format that is future proof and
  complete.  It is additionally supported by the upstream
  wireguard-tools (which we plan to merge in to base soon)
- if_wg now conforms to the WireGuard protocol and is more closely
  aligned with security auditing guidelines

Note that the driver has been rebased away from using iflib.  iflib
poses a number of challenges for a cloned device trying to operate in a
vnet that are non-trivial to solve and adds complexity to the
implementation for little gain.

The crypto implementation that was previously added to the tree was a
super complex integration of what previously appeared in an old out of
tree Linux module, which has been reduced to crypto.c containing simple
boring reference implementations.  This is part of a near-to-mid term
goal to work with FreeBSD kernel crypto folks and take advantage of or
improve accelerated crypto already offered elsewhere.

There's additional test suite effort underway out-of-tree taking
advantage of the aforementioned jail-friendly semantics to test a number
of real-world topologies, based on netns.sh.

Also note that this is still a work in progress; work going further will
be much smaller in nature.

MFC after:	1 month (maybe)

1 files changed, 1705 insertions, 0 deletions

diff --git a/sys/dev/if_wg/crypto.c b/sys/dev/if_wg/crypto.c
new file mode 100644
index 000000000000..f28585429272
--- /dev/null
+++ b/sys/dev/if_wg/crypto.c
@@ -0,0 +1,1705 @@
+/*
+ * Copyright (C) 2015-2021 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+
+#include <sys/types.h>
+#include <sys/endian.h>
+#include <sys/systm.h>
+
+#include "crypto.h"
+
+#ifndef ARRAY_SIZE
+#define ARRAY_SIZE(x) (sizeof(x) / sizeof((x)[0]))
+#endif
+#ifndef noinline
+#define noinline __attribute__((noinline))
+#endif
+#ifndef __aligned
+#define __aligned(x) __attribute__((aligned(x)))
+#endif
+#ifndef DIV_ROUND_UP
+#define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
+#endif
+
+#define le32_to_cpup(a) le32toh(*(a))
+#define le64_to_cpup(a) le64toh(*(a))
+#define cpu_to_le32(a) htole32(a)
+#define cpu_to_le64(a) htole64(a)
+
+static inline uint32_t get_unaligned_le32(const uint8_t *a)
+{
+	uint32_t l;
+	__builtin_memcpy(&l, a, sizeof(l));
+	return le32_to_cpup(&l);
+}
+static inline uint64_t get_unaligned_le64(const uint8_t *a)
+{
+	uint64_t l;
+	__builtin_memcpy(&l, a, sizeof(l));
+	return le64_to_cpup(&l);
+}
+static inline void put_unaligned_le32(uint32_t s, uint8_t *d)
+{
+	uint32_t l = cpu_to_le32(s);
+	__builtin_memcpy(d, &l, sizeof(l));
+}
+static inline void cpu_to_le32_array(uint32_t *buf, unsigned int words)
+{
+        while (words--) {
+		*buf = cpu_to_le32(*buf);
+		++buf;
+	}
+}
+static inline void le32_to_cpu_array(uint32_t *buf, unsigned int words)
+{
+        while (words--) {
+		*buf = le32_to_cpup(buf);
+		++buf;
+        }
+}
+
+static inline uint32_t rol32(uint32_t word, unsigned int shift)
+{
+        return (word << (shift & 31)) | (word >> ((-shift) & 31));
+}
+static inline uint32_t ror32(uint32_t word, unsigned int shift)
+{
+	return (word >> (shift & 31)) | (word << ((-shift) & 31));
+}
+
+static void xor_cpy(uint8_t *dst, const uint8_t *src1, const uint8_t *src2,
+		    size_t len)
+{
+	size_t i;
+
+	for (i = 0; i < len; ++i)
+		dst[i] = src1[i] ^ src2[i];
+}
+
+#define QUARTER_ROUND(x, a, b, c, d) ( \
+	x[a] += x[b], \
+	x[d] = rol32((x[d] ^ x[a]), 16), \
+	x[c] += x[d], \
+	x[b] = rol32((x[b] ^ x[c]), 12), \
+	x[a] += x[b], \
+	x[d] = rol32((x[d] ^ x[a]), 8), \
+	x[c] += x[d], \
+	x[b] = rol32((x[b] ^ x[c]), 7) \
+)
+
+#define C(i, j) (i * 4 + j)
+
+#define DOUBLE_ROUND(x) ( \
+	/* Column Round */ \
+	QUARTER_ROUND(x, C(0, 0), C(1, 0), C(2, 0), C(3, 0)), \
+	QUARTER_ROUND(x, C(0, 1), C(1, 1), C(2, 1), C(3, 1)), \
+	QUARTER_ROUND(x, C(0, 2), C(1, 2), C(2, 2), C(3, 2)), \
+	QUARTER_ROUND(x, C(0, 3), C(1, 3), C(2, 3), C(3, 3)), \
+	/* Diagonal Round */ \
+	QUARTER_ROUND(x, C(0, 0), C(1, 1), C(2, 2), C(3, 3)), \
+	QUARTER_ROUND(x, C(0, 1), C(1, 2), C(2, 3), C(3, 0)), \
+	QUARTER_ROUND(x, C(0, 2), C(1, 3), C(2, 0), C(3, 1)), \
+	QUARTER_ROUND(x, C(0, 3), C(1, 0), C(2, 1), C(3, 2)) \
+)
+
+#define TWENTY_ROUNDS(x) ( \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x), \
+	DOUBLE_ROUND(x) \
+)
+
+enum chacha20_lengths {
+	CHACHA20_NONCE_SIZE = 16,
