From 045a0ffe358b81609e5b93e1f02e948b581304a3 Mon Sep 17 00:00:00 2001 From: Matt Braithwaite Date: Mon, 18 Apr 2016 11:30:19 -0700 Subject: [PATCH] Import `newhope' (post-quantum key exchange). This derives from the reference implementation: Source: https://github.com/tpoeppelmann/newhope/tree/master/ref at bc06c1ac Paper: https://eprint.iacr.org/2015/1092 However, it does not interoperate, due to the replacement of SHAKE-128 with AES-CTR (for polynomial generation) and the replacement of SHA-3 with SHA-256 (for key whitening). Change-Id: I6a55507aea85331245e2fbd41bae5cc049fdca3c Reviewed-on: https://boringssl-review.googlesource.com/7690 Reviewed-by: Adam Langley --- .clang-format | 3 + crypto/CMakeLists.txt | 2 + crypto/newhope/CMakeLists.txt | 22 +++ crypto/newhope/error_correction.c | 134 +++++++++++++ crypto/newhope/internal.h | 95 ++++++++++ crypto/newhope/newhope.c | 156 +++++++++++++++ crypto/newhope/newhope_test.c | 144 ++++++++++++++ crypto/newhope/ntt.c | 148 +++++++++++++++ crypto/newhope/poly.c | 184 ++++++++++++++++++ crypto/newhope/precomp.c | 306 ++++++++++++++++++++++++++++++ crypto/newhope/reduce.c | 42 ++++ include/openssl/base.h | 1 + include/openssl/newhope.h | 78 ++++++++ tool/speed.cc | 33 +++- util/all_tests.json | 3 +- util/doc.config | 1 + 16 files changed, 1350 insertions(+), 2 deletions(-) create mode 100644 crypto/newhope/CMakeLists.txt create mode 100644 crypto/newhope/error_correction.c create mode 100644 crypto/newhope/internal.h create mode 100644 crypto/newhope/newhope.c create mode 100644 crypto/newhope/newhope_test.c create mode 100644 crypto/newhope/ntt.c create mode 100644 crypto/newhope/poly.c create mode 100644 crypto/newhope/precomp.c create mode 100644 crypto/newhope/reduce.c create mode 100644 include/openssl/newhope.h diff --git a/.clang-format b/.clang-format index 43032d44..5865a706 100644 --- a/.clang-format +++ b/.clang-format @@ -2,3 +2,6 @@ BasedOnStyle: Google MaxEmptyLinesToKeep: 3 AllowShortIfStatementsOnASingleLine: false AllowShortLoopsOnASingleLine: false +DerivePointerAlignment: false +PointerAlignment: Right + diff --git a/crypto/CMakeLists.txt b/crypto/CMakeLists.txt index 7a6b5914..277a0ef9 100644 --- a/crypto/CMakeLists.txt +++ b/crypto/CMakeLists.txt @@ -74,6 +74,7 @@ add_subdirectory(conf) add_subdirectory(chacha) add_subdirectory(poly1305) add_subdirectory(curve25519) +add_subdirectory(newhope) # Level 1, depends only on 0.* add_subdirectory(digest) @@ -167,6 +168,7 @@ add_library( $ $ $ + $ ) if(NOT MSVC AND NOT ANDROID) diff --git a/crypto/newhope/CMakeLists.txt b/crypto/newhope/CMakeLists.txt new file mode 100644 index 00000000..385cd6a7 --- /dev/null +++ b/crypto/newhope/CMakeLists.txt @@ -0,0 +1,22 @@ +add_library( + newhope + + OBJECT + + error_correction.c + newhope.c + ntt.c + poly.c + precomp.c + reduce.c +) + +add_executable( + newhope_test + + newhope_test.c + $ +) + +target_link_libraries(newhope_test crypto) +add_dependencies(all_tests newhope_test) diff --git a/crypto/newhope/error_correction.c b/crypto/newhope/error_correction.c new file mode 100644 index 00000000..e4ac1c26 --- /dev/null +++ b/crypto/newhope/error_correction.c @@ -0,0 +1,134 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 + +#include +#include + +#include "internal.h" + + +/* See paper for details on the error reconciliation */ + +static int32_t abs_32(int32_t v) { + int32_t mask = v >> 31; + return (v ^ mask) - mask; +} + +static int32_t f(int32_t* v0, int32_t* v1, int32_t x) { + int32_t xit, t, r, b; + + /* Next 6 lines compute t = x/PARAM_Q */ + b = x * 2730; + t = b >> 25; + b = x - t * 12289; + b = 12288 - b; + b >>= 31; + t -= b; + + r = t & 1; + xit = (t >> 1); + *v0 = xit + r; /* v0 = round(x/(2*PARAM_Q)) */ + + t -= 1; + r = t & 1; + *v1 = (t >> 1) + r; + + return abs_32(x - ((*v0) * 2 * PARAM_Q)); +} + +static int32_t g(int32_t x) { + int32_t t, c, b; + + /* Next 6 lines compute t = x/(4*PARAM_Q); */ + b = x * 2730; + t = b >> 27; + b = x - t * 49156; + b = 49155 - b; + b >>= 31; + t -= b; + + c = t & 1; + t = (t >> 1) + c; /* t = round(x/(8*PARAM_Q)) */ + + t *= 8 * PARAM_Q; + + return abs_32(t - x); +} + +static int16_t LDDecode(int32_t xi0, int32_t xi1, int32_t xi2, int32_t xi3) { + int32_t t; + + t = g(xi0); + t += g(xi1); + t += g(xi2); + t += g(xi3); + + t -= 8 * PARAM_Q; + t >>= 31; + return t & 1; +} + +void newhope_helprec(NEWHOPE_POLY* c, const NEWHOPE_POLY* v) { + int32_t v0[4], v1[4], v_tmp[4], k; + uint8_t rbit; + uint8_t rand[32]; + unsigned i; + + /* The reference implementation calls ChaCha20 here. */ + RAND_bytes(rand, sizeof(rand)); + + for (i = 0; i < 256; i++) { + rbit = (rand[i >> 3] >> (i & 7)) & 1; + + k = f(v0 + 0, v1 + 0, 8 * v->coeffs[0 + i] + 4 * rbit); + k += f(v0 + 1, v1 + 1, 8 * v->coeffs[256 + i] + 4 * rbit); + k += f(v0 + 2, v1 + 2, 8 * v->coeffs[512 + i] + 4 * rbit); + k += f(v0 + 3, v1 + 3, 8 * v->coeffs[768 + i] + 4 * rbit); + + k = (2 * PARAM_Q - 1 - k) >> 31; + + v_tmp[0] = ((~k) & v0[0]) ^ (k & v1[0]); + v_tmp[1] = ((~k) & v0[1]) ^ (k & v1[1]); + v_tmp[2] = ((~k) & v0[2]) ^ (k & v1[2]); + v_tmp[3] = ((~k) & v0[3]) ^ (k & v1[3]); + + c->coeffs[0 + i] = (v_tmp[0] - v_tmp[3]) & 3; + c->coeffs[256 + i] = (v_tmp[1] - v_tmp[3]) & 3; + c->coeffs[512 + i] = (v_tmp[2] - v_tmp[3]) & 3; + c->coeffs[768 + i] = (-k + 2 * v_tmp[3]) & 3; + } +} + +void newhope_reconcile(uint8_t* key, const NEWHOPE_POLY* v, + const NEWHOPE_POLY* c) { + int i; + int32_t tmp[4]; + + memset(key, 0, KEY_LENGTH); + + for (i = 0; i < 256; i++) { + tmp[0] = 16 * PARAM_Q + 8 * (int32_t)v->coeffs[0 + i] - + PARAM_Q * (2 * c->coeffs[0 + i] + c->coeffs[768 + i]); + tmp[1] = 16 * PARAM_Q + 8 * (int32_t)v->coeffs[256 + i] - + PARAM_Q * (2 * c->coeffs[256 + i] + c->coeffs[768 + i]); + tmp[2] = 16 * PARAM_Q + 8 * (int32_t)v->coeffs[512 + i] - + PARAM_Q * (2 * c->coeffs[512 + i] + c->coeffs[768 + i]); + tmp[3] = 16 * PARAM_Q + 8 * (int32_t)v->coeffs[768 + i] - + PARAM_Q * (c->coeffs[768 + i]); + + key[i >> 3] |= LDDecode(tmp[0], tmp[1], tmp[2], tmp[3]) << (i & 7); + } +} diff --git a/crypto/newhope/internal.h b/crypto/newhope/internal.h new file mode 100644 index 00000000..a5473d8e --- /dev/null +++ b/crypto/newhope/internal.h @@ -0,0 +1,95 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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. */ + +#ifndef OPENSSL_HEADER_NEWHOPE_INTERNAL_H +#define OPENSSL_HEADER_NEWHOPE_INTERNAL_H + +#include +#include + +#include "../internal.h" + + +/* The number of polynomial coefficients. */ +#define PARAM_N 1024 + +/* The width the noise distribution. */ +#define PARAM_K 16 + +/* Modulus. */ +#define PARAM_Q 12289 + +/* KEY_LENGTH is the size of the result of the key agreement. This result is + * not exposed to callers: instead, it is whitened with SHA-256, whose output + * happens to be the same