+	CHACHA20_KEY_SIZE = 32,
+	CHACHA20_KEY_WORDS = CHACHA20_KEY_SIZE / sizeof(uint32_t),
+	CHACHA20_BLOCK_SIZE = 64,
+	CHACHA20_BLOCK_WORDS = CHACHA20_BLOCK_SIZE / sizeof(uint32_t),
+	HCHACHA20_NONCE_SIZE = CHACHA20_NONCE_SIZE,
+	HCHACHA20_KEY_SIZE = CHACHA20_KEY_SIZE
+};
+
+enum chacha20_constants { /* expand 32-byte k */
+	CHACHA20_CONSTANT_EXPA = 0x61707865U,
+	CHACHA20_CONSTANT_ND_3 = 0x3320646eU,
+	CHACHA20_CONSTANT_2_BY = 0x79622d32U,
+	CHACHA20_CONSTANT_TE_K = 0x6b206574U
+};
+
+struct chacha20_ctx {
+	union {
+		uint32_t state[16];
+		struct {
+			uint32_t constant[4];
+			uint32_t key[8];
+			uint32_t counter[4];
+		};
+	};
+};
+
+static void chacha20_init(struct chacha20_ctx *ctx,
+			  const uint8_t key[CHACHA20_KEY_SIZE],
+			  const uint64_t nonce)
+{
+	ctx->constant[0] = CHACHA20_CONSTANT_EXPA;
+	ctx->constant[1] = CHACHA20_CONSTANT_ND_3;
+	ctx->constant[2] = CHACHA20_CONSTANT_2_BY;
+	ctx->constant[3] = CHACHA20_CONSTANT_TE_K;
+	ctx->key[0] = get_unaligned_le32(key + 0);
+	ctx->key[1] = get_unaligned_le32(key + 4);
+	ctx->key[2] = get_unaligned_le32(key + 8);
+	ctx->key[3] = get_unaligned_le32(key + 12);
+	ctx->key[4] = get_unaligned_le32(key + 16);
+	ctx->key[5] = get_unaligned_le32(key + 20);
+	ctx->key[6] = get_unaligned_le32(key + 24);
+	ctx->key[7] = get_unaligned_le32(key + 28);
+	ctx->counter[0] = 0;
+	ctx->counter[1] = 0;
+	ctx->counter[2] = nonce & 0xffffffffU;
+	ctx->counter[3] = nonce >> 32;
+}
+
+static void chacha20_block(struct chacha20_ctx *ctx, uint32_t *stream)
+{
+	uint32_t x[CHACHA20_BLOCK_WORDS];
+	int i;
+
+	for (i = 0; i < ARRAY_SIZE(x); ++i)
+		x[i] = ctx->state[i];
+
+	TWENTY_ROUNDS(x);
+
+	for (i = 0; i < ARRAY_SIZE(x); ++i)
+		stream[i] = cpu_to_le32(x[i] + ctx->state[i]);
+
+	ctx->counter[0] += 1;
+}
+
+static void chacha20(struct chacha20_ctx *ctx, uint8_t *out, const uint8_t *in,
+		     uint32_t len)
+{
+	uint32_t buf[CHACHA20_BLOCK_WORDS];
+
+	while (len >= CHACHA20_BLOCK_SIZE) {
+		chacha20_block(ctx, buf);
+		xor_cpy(out, in, (uint8_t *)buf, CHACHA20_BLOCK_SIZE);
+		len -= CHACHA20_BLOCK_SIZE;
+		out += CHACHA20_BLOCK_SIZE;
+		in += CHACHA20_BLOCK_SIZE;
+	}
+	if (len) {
+		chacha20_block(ctx, buf);
+		xor_cpy(out, in, (uint8_t *)buf, len);
+	}
+}
+
+static void hchacha20(uint32_t derived_key[CHACHA20_KEY_WORDS],
+		      const uint8_t nonce[HCHACHA20_NONCE_SIZE],
+		      const uint8_t key[HCHACHA20_KEY_SIZE])
+{
+	uint32_t x[] = { CHACHA20_CONSTANT_EXPA,
+		    CHACHA20_CONSTANT_ND_3,
+		    CHACHA20_CONSTANT_2_BY,
+		    CHACHA20_CONSTANT_TE_K,
+		    get_unaligned_le32(key +  0),
+		    get_unaligned_le32(key +  4),
+		    get_unaligned_le32(key +  8),
+		    get_unaligned_le32(key + 12),
+		    get_unaligned_le32(key + 16),
+		    get_unaligned_le32(key + 20),
+		    get_unaligned_le32(key + 24),
+		    get_unaligned_le32(key + 28),
+		    get_unaligned_le32(nonce +  0),
+		    get_unaligned_le32(nonce +  4),
+		    get_unaligned_le32(nonce +  8),
+		    get_unaligned_le32(nonce + 12)
+	};
+
+	TWENTY_ROUNDS(x);
+
+	memcpy(derived_key + 0, x +  0, sizeof(uint32_t) * 4);
+	memcpy(derived_key + 4, x + 12, sizeof(uint32_t) * 4);
+}
+
+enum poly1305_lengths {
+	POLY1305_BLOCK_SIZE = 16,
+	POLY1305_KEY_SIZE = 32,
+	POLY1305_MAC_SIZE = 16
+};
+
+struct poly1305_internal {
+	uint32_t h[5];
+	uint32_t r[5];
+	uint32_t s[4];
+};
+
+struct poly1305_ctx {
+	struct poly1305_internal state;
+	uint32_t nonce[4];
+	uint8_t data[POLY1305_BLOCK_SIZE];
+	size_t num;
+};
+
+static void poly1305_init_core(struct poly1305_internal *st,
+			       const uint8_t key[16])
+{
+	/* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
+	st->r[0] = (get_unaligned_le32(&key[0])) & 0x3ffffff;
+	st->r[1] = (get_unaligned_le32(&key[3]) >> 2) & 0x3ffff03;
+	st->r[2] = (get_unaligned_le32(&key[6]) >> 4) & 0x3ffc0ff;
+	st->r[3] = (get_unaligned_le32(&key[9]) >> 6) & 0x3f03fff;
+	st->r[4] = (get_unaligned_le32(&key[12]) >> 8) & 0x00fffff;
+
+	/* s = 5*r */
+	st->s[0] = st->r[1] * 5;
+	st->s[1] = st->r[2] * 5;
+	st->s[2] = st->r[3] * 5;
+	st->s[3] = st->r[4] * 5;
+
+	/* h = 0 */
+	st->h[0] = 0;
+	st->h[1] = 0;
+	st->h[2] = 0;
+	st->h[3] = 0;
+	st->h[4] = 0;
+}
+
+static void poly1305_blocks_core(struct poly1305_internal *st,
+				 const uint8_t *input, size_t len,
+				 const uint32_t padbit)
+{
+	const uint32_t hibit = padbit << 24;
+	uint32_t r0, r1, r2, r3, r4;
+	uint32_t s1, s2, s3, s4;
+	uint32_t h0, h1, h2, h3, h4;
+	uint64_t d0, d1, d2, d3, d4;
+	uint32_t c;
+
+	r0 = st->r[0];
+	r1 = st->r[1];
+	r2 = st->r[2];
+	r3 = st->r[3];
+	r4 = st->r[4];
+
+	s1 = st->s[0];
+	s2 = st->s[1];
+	s3 = st->s[2];
+	s4 = st->s[3];
+
+	h0 = st->h[0];
+	h1 = st->h[1];
+	h2 = st->h[2];
+	h3 = st->h[3];
+	h4 = st->h[4];
+
+	while (len >= POLY1305_BLOCK_SIZE) {
+		/* h += m[i] */
+		h0 += (get_unaligned_le32(&input[0])) & 0x3ffffff;
+		h1 += (get_unaligned_le32(&input[3]) >> 2) & 0x3ffffff;
+		h2 += (get_unaligned_le32(&input[6]) >> 4) & 0x3ffffff;
+		h3 += (get_unaligned_le32(&input[9]) >> 6) & 0x3ffffff;
+		h4 += (get_unaligned_le32(&input[12]) >> 8) | hibit;
+
+		/* h *= r */
+		d0 = ((uint64_t)h0 * r0) + ((uint64_t)h1 * s4) +
+		     ((uint64_t)h2 * s3) + ((uint64_t)h3 * s2) +
+		     ((uint64_t)h4 * s1);
+		d1 = ((uint64_t)h0 * r1) + ((uint64_t)h1 * r0) +
+		     ((uint64_t)h2 * s4) + ((uint64_t)h3 * s3) +
+		     ((uint64_t)h4 * s2);
+		d2 = ((uint64_t)h0 * r2) + ((uint64_t)h1 * r1) +
+		     ((uint64_t)h2 * r0) + ((uint64_t)h3 * s4) +
+		     ((uint64_t)h4 * s3);
+		d3 = ((uint64_t)h0 * r3) + ((uint64_t)h1 * r2) +
+		     ((uint64_t)h2 * r1) + ((uint64_t)h3 * r0) +
+		     ((uint64_t)h4 * s4);
+		d4 = ((uint64_t)h0 * r4) + ((uint64_t)h1 * r3) +
+		     ((uint64_t)h2 * r2) + ((uint64_t)h3 * r1) +
+		     ((uint64_t)h4 * r0);
+
+		/* (partial) h %= p */
+		c = (uint32_t)(d0 >> 26);
+		h0 = (uint32_t)d0 & 0x3ffffff;
+		d1 += c;
+		c = (uint32_t)(d1 >> 26);
+		h1 = (uint32_t)d1 & 0x3ffffff;
+		d2 += c;
+		c = (uint32_t)(d2 >> 26);
+		h2 = (uint32_t)d2 & 0x3ffffff;
+		d3 += c;
+		c = (uint32_t)(d3 >> 26);
+		h3 = (uint32_t)d3 & 0x3ffffff;
+		d4 += c;
+		c = (uint32_t)(d4 >> 26);
+		h4 = (uint32_t)d4 & 0x3ffffff;
+		h0 += c * 5;
+		c = (h0 >> 26);
+		h0 = h0 & 0x3ffffff;
+		h1 += c;
+
+		input += POLY1305_BLOCK_SIZE;
+		len -= POLY1305_BLOCK_SIZE;
+	}
+
+	st->h[0] = h0;
+	st->h[1] = h1;
+	st->h[2] = h2;
+	st->h[3] = h3;
+	st->h[4] = h4;
+}
+
+static void poly1305_emit_core(struct poly1305_internal *st, uint8_t mac[16],
+			       const uint32_t nonce[4])
+{
+	uint32_t h0, h1, h2, h3, h4, c;
+	uint32_t g0, g1, g2, g3, g4;
+	uint64_t f;
+	uint32_t mask;
+
+	/* fully carry h */
+	h0 = st->h[0];
+	h1 = st->h[1];
+	h2 = st->h[2];
+	h3 = st->h[3];
+	h4 = st->h[4];
+
+	c = h1 >> 26;
+	h1 = h1 & 0x3ffffff;
+	h2 += c;
+	c = h2 >> 26;
+	h2 = h2 & 0x3ffffff;
+	h3 += c;
+	c = h3 >> 26;
+	h3 = h3 & 0x3ffffff;
+	h4 += c;
+	c = h4 >> 26;
+	h4 = h4 & 0x3ffffff;
+	h0 += c * 5;
+	c = h0 >> 26;
+	h0 = h0 & 0x3ffffff;
+	h1 += c;
+
+	/* compute h + -p */
+	g0 = h0 + 5;
+	c = g0 >> 26;
+	g0 &= 0x3ffffff;
+	g1 = h1 + c;
+	c = g1 >> 26;
+	g1 &= 0x3ffffff;
+	g2 = h2 + c;
+	c = g2 >> 26;
+	g2 &= 0x3ffffff;
+	g3 = h3 + c;
+	c = g3 >> 26;
+	g3 &= 0x3ffffff;
+	g4 = h4 + c - (1UL << 26);
+
+	/* select h if h < p, or h + -p if h >= p */
+	mask = (g4 >> ((sizeof(uint32_t) * 8) - 1)) - 1;
+	g0 &= mask;
+	g1 &= mask;
+	g2 &= mask;
+	g3 &= mask;
+	g4 &= mask;
+	mask = ~mask;
+
+	h0 = (h0 & mask) | g0;
+	h1 = (h1 & mask) | g1;
+	h2 = (h2 & mask) | g2;
+	h3 = (h3 & mask) | g3;
+	h4 = (h4 & mask) | g4;
+
+	/* h = h % (2^128) */
+	h0 = ((h0) | (h1 << 26)) & 0xffffffff;
+	h1 = ((h1 >> 6) | (h2 << 20)) & 0xffffffff;
+	h2 = ((h2 >> 12) | (h3 << 14)) & 0xffffffff;
+	h3 = ((h3 >> 18) | (h4 << 8)) & 0xffffffff;
+
+	/* mac = (h + nonce) % (2^128) */
+	f = (uint64_t)h0 + nonce[0];
+	h0 = (uint32_t)f;
+	f = (uint64_t)h1 + nonce[1] + (f >> 32);
+	h1 = (uint32_t)f;
+	f = (uint64_t)h2 + nonce[2] + (f >> 32);
+	h2 = (uint32_t)f;
+	f = (uint64_t)h3 + nonce[3] + (f >> 32);
+	h3 = (uint32_t)f;
+
+	put_unaligned_le32(h0, &mac[0]);
+	put_unaligned_le32(h1, &mac[4]);
+	put_unaligned_le32(h2, &mac[8]);
+	put_unaligned_le32(h3, &mac[12]);
+}
+
+static void poly1305_init(struct poly1305_ctx *ctx,
+			  const uint8_t key[POLY1305_KEY_SIZE])
+{
+	ctx->nonce[0] = get_unaligned_le32(&key[16]);
+	ctx->nonce[1] = get_unaligned_le32(&key[20]);
+	ctx->nonce[2] = get_unaligned_le32(&key[24]);
+	ctx->nonce[3] = get_unaligned_le32(&key[28]);
+
+	poly1305_init_core(&ctx->state, key);
+
+	ctx->num = 0;
+}
+
+static void poly1305_update(struct poly1305_ctx *ctx, const uint8_t *input,
+			    size_t len)
+{