size. */ +#define KEY_LENGTH 32 + +/* Polynomial coefficients in unpacked form. */ +struct newhope_poly_st { + alignas(32) uint16_t coeffs[PARAM_N]; +}; + +/* The packed form is 14 bits per coefficient, or 1792 bytes. */ +#define POLY_BYTES ((1024 * 14) / 8) + +/* SEED_LENGTH is the length of the AES-CTR seed used to derive a polynomial. */ +#define SEED_LENGTH 32 + +/* newhope_poly_uniform generates the polynomial |a| using AES-CTR mode with the + * seed + * |seed|. (In the reference implementation this was done with SHAKE-128.) */ +void newhope_poly_uniform(NEWHOPE_POLY* a, const uint8_t* seed); + +/* newhope_poly_getnoise sets |r| to a random polynomial where the coefficients + * are + * sampled from the noise distribution. (In the reference implementation, this + * is given a random seed and a nonce.)*/ +void newhope_poly_getnoise(NEWHOPE_POLY* r); + +/* newhope_poly_frombytes unpacks the packed polynomial coefficients in |a| into + * |r|. */ +void newhope_poly_frombytes(NEWHOPE_POLY* r, const uint8_t* a); + +/* newhope_poly_tobytes packs the polynomial |p| into the compact representation + * |r|. */ +void newhope_poly_tobytes(uint8_t* r, const NEWHOPE_POLY* p); + +void newhope_helprec(NEWHOPE_POLY* c, const NEWHOPE_POLY* v); + +/* newhope_reconcile performs the error-reconciliation step using the input |v| + * and + * reconciliation data |c|, writing the resulting key to |key|. */ +void newhope_reconcile(uint8_t* key, const NEWHOPE_POLY* v, + const NEWHOPE_POLY* c); + +/* newhope_poly_ntt performs NTT(r) in-place. */ +void newhope_poly_ntt(NEWHOPE_POLY* r); + +/* newhope_poly_invntt performs the inverse of NTT(r) in-place. */ +void newhope_poly_invntt(NEWHOPE_POLY* r); + +void newhope_poly_add(NEWHOPE_POLY* r, const NEWHOPE_POLY* a, + const NEWHOPE_POLY* b); +void newhope_poly_pointwise(NEWHOPE_POLY* r, const NEWHOPE_POLY* a, + const NEWHOPE_POLY* b); + +uint16_t newhope_montgomery_reduce(uint32_t a); +uint16_t newhope_barrett_reduce(uint16_t a); + +void newhope_bitrev_vector(uint16_t* poly); +void newhope_mul_coefficients(uint16_t* poly, const uint16_t* factors); +void newhope_ntt(uint16_t* poly, const uint16_t* omegas); + + +#endif /* OPENSSL_HEADER_NEWHOPE_INTERNAL_H */ diff --git a/crypto/newhope/newhope.c b/crypto/newhope/newhope.c new file mode 100644 index 00000000..6399bdbf --- /dev/null +++ b/crypto/newhope/newhope.c @@ -0,0 +1,156 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 + +#include +#include + +#include "internal.h" + + +NEWHOPE_POLY *NEWHOPE_POLY_new(void) { + return (NEWHOPE_POLY *)OPENSSL_malloc(sizeof(NEWHOPE_POLY)); +} + +void NEWHOPE_POLY_free(NEWHOPE_POLY *p) { OPENSSL_free(p); } + +/* Encodes reconciliation data from |c| into |r|. */ +static void encode_rec(const NEWHOPE_POLY *c, uint8_t *r) { + int i; + for (i = 0; i < PARAM_N / 4; i++) { + r[i] = c->coeffs[4 * i] | (c->coeffs[4 * i + 1] << 2) | + (c->coeffs[4 * i + 2] << 4) | (c->coeffs[4 * i + 3] << 6); + } +} + +/* Decodes reconciliation data from |r| into |c|. */ +static void decode_rec(const uint8_t *r, NEWHOPE_POLY *c) { + int i; + for (i = 0; i < PARAM_N / 4; i++) { + c->coeffs[4 * i + 0] = r[i] & 0x03; + c->coeffs[4 * i + 1] = (r[i] >> 2) & 0x03; + c->coeffs[4 * i + 2] = (r[i] >> 4) & 0x03; + c->coeffs[4 * i + 3] = (r[i] >> 6); + } +} + +void NEWHOPE_keygen(uint8_t *servermsg, NEWHOPE_POLY *sk) { + newhope_poly_getnoise(sk); + newhope_poly_ntt(sk); + + /* The first part of the server's message is the seed, which compactly encodes + * a. */ + NEWHOPE_POLY a; + uint8_t *seed = &servermsg[POLY_BYTES]; + RAND_bytes(seed, SEED_LENGTH); + newhope_poly_uniform(&a, seed); + + NEWHOPE_POLY e; + newhope_poly_getnoise(&e); + newhope_poly_ntt(&e); + + /* The second part of the server's message is the polynomial pk = a*sk+e */ + NEWHOPE_POLY r, pk; + newhope_poly_pointwise(&r, sk, &a); + newhope_poly_add(&pk, &e, &r); + newhope_poly_tobytes(servermsg, &pk); +} + +int NEWHOPE_client_compute_key( + uint8_t key[SHA256_DIGEST_LENGTH], + uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH], + const uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH], size_t msg_len) { + if (msg_len != NEWHOPE_SERVERMSG_LENGTH) { + return 0; + } + + /* Generate the same |a| as the server, from the server's seed. */ + NEWHOPE_POLY a; + const uint8_t *seed = &servermsg[POLY_BYTES]; + newhope_poly_uniform(&a, seed); + + NEWHOPE_POLY pk; + newhope_poly_frombytes(&pk, servermsg); + + NEWHOPE_POLY sp; + newhope_poly_getnoise(&sp); + newhope_poly_ntt(&sp); + + NEWHOPE_POLY ep; + newhope_poly_getnoise(&ep); + newhope_poly_ntt(&ep); + + NEWHOPE_POLY epp; + newhope_poly_getnoise(&epp); + + /* The first part of the client's message is the polynomial bp=e'+a*s' */ + NEWHOPE_POLY bp; + newhope_poly_pointwise(&bp, &a, &sp); + newhope_poly_add(&bp, &bp, &ep); + newhope_poly_tobytes(clientmsg, &bp); + + /* v = pk * s' + e'' */ + NEWHOPE_POLY v; + newhope_poly_pointwise(&v, &pk, &sp); + newhope_poly_invntt(&v); + newhope_poly_add(&v, &v, &epp); + + /* The second part of the client's message is the reconciliation data derived + * from v. */ + NEWHOPE_POLY c; + uint8_t *reconciliation = &clientmsg[POLY_BYTES]; + newhope_helprec(&c, &v); + encode_rec(&c, reconciliation); + + uint8_t k[KEY_LENGTH]; + newhope_reconcile(k, &v, &c); + SHA256_CTX ctx; + if (!SHA256_Init(&ctx) || + !SHA256_Update(&ctx, k, KEY_LENGTH) || + !SHA256_Final(key, &ctx)) { + return 0; + } + + return 1; +} + +int NEWHOPE_server_compute_key( + uint8_t key[SHA256_DIGEST_LENGTH], const NEWHOPE_POLY *sk, + const uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH], size_t msg_len) { + if (msg_len != NEWHOPE_CLIENTMSG_LENGTH) { + return 0; + } + NEWHOPE_POLY bp; + newhope_poly_frombytes(&bp, clientmsg); + + NEWHOPE_POLY v; + newhope_poly_pointwise(&v, sk, &bp); + newhope_poly_invntt(&v); + + NEWHOPE_POLY c; + const uint8_t *reconciliation = &clientmsg[POLY_BYTES]; + decode_rec(reconciliation, &c); + + uint8_t k[KEY_LENGTH]; + newhope_reconcile(k, &v, &c); + SHA256_CTX ctx; + if (!SHA256_Init(&ctx) || + !SHA256_Update(&ctx, k, KEY_LENGTH) || + !SHA256_Final(key, &ctx)) { + return 0; + } + + return 1; +} diff --git a/crypto/newhope/newhope_test.c b/crypto/newhope/newhope_test.c new file mode 100644 index 00000000..cb0fcca0 --- /dev/null +++ b/crypto/newhope/newhope_test.c @@ -0,0 +1,144 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 +#include +#include + +#include +#include + +#include "internal.h" + + +#define NTESTS 1000 + +static int test_keys() { + NEWHOPE_POLY *sk = NEWHOPE_POLY_new(); + uint8_t server_key[SHA256_DIGEST_LENGTH], client_key[SHA256_DIGEST_LENGTH]; + uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH]; + uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH]; + int i; + + for (i = 0; i < NTESTS; i++) { + /* Alice generates a public key */ + NEWHOPE_keygen(servermsg, sk); + + /* Bob derives a secret key and creates a response */ + if (!NEWHOPE_client_compute_key(client_key, clientmsg, servermsg, + sizeof(servermsg))) { + fprintf(stderr, "ERROR client key exchange failed\n"); + return 0; + } + + /* Alice uses Bob's response to get her secret key */ + if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg, + sizeof(clientmsg))) { + fprintf(stderr, "ERROR server key exchange failed\n"); + return 0; + } + + if (memcmp(server_key, client_key, SHA256_DIGEST_LENGTH) != 0) { + fprintf(stderr, "ERROR keys did not agree\n"); + return 0; + } + } + + NEWHOPE_POLY_free(sk); + return 1; +} + +static int test_invalid_sk_a() { + NEWHOPE_POLY *sk = NEWHOPE_POLY_new(); + uint8_t server_key[SHA256_DIGEST_LENGTH], client_key[SHA256_DIGEST_LENGTH]; + uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH]; + uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH]; + int i; + + for (i = 0; i < NTESTS; i++) { + /* Alice generates a public key */ + NEWHOPE_keygen(servermsg, sk); + + /* Bob derives a secret key and creates a response */ + if (!NEWHOPE_client_compute_key(client_key, clientmsg, servermsg, + sizeof(servermsg))) { + fprintf(stderr, "ERROR client key exchange failed\n"); + return 0; + } + + /* Overwrite the secret key */ + newhope_poly_getnoise(sk); + + /* Alice uses Bob's response to get her secret key */ + if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg, + sizeof(clientmsg))) { + fprintf(stderr, "ERROR server key exchange failed\n"); + return 0; + } + + if (memcmp(server_key, client_key, SHA256_DIGEST_LENGTH) == 0) { + fprintf(stderr, "ERROR invalid sk_a\n"); + return 0; + } + } + + NEWHOPE_POLY_free(sk); + return 1; +} + +static int test_invalid_ciphertext() { + NEWHOPE_POLY *sk = NEWHOPE_POLY_new(); + uint8_t server_key[SHA256_DIGEST_LENGTH], client_key[SHA256_DIGEST_LENGTH]; + uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH]; + uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH]; + int i; + + for (i = 0; i < 10; i++) { + /* Alice generates a public key */ + NEWHOPE_keygen(servermsg, sk); + + /* Bob derives a secret key and creates a response */ + if (!NEWHOPE_client_compute_key(client_key, clientmsg, servermsg, + sizeof(servermsg))) { + fprintf(stderr, "ERROR client key exchange failed\n"); + return 0; + } + + /* Change some byte in the "ciphertext" */ + clientmsg[42] ^= 1; + + /* Alice uses Bob's response to get her secret key */ + if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg, + sizeof(clientmsg))) { + fprintf(stderr, "ERROR server key exchange failed\n"); + return 0; + } + + if (!memcmp(server_key, client_key, SHA256_DIGEST_LENGTH)) { + fprintf(stderr, "ERROR invalid clientmsg\n"); + return 0; + } + } + + NEWHOPE_POLY_free(sk); + return 1; +} + +int main() { + if (!test_keys() || !test_invalid_sk_a() || !test_invalid_ciphertext()) { + return 1; + } + printf("PASS\n"); + return 0; +} diff --git a/crypto/newhope/ntt.c b/crypto/newhope/ntt.c new file mode 100644 index 00000000..163a9d1a --- /dev/null +++ b/crypto/newhope/ntt.c @@ -0,0 +1,148 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 "internal.h" + + +static uint16_t bitrev_table[1024] = { + 0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, 192, 704, + 448, 960, 32, 544, 288, 800, 160, 672, 416, 928, 96, 608, 352, 864, + 224, 736, 480, 992, 16, 528, 272, 784, 144, 656, 400, 912, 80, 592, + 