+	const size_t num = ctx->num;
+	size_t rem;
+
+	if (num) {
+		rem = POLY1305_BLOCK_SIZE - num;
+		if (len < rem) {
+			memcpy(ctx->data + num, input, len);
+			ctx->num = num + len;
+			return;
+		}
+		memcpy(ctx->data + num, input, rem);
+		poly1305_blocks_core(&ctx->state, ctx->data,
+				     POLY1305_BLOCK_SIZE, 1);
+		input += rem;
+		len -= rem;
+	}
+
+	rem = len % POLY1305_BLOCK_SIZE;
+	len -= rem;
+
+	if (len >= POLY1305_BLOCK_SIZE) {
+		poly1305_blocks_core(&ctx->state, input, len, 1);
+		input += len;
+	}
+
+	if (rem)
+		memcpy(ctx->data, input, rem);
+
+	ctx->num = rem;
+}
+
+static void poly1305_final(struct poly1305_ctx *ctx,
+			   uint8_t mac[POLY1305_MAC_SIZE])
+{
+	size_t num = ctx->num;
+
+	if (num) {
+		ctx->data[num++] = 1;
+		while (num < POLY1305_BLOCK_SIZE)
+			ctx->data[num++] = 0;
+		poly1305_blocks_core(&ctx->state, ctx->data,
+				     POLY1305_BLOCK_SIZE, 0);
+	}
+
+	poly1305_emit_core(&ctx->state, mac, ctx->nonce);
+
+	explicit_bzero(ctx, sizeof(*ctx));
+}
+
+
+static const uint8_t pad0[16] = { 0 };
+
+void
+chacha20poly1305_encrypt(uint8_t *dst, const uint8_t *src, const size_t src_len,
+			 const uint8_t *ad, const size_t ad_len,
+			 const uint64_t nonce,
+			 const uint8_t key[CHACHA20POLY1305_KEY_SIZE])
+{
+	struct poly1305_ctx poly1305_state;
+	struct chacha20_ctx chacha20_state;
+	union {
+		uint8_t block0[POLY1305_KEY_SIZE];
+		uint64_t lens[2];
+	} b = { { 0 } };
+
+	chacha20_init(&chacha20_state, key, nonce);
+	chacha20(&chacha20_state, b.block0, b.block0, sizeof(b.block0));
+	poly1305_init(&poly1305_state, b.block0);
+
+	poly1305_update(&poly1305_state, ad, ad_len);
+	poly1305_update(&poly1305_state, pad0, (0x10 - ad_len) & 0xf);
+
+	chacha20(&chacha20_state, dst, src, src_len);
+
+	poly1305_update(&poly1305_state, dst, src_len);
+	poly1305_update(&poly1305_state, pad0, (0x10 - src_len) & 0xf);
+
+	b.lens[0] = cpu_to_le64(ad_len);
+	b.lens[1] = cpu_to_le64(src_len);
+	poly1305_update(&poly1305_state, (uint8_t *)b.lens, sizeof(b.lens));
+
+	poly1305_final(&poly1305_state, dst + src_len);
+
+	explicit_bzero(&chacha20_state, sizeof(chacha20_state));
+	explicit_bzero(&b, sizeof(b));
+}
+
+bool
+chacha20poly1305_decrypt(uint8_t *dst, const uint8_t *src, const size_t src_len,
+			 const uint8_t *ad, const size_t ad_len,
+			 const uint64_t nonce,
+			 const uint8_t key[CHACHA20POLY1305_KEY_SIZE])
+{
+	struct poly1305_ctx poly1305_state;
+	struct chacha20_ctx chacha20_state;
+	bool ret;
+	size_t dst_len;
+	union {
+		uint8_t block0[POLY1305_KEY_SIZE];
+		uint8_t mac[POLY1305_MAC_SIZE];
+		uint64_t lens[2];
+	} b = { { 0 } };
+
+	if (src_len < POLY1305_MAC_SIZE)
+		return false;
+
+	chacha20_init(&chacha20_state, key, nonce);
+	chacha20(&chacha20_state, b.block0, b.block0, sizeof(b.block0));
+	poly1305_init(&poly1305_state, b.block0);
+
+	poly1305_update(&poly1305_state, ad, ad_len);
+	poly1305_update(&poly1305_state, pad0, (0x10 - ad_len) & 0xf);
+
+	dst_len = src_len - POLY1305_MAC_SIZE;
+	poly1305_update(&poly1305_state, src, dst_len);
+	poly1305_update(&poly1305_state, pad0, (0x10 - dst_len) & 0xf);
+
+	b.lens[0] = cpu_to_le64(ad_len);
+	b.lens[1] = cpu_to_le64(dst_len);
+	poly1305_update(&poly1305_state, (uint8_t *)b.lens, sizeof(b.lens));
+
+	poly1305_final(&poly1305_state, b.mac);
+
+	ret = timingsafe_bcmp(b.mac, src + dst_len, POLY1305_MAC_SIZE) == 0;
+	if (ret)
+		chacha20(&chacha20_state, dst, src, dst_len);
+
+	explicit_bzero(&chacha20_state, sizeof(chacha20_state));
+	explicit_bzero(&b, sizeof(b));
+
+	return ret;
+}
+
+void
+xchacha20poly1305_encrypt(uint8_t *dst, const uint8_t *src,
+			  const size_t src_len, const uint8_t *ad,
+			  const size_t ad_len,
+			  const uint8_t nonce[XCHACHA20POLY1305_NONCE_SIZE],
+			  const uint8_t key[CHACHA20POLY1305_KEY_SIZE])
+{
+	uint32_t derived_key[CHACHA20_KEY_WORDS];
+
+	hchacha20(derived_key, nonce, key);
+	cpu_to_le32_array(derived_key, ARRAY_SIZE(derived_key));
+	chacha20poly1305_encrypt(dst, src, src_len, ad, ad_len,
+				 get_unaligned_le64(nonce + 16),
+				 (uint8_t *)derived_key);
+	explicit_bzero(derived_key, CHACHA20POLY1305_KEY_SIZE);
+}
+
+bool
+xchacha20poly1305_decrypt(uint8_t *dst, const uint8_t *src,
+			  const size_t src_len,  const uint8_t *ad,
+			  const size_t ad_len,
+			  const uint8_t nonce[XCHACHA20POLY1305_NONCE_SIZE],