336, 848, 208, 720, 464, 976, 48, 560, 304, 816, 176, 688, 432, 944, + 112, 624, 368, 880, 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, + 392, 904, 72, 584, 328, 840, 200, 712, 456, 968, 40, 552, 296, 808, + 168, 680, 424, 936, 104, 616, 360, 872, 232, 744, 488, 1000, 24, 536, + 280, 792, 152, 664, 408, 920, 88, 600, 344, 856, 216, 728, 472, 984, + 56, 568, 312, 824, 184, 696, 440, 952, 120, 632, 376, 888, 248, 760, + 504, 1016, 4, 516, 260, 772, 132, 644, 388, 900, 68, 580, 324, 836, + 196, 708, 452, 964, 36, 548, 292, 804, 164, 676, 420, 932, 100, 612, + 356, 868, 228, 740, 484, 996, 20, 532, 276, 788, 148, 660, 404, 916, + 84, 596, 340, 852, 212, 724, 468, 980, 52, 564, 308, 820, 180, 692, + 436, 948, 116, 628, 372, 884, 244, 756, 500, 1012, 12, 524, 268, 780, + 140, 652, 396, 908, 76, 588, 332, 844, 204, 716, 460, 972, 44, 556, + 300, 812, 172, 684, 428, 940, 108, 620, 364, 876, 236, 748, 492, 1004, + 28, 540, 284, 796, 156, 668, 412, 924, 92, 604, 348, 860, 220, 732, + 476, 988, 60, 572, 316, 828, 188, 700, 444, 956, 124, 636, 380, 892, + 252, 764, 508, 1020, 2, 514, 258, 770, 130, 642, 386, 898, 66, 578, + 322, 834, 194, 706, 450, 962, 34, 546, 290, 802, 162, 674, 418, 930, + 98, 610, 354, 866, 226, 738, 482, 994, 18, 530, 274, 786, 146, 658, + 402, 914, 82, 594, 338, 850, 210, 722, 466, 978, 50, 562, 306, 818, + 178, 690, 434, 946, 114, 626, 370, 882, 242, 754, 498, 1010, 10, 522, + 266, 778, 138, 650, 394, 906, 74, 586, 330, 842, 202, 714, 458, 970, + 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362, 874, 234, 746, + 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, 90, 602, 346, 858, + 218, 730, 474, 986, 58, 570, 314, 826, 186, 698, 442, 954, 122, 634, + 378, 890, 250, 762, 506, 1018, 6, 518, 262, 774, 134, 646, 390, 902, + 70, 582, 326, 838, 198, 710, 454, 966, 38, 550, 294, 806, 166, 678, + 422, 934, 102, 614, 358, 870, 230, 742, 486, 998, 22, 534, 278, 790, + 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, 54, 566, + 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, 246, 758, 502, 1014, + 14, 526, 270, 782, 142, 654, 398, 910, 78, 590, 334, 846, 206, 718, + 462, 974, 46, 558, 302, 814, 174, 686, 430, 942, 110, 622, 366, 878, + 238, 750, 494, 1006, 30, 542, 286, 798, 158, 670, 414, 926, 94, 606, + 350, 862, 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446, 958, + 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, 129, 641, + 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, 33, 545, 289, 801, + 161, 673, 417, 929, 97, 609, 353, 865, 225, 737, 481, 993, 17, 529, + 273, 785, 145, 657, 401, 913, 81, 593, 337, 849, 209, 721, 465, 977, + 49, 561, 305, 817, 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, + 497, 1009, 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, + 201, 713, 457, 969, 41, 553, 297, 809, 169, 681, 425, 937, 105, 617, + 361, 873, 233, 745, 489, 1001, 25, 537, 281, 793, 153, 665, 409, 921, + 89, 601, 345, 857, 217, 729, 473, 985, 57, 569, 313, 825, 185, 697, + 441, 953, 121, 633, 377, 889, 249, 761, 505, 1017, 5, 517, 261, 773, + 133, 645, 389, 901, 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, + 293, 805, 165, 677, 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, + 21, 533, 277, 789, 149, 661, 405, 917, 85, 597, 341, 853, 213, 725, + 469, 981, 53, 565, 309, 821, 181, 693, 437, 949, 117, 629, 373, 885, + 245, 757, 501, 1013, 13, 525, 269, 781, 