+			  const uint8_t key[CHACHA20POLY1305_KEY_SIZE])
+{
+	bool ret;
+	uint32_t derived_key[CHACHA20_KEY_WORDS];
+
+	hchacha20(derived_key, nonce, key);
+	cpu_to_le32_array(derived_key, ARRAY_SIZE(derived_key));
+	ret = chacha20poly1305_decrypt(dst, src, src_len, ad, ad_len,
+				       get_unaligned_le64(nonce + 16),
+				       (uint8_t *)derived_key);
+	explicit_bzero(derived_key, CHACHA20POLY1305_KEY_SIZE);
+	return ret;
+}
+
+
+static const uint32_t blake2s_iv[8] = {
+	0x6A09E667UL, 0xBB67AE85UL, 0x3C6EF372UL, 0xA54FF53AUL,
+	0x510E527FUL, 0x9B05688CUL, 0x1F83D9ABUL, 0x5BE0CD19UL
+};
+
+static const uint8_t blake2s_sigma[10][16] = {
+	{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 },
+	{ 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 },
+	{ 11, 8, 12, 0, 5, 2, 15, 13, 10, 14, 3, 6, 7, 1, 9, 4 },
+	{ 7, 9, 3, 1, 13, 12, 11, 14, 2, 6, 5, 10, 4, 0, 15, 8 },
+	{ 9, 0, 5, 7, 2, 4, 10, 15, 14, 1, 11, 12, 6, 8, 3, 13 },
+	{ 2, 12, 6, 10, 0, 11, 8, 3, 4, 13, 7, 5, 15, 14, 1, 9 },
+	{ 12, 5, 1, 15, 14, 13, 4, 10, 0, 7, 6, 3, 9, 2, 8, 11 },
+	{ 13, 11, 7, 14, 12, 1, 3, 9, 5, 0, 15, 4, 8, 6, 2, 10 },
+	{ 6, 15, 14, 9, 11, 3, 0, 8, 12, 2, 13, 7, 1, 4, 10, 5 },
+	{ 10, 2, 8, 4, 7, 6, 1, 5, 15, 11, 9, 14, 3, 12, 13, 0 },
+};
+
+static inline void blake2s_set_lastblock(struct blake2s_state *state)
+{
+	state->f[0] = -1;
+}
+
+static inline void blake2s_increment_counter(struct blake2s_state *state,
+					     const uint32_t inc)
+{
+	state->t[0] += inc;
+	state->t[1] += (state->t[0] < inc);
+}
+
+static inline void blake2s_init_param(struct blake2s_state *state,
+				      const uint32_t param)
+{
+	int i;
+
+	memset(state, 0, sizeof(*state));
+	for (i = 0; i < 8; ++i)
+		state->h[i] = blake2s_iv[i];
+	state->h[0] ^= param;
+}
+
+void blake2s_init(struct blake2s_state *state, const size_t outlen)
+{
+	blake2s_init_param(state, 0x01010000 | outlen);
+	state->outlen = outlen;
+}
+
+void blake2s_init_key(struct blake2s_state *state, const size_t outlen,
+		      const uint8_t *key, const size_t keylen)
+{
+	uint8_t block[BLAKE2S_BLOCK_SIZE] = { 0 };
+
+	blake2s_init_param(state, 0x01010000 | keylen << 8 | outlen);
+	state->outlen = outlen;
+	memcpy(block, key, keylen);
+	blake2s_update(state, block, BLAKE2S_BLOCK_SIZE);
+	explicit_bzero(block, BLAKE2S_BLOCK_SIZE);
+}
+
+static inline void blake2s_compress(struct blake2s_state *state,
+				    const uint8_t *block, size_t nblocks,
+				    const uint32_t inc)
+{
+	uint32_t m[16];
+	uint32_t v[16];
+	int i;
+
+	while (nblocks > 0) {
+		blake2s_increment_counter(state, inc);
+		memcpy(m, block, BLAKE2S_BLOCK_SIZE);
+		le32_to_cpu_array(m, ARRAY_SIZE(m));
+		memcpy(v, state->h, 32);
+		v[ 8] = blake2s_iv[0];
+		v[ 9] = blake2s_iv[1];
+		v[10] = blake2s_iv[2];
+		v[11] = blake2s_iv[3];
+		v[12] = blake2s_iv[4] ^ state->t[0];
+		v[13] = blake2s_iv[5] ^ state->t[1];
+		v[14] = blake2s_iv[6] ^ state->f[0];
+		v[15] = blake2s_iv[7] ^ state->f[1];
+
+#define G(r, i, a, b, c, d) do { \
+	a += b + m[blake2s_sigma[r][2 * i + 0]]; \
+	d = ror32(d ^ a, 16); \
+	c += d; \
+	b = ror32(b ^ c, 12); \
+	a += b + m[blake2s_sigma[r][2 * i + 1]]; \
+	d = ror32(d ^ a, 8); \
+	c += d; \
+	b = ror32(b ^ c, 7); \
+} while (0)
+
+#define ROUND(r) do { \
+	G(r, 0, v[0], v[ 4], v[ 8], v[12]); \
+	G(r, 1, v[1], v[ 5], v[ 9], v[13]); \
+	G(r, 2, v[2], v[ 6], v[10], v[14]); \
+	G(r, 3, v[3], v[ 7], v[11], v[15]); \
+	G(r, 4, v[0], v[ 5], v[10], v[15]); \
+	G(r, 5, v[1], v[ 6], v[11], v[12]); \
+	G(r, 6, v[2], v[ 7], v[ 8], v[13]); \
+	G(r, 7, v[3], v[ 4], v[ 9], v[14]); \
+} while (0)
+		ROUND(0);
+		ROUND(1);
+		ROUND(2);
+		ROUND(3);
+		ROUND(4);
+		ROUND(5);
+		ROUND(6);
+		ROUND(7);
+		ROUND(8);
+		ROUND(9);
+
+#undef G
+#undef ROUND
+
+		for (i = 0; i < 8; ++i)
+			state->h[i] ^= v[i] ^ v[i + 8];
+
+		block += BLAKE2S_BLOCK_SIZE;
+		--nblocks;
+	}
+}
+
+void blake2s_update(struct blake2s_state *state, const uint8_t *in, size_t inlen)
+{
+	const size_t fill = BLAKE2S_BLOCK_SIZE - state->buflen;
+
+	if (!inlen)
+		return;
+	if (inlen > fill) {
+		memcpy(state->buf + state->buflen, in, fill);
+		blake2s_compress(state, state->buf, 1, BLAKE2S_BLOCK_SIZE);
+		state->buflen = 0;
+		in += fill;
+		inlen -= fill;
+	}
+	if (inlen > BLAKE2S_BLOCK_SIZE) {
+		const size_t nblocks = DIV_ROUND_UP(inlen, BLAKE2S_BLOCK_SIZE);
+		/* Hash one less (full) block than strictly possible */
+		blake2s_compress(state, in, nblocks - 1, BLAKE2S_BLOCK_SIZE);
+		in += BLAKE2S_BLOCK_SIZE * (nblocks - 1);
+		inlen -= BLAKE2S_BLOCK_SIZE * (nblocks - 1);
+	}
+	memcpy(state->buf + state->buflen, in, inlen);
+	state->buflen += inlen;
+}
+
+void blake2s_final(struct blake2s_state *state, uint8_t *out)
+{
+	blake2s_set_lastblock(state);
+	memset(state->buf + state->buflen, 0,
+	       BLAKE2S_BLOCK_SIZE - state->buflen); /* Padding */
+	blake2s_compress(state, state->buf, 1, state->buflen);
+	cpu_to_le32_array(state->h, ARRAY_SIZE(state->h));
+	memcpy(out, state->h, state->outlen);
+	explicit_bzero(state, sizeof(*state));
+}
+
+void blake2s(uint8_t *out, const uint8_t *in, const uint8_t *key,
+	     const size_t outlen, const size_t inlen, const size_t keylen)
+{
+	struct blake2s_state state;
+
+	if (keylen)
+		blake2s_init_key(&state, outlen, key, keylen);
+	else
+		blake2s_init(&state, outlen);
+
+	blake2s_update(&state, in, inlen);
+	blake2s_final(&state, out);
+}
+
+void blake2s_hmac(uint8_t *out, const uint8_t *in, const uint8_t *key, const size_t outlen,
+		  const size_t inlen, const size_t keylen)
+{
+	struct blake2s_state state;
+	uint8_t x_key[BLAKE2S_BLOCK_SIZE] __aligned(sizeof(uint32_t)) = { 0 };
+	uint8_t i_hash[BLAKE2S_HASH_SIZE] __aligned(sizeof(uint32_t));
+	int i;
+
+	if (keylen > BLAKE2S_BLOCK_SIZE) {
+		blake2s_init(&state, BLAKE2S_HASH_SIZE);
+		blake2s_update(&state, key, keylen);
+		blake2s_final(&state, x_key);
+	} else
+		memcpy(x_key, key, keylen);
+
+	for (i = 0; i < BLAKE2S_BLOCK_SIZE; ++i)
+		x_key[i] ^= 0x36;
+
+	blake2s_init(&state, BLAKE2S_HASH_SIZE);
+	blake2s_update(&state, x_key, BLAKE2S_BLOCK_SIZE);
+	blake2s_update(&state, in, inlen);
+	blake2s_final(&state, i_hash);
+
+	for (i = 0; i < BLAKE2S_BLOCK_SIZE; ++i)
+		x_key[i] ^= 0x5c ^ 0x36;
+
+	blake2s_init(&state, BLAKE2S_HASH_SIZE);
+	blake2s_update(&state, x_key, BLAKE2S_BLOCK_SIZE);
+	blake2s_update(&state, i_hash, BLAKE2S_HASH_SIZE);
+	blake2s_final(&state, i_hash);
+
+	memcpy(out, i_hash, outlen);
+	explicit_bzero(x_key, BLAKE2S_BLOCK_SIZE);
+	explicit_bzero(i_hash, BLAKE2S_HASH_SIZE);
+}
+
+
+/* Below here is fiat's implementation of x25519.
+ *
+ * Copyright (C) 2015-2016 The fiat-crypto Authors.
+ * Copyright (C) 2018-2021 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ *
+ * This is a machine-generated formally verified implementation of Curve25519
+ * ECDH from: <https://github.com/mit-plv/fiat-crypto>. Though originally
+ * machine generated, it has been tweaked to be suitable for use in the kernel.
+ * It is optimized for 32-bit machines and machines that cannot work efficiently
+ * with 128-bit integer types.
+ */
+
+/* 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;
+
+static inline void fe_frombytes_impl(uint32_t h[10], const uint8_t *s)
+{
+	/* Ignores top bit of s. */
+	uint32_t a0 = get_unaligned_le32(s);
+	uint32_t a1 = get_unaligned_le32(s+4);
+	uint32_t a2 = get_unaligned_le32(s+8);
+	uint32_t a3 = get_unaligned_le32(s+12);
+	uint32_t a4 = get_unaligned_le32(s+16);
+	uint32_t a5 = get_unaligned_le32(s+20);
+	uint32_t a6 = get_unaligned_le32(s+24);
+	uint32_t a7 = get_unaligned_le32(s+28);
+	h[0] = a0&((1<<26)-1);                    /* 26 used, 32-26 left.   26 */
+	h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 =  6+19 = 25 */
+	h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
+	h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) +  6 = 19+ 6 = 25 */
+	h[4] = (a3>> 6);                          /* (32- 6)              = 26 */
+	h[5] = a4&((1<<25)-1);                    /*                        25 */
+	h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 =  7+19 = 26 */
+	h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
+	h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) +  6 = 20+ 6 = 26 */
+	h[9] = (a7>> 6)&((1<<25)-1); /*                                     25 */
+}
+
+static inline void fe_frombytes(fe *h, const uint8_t *s)
+{
+	fe_frombytes_impl(h->v, s);
+}
+
+static inline uint8_t /*bool*/
+addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
+{
+	/* This function extracts 25 bits of result and 1 bit of carry
+	 * (26 total), so a 32-bit intermediate is sufficient.