141, 653, 397, 909, 77, 589, + 333, 845, 205, 717, 461, 973, 45, 557, 301, 813, 173, 685, 429, 941, + 109, 621, 365, 877, 237, 749, 493, 1005, 29, 541, 285, 797, 157, 669, + 413, 925, 93, 605, 349, 861, 221, 733, 477, 989, 61, 573, 317, 829, + 189, 701, 445, 957, 125, 637, 381, 893, 253, 765, 509, 1021, 3, 515, + 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, 195, 707, 451, 963, + 35, 547, 291, 803, 163, 675, 419, 931, 99, 611, 355, 867, 227, 739, + 483, 995, 19, 531, 275, 787, 147, 659, 403, 915, 83, 595, 339, 851, + 211, 723, 467, 979, 51, 563, 307, 819, 179, 691, 435, 947, 115, 627, + 371, 883, 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, + 75, 587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, 171, 683, + 427, 939, 107, 619, 363, 875, 235, 747, 491, 1003, 27, 539, 283, 795, + 155, 667, 411, 923, 91, 603, 347, 859, 219, 731, 475, 987, 59, 571, + 315, 827, 187, 699, 443, 955, 123, 635, 379, 891, 251, 763, 507, 1019, + 7, 519, 263, 775, 135, 647, 391, 903, 71, 583, 327, 839, 199, 711, + 455, 967, 39, 551, 295, 807, 167, 679, 423, 935, 103, 615, 359, 871, + 231, 743, 487, 999, 23, 535, 279, 791, 151, 663, 407, 919, 87, 599, + 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, 183, 695, 439, 951, + 119, 631, 375, 887, 247, 759, 503, 1015, 15, 527, 271, 783, 143, 655, + 399, 911, 79, 591, 335, 847, 207, 719, 463, 975, 47, 559, 303, 815, + 175, 687, 431, 943, 111, 623, 367, 879, 239, 751, 495, 1007, 31, 543, + 287, 799, 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479, 991, + 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, 255, 767, + 511, 1023}; + +void newhope_bitrev_vector(uint16_t* poly) { + unsigned int i, r; + uint16_t tmp; + + for (i = 0; i < PARAM_N; i++) { + r = bitrev_table[i]; + if (i < r) { + tmp = poly[i]; + poly[i] = poly[r]; + poly[r] = tmp; + } + } +} + +void newhope_mul_coefficients(uint16_t* poly, const uint16_t* factors) { + unsigned int i; + + for (i = 0; i < PARAM_N; i++) { + poly[i] = newhope_montgomery_reduce((poly[i] * factors[i])); + } +} + +/* GS_bo_to_no; omegas need to be in Montgomery domain */ +void newhope_ntt(uint16_t* a, const uint16_t* omega) { + int i, start, j, jTwiddle, distance; + uint16_t temp, W; + + for (i = 0; i < 10; i += 2) { + /* Even level */ + distance = (1 << i); + for (start = 0; start < distance; start++) { + jTwiddle = 0; + for (j = start; j < PARAM_N - 1; j += 2 * distance) { + W = omega[jTwiddle++]; + temp = a[j]; + a[j] = (temp + a[j + distance]); /* Omit reduction (be lazy) */ + a[j + distance] = newhope_montgomery_reduce( + (W * ((uint32_t)temp + 3 * PARAM_Q - a[j + distance]))); + } + } + + /* Odd level */ + distance <<= 1; + for (start = 0; start < distance; start++) { + jTwiddle = 0; + for (j = start; j < PARAM_N - 1; j += 2 * distance) { + W = omega[jTwiddle++]; + temp = a[j]; + a[j] = newhope_barrett_reduce((temp + a[j + distance])); + a[j + distance] = newhope_montgomery_reduce( + (W * ((uint32_t)temp + 3 * PARAM_Q - a[j + distance]))); + } + } + } +} diff --git a/crypto/newhope/poly.c b/crypto/newhope/poly.c new file mode 100644 index 00000000..ce6451e4 --- /dev/null +++ b/crypto/newhope/poly.c @@ -0,0 +1,184 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 +#include + +#include +#include + +#include "internal.h" + + +extern uint16_t newhope_omegas_montgomery[]; +extern uint16_t newhope_omegas_inv_montgomery[]; + +extern uint16_t newhope_psis