+	 */
+	uint32_t x = a + b + c;
+	*low = x & ((1 << 25) - 1);
+	return (x >> 25) & 1;
+}
+
+static inline uint8_t /*bool*/
+addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
+{
+	/* This function extracts 26 bits of result and 1 bit of carry
+	 * (27 total), so a 32-bit intermediate is sufficient.
+	 */
+	uint32_t x = a + b + c;
+	*low = x & ((1 << 26) - 1);
+	return (x >> 26) & 1;
+}
+
+static inline uint8_t /*bool*/
+subborrow_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
+{
+	/* This function extracts 25 bits of result and 1 bit of borrow
+	 * (26 total), so a 32-bit intermediate is sufficient.
+	 */
+	uint32_t x = a - b - c;
+	*low = x & ((1 << 25) - 1);
+	return x >> 31;
+}
+
+static inline uint8_t /*bool*/
+subborrow_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
+{
+	/* This function extracts 26 bits of result and 1 bit of borrow
+	 *(27 total), so a 32-bit intermediate is sufficient.
+	 */
+	uint32_t x = a - b - c;
+	*low = x & ((1 << 26) - 1);
+	return x >> 31;
+}
+
+static inline uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz)
+{
+	t = -!!t; /* all set if nonzero, 0 if 0 */
+	return (t&nz) | ((~t)&z);
+}
+
+static inline void fe_freeze(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];
+	uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
+	uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
+	uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
+	uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
+	uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
+	uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
+	uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
+	uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
+	uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
+	uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
+	uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff);
+	uint32_t x50 = (x49 & 0x3ffffed);
+	uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
+	uint32_t x54 = (x49 & 0x1ffffff);
+	uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
+	uint32_t x58 = (x49 & 0x3ffffff);
+	uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
+	uint32_t x62 = (x49 & 0x1ffffff);
+	uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
+	uint32_t x66 = (x49 & 0x3ffffff);
+	uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
+	uint32_t x70 = (x49 & 0x1ffffff);
+	uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
+	uint32_t x74 = (x49 & 0x3ffffff);
+	uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
+	uint32_t x78 = (x49 & 0x1ffffff);
+	uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
+	uint32_t x82 = (x49 & 0x3ffffff);
+	uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
+	uint32_t x86 = (x49 & 0x1ffffff);
+	uint32_t x88; addcarryx_u25(x85, x47, x86, &x88);
+	out[0] = x52;
+	out[1] = x56;
+	out[2] = x60;
+	out[3] = x64;
+	out[4] = x68;
+	out[5] = x72;
+	out[6] = x76;
+	out[7] = x80;
+	out[8] = x84;
+	out[9] = x88;
+}
+
+static inline void fe_tobytes(uint8_t s[32], const fe *f)
+{
+	uint32_t h[10];
+	fe_freeze(h, f->v);
+	s[0] = h[0] >> 0;
+	s[1] = h[0] >> 8;
+	s[2] = h[0] >> 16;
+	s[3] = (h[0] >> 24) | (h[1] << 2);
+	s[4] = h[1] >> 6;
+	s[5] = h[1] >> 14;
+	s[6] = (h[1] >> 22) | (h[2] << 3);
+	s[7] = h[2] >> 5;
+	s[8] = h[2] >> 13;
+	s[9] = (h[2] >> 21) | (h[3] << 5);
+	s[10] = h[3] >> 3;
+	s[11] = h[3] >> 11;
+	s[12] = (h[3] >> 19) | (h[4] << 6);
+	s[13] = h[4] >> 2;
+	s[14] = h[4] >> 10;
+	s[15] = h[4] >> 18;
+	s[16] = h[5] >> 0;
+	s[17] = h[5] >> 8;
+	s[18] = h[5] >> 16;
+	s[19] = (h[5] >> 24) | (h[6] << 1);
+	s[20] = h[6] >> 7;
+	s[21] = h[6] >> 15;
+	s[22] = (h[6] >> 23) | (h[7] << 3);
+	s[23] = h[7] >> 5;
+	s[24] = h[7] >> 13;
+	s[25] = (h[7] >> 21) | (h[8] << 4);
+	s[26] = h[8] >> 4;
+	s[27] = h[8] >> 12;
+	s[28] = (h[8] >> 20) | (h[9] << 6);
+	s[29] = h[9] >> 2;
+	s[30] = h[9] >> 10;
+	s[31] = h[9] >> 18;
+}
+
+/* h = f */
+static inline void fe_copy(fe *h, const fe *f)
+{
+	memmove(h, f, sizeof(uint32_t) * 10);
+}
+
+static inline void fe_copy_lt(fe_loose *h, const fe *f)
+{
+	memmove(h, f, sizeof(uint32_t) * 10);
+}
+
+/* h = 0 */
+static inline void fe_0(fe *h)
+{
+	memset(h, 0, sizeof(uint32_t) * 10);
+}
+
+/* h = 1 */
+static inline void fe_1(fe *h)
+{
+	memset(h, 0, sizeof(uint32_t) * 10);
+	h->v[0] = 1;
+}
+
+static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[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 = in2[9];
+	const uint32_t x39 = in2[8];
+	const uint32_t x37 = in2[7];
+	const uint32_t x35 = in2[6];
+	const uint32_t x33 = in2[5];
+	const uint32_t x31 = in2[4];
+	const uint32_t x29 = in2[3];
+	const uint32_t x27 = in2[2];
+	const uint32_t x25 = in2[1];
+	const uint32_t x23 = in2[0];
+	out[0] = (x5 + x23);
+	out[1] = (x7 + x25);
+	out[2] = (x9 + x27);
+	out[3] = (x11 + x29);
+	out[4] = (x13 + x31);
+	out[5] = (x15 + x33);
+	out[6] = (x17 + x35);
+	out[7] = (x19 + x37);
+	out[8] = (x21 + x39);
+	out[9] = (x20 + x38);
+}
+
+/* h = f + g
+ * Can overlap h with f or g.
+ */
+static inline void fe_add(fe_loose *h, const fe *f, const fe *g)
+{
+	fe_add_impl(h->v, f->v, g->v);
+}
+
+static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[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 = in2[9];
+	const uint32_t x39 = in2[8];
+	const uint32_t x37 = in2[7];
+	const uint32_t x35 = in2[6];
+	const uint32_t x33 = in2[5];
+	const uint32_t x31 = in2[4];
+	const uint32_t x29 = in2[3];
+	const uint32_t x27 = in2[2];
+	const uint32_t x25 = in2[1];
+	const uint32_t x23 = in2[0];
+	out[0] = ((0x7ffffda + x5) - x23);
+	out[1] = ((0x3fffffe + x7) - x25);
+	out[2] = ((0x7fffffe + x9) - x27);
+	out[3] = ((0x3fffffe + x11) - x29);
+	out[4] = ((0x7fffffe + x13) - x31);
+	out[5] = ((0x3fffffe + x15) - x33);
+	out[6] = ((0x7fffffe + x17) - x35);
+	out[7] = ((0x3fffffe + x19) - x37);
+	out[8] = ((0x7fffffe + x21) - x39);
+	out[9] = ((0x3fffffe + x20) - x38);
+}
+
+/* h = f - g
+ * Can overlap h with f or g.
+ */
+static inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
+{
+	fe_sub_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[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 = in2[9];
+	const uint32_t x39 = in2[8];
+	const uint32_t x37 = in2[7];
+	const uint32_t x35 = in2[6];
+	const uint32_t x33 = in2[5];
+	const uint32_t x31 = in2[4];
+	const uint32_t x29 = in2[3];
+	const uint32_t x27 = in2[2];
+	const uint32_t x25 = in2[1];
+	const uint32_t x23 = in2[0];
+	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 inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
+{
+	fe_mul_impl(h->v, f->v, g->v);
+}
+
+static inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
+{
+	fe_mul_impl(h->v, f->v, g->v);
+}
+
+static inline 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_sqr_impl(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 inline void fe_sq_tl(fe *h, const fe_loose *f)
+{
+	fe_sqr_impl(h->v, f->v);
+}
+
+static inline void fe_sq_tt(fe *h, const fe *f)
+{
+	fe_sqr_impl(h->v, f->v);
+}
+
+static inline 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 inline void fe_invert(fe *out, const fe *z)
+{
+	fe_loose l;
+	fe_copy_lt(&l, z);
+	fe_loose_invert(out, &l);
+}
+
+/* Replace (f,g) with (g,f) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
+ *
+ * Preconditions: b in {0,1}
+ */
+static inline void fe_cswap(fe *f, fe *g, unsigned int b)
+{
+	unsigned 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;
+	}
+}
+
+/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
+static inline void fe_mul_121666_impl(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 inline void fe_mul121666(fe *h, const fe_loose *f)
+{
+	fe_mul_121666_impl(h->v, f->v);
+}
+
+static const uint8_t curve25519_null_point[CURVE25519_KEY_SIZE];
+
+bool curve25519(uint8_t out[CURVE25519_KEY_SIZE],
+		const uint8_t scalar[CURVE25519_KEY_SIZE],
+		const uint8_t point[CURVE25519_KEY_SIZE])
+{
+	fe x1, x2, z2, x3, z3;
+	fe_loose x2l, z2l, x3l;
+	unsigned swap = 0;
+	int pos;
+	uint8_t e[32];
+
+	memcpy(e, scalar, 32);
+	curve25519_clamp_secret(e);
+
+	/* The following implementation was transcribed to Coq and proven to
+	 * correspond to unary scalar multiplication in affine coordinates given
+	 * that x1 != 0 is the x coordinate of some point on the curve. It was
+	 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives
+	 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was
+	 * quantified over the underlying field, so it applies to Curve25519
+	 * itself and the quadratic twist of Curve25519. It was not proven in
+	 * Coq that prime-field arithmetic correctly simulates extension-field
+	 * arithmetic on prime-field values. The decoding of the byte array
+	 * representation of e was not considered.
+	 *
+	 * Specification of Montgomery curves in affine coordinates:
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
+	 *
+	 * Proof that these form a group that is isomorphic to a Weierstrass
+	 * curve:
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
+	 *
+	 * Coq transcription and correctness proof of the loop
+	 * (where scalarbits=255):
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
+	 * preconditions: 0 <= e < 2^255 (not necessarily e < order),
+	 * fe_invert(0) = 0
+	 */
+	fe_frombytes(&x1, point);
+	fe_1(&x2);
+	fe_0(&z2);
+	fe_copy(&x3, &x1);
+	fe_1(&z3);
+
+	for (pos = 254; pos >= 0; --pos) {
+		fe tmp0, tmp1;
+		fe_loose tmp0l, tmp1l;
+		/* loop invariant as of right before the test, for the case
+		 * where x1 != 0:
+		 *   pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3
+		 *   is nonzero
+		 *   let r := e >> (pos+1) in the following equalities of
+		 *   projective points:
+		 *   to_xz (r*P)     === if swap then (x3, z3) else (x2, z2)
+		 *   to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
+		 *   x1 is the nonzero x coordinate of the nonzero
+		 *   point (r*P-(r+1)*P)
+		 */
+		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+		swap ^= b;
+		fe_cswap(&x2, &x3, swap);
+		fe_cswap(&z2, &z3, swap);
+		swap = b;
+		/* Coq transcription of ladderstep formula (called from
+		 * transcribed loop):
+		 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
+		 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
+		 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
+		 * x1  = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
+		 */
+		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_mul121666(&z3, &tmp1l);
+		fe_sq_tl(&x3, &x3l);
+		fe_add(&tmp0l, &tmp0, &z3);
+		fe_mul_ttt(&z3, &x1, &z2);
+		fe_mul_tll(&z2, &tmp1l, &tmp0l);
+	}
+	/* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3)
+	 * else (x2, z2)
+	 */
+	fe_cswap(&x2, &x3, swap);
+	fe_cswap(&z2, &z3, swap);
+
+	fe_invert(&z2, &z2);
+	fe_mul_ttt(&x2, &x2, &z2);
+	fe_tobytes(out, &x2);
+
+	explicit_bzero(&x1, sizeof(x1));
+	explicit_bzero(&x2, sizeof(x2));
+	explicit_bzero(&z2, sizeof(z2));
+	explicit_bzero(&x3, sizeof(x3));
+	explicit_bzero(&z3, sizeof(z3));
+	explicit_bzero(&x2l, sizeof(x2l));
+	explicit_bzero(&z2l, sizeof(z2l));
+	explicit_bzero(&x3l, sizeof(x3l));
+	explicit_bzero(&e, sizeof(e));
+
+	return timingsafe_bcmp(out, curve25519_null_point, CURVE25519_KEY_SIZE) != 0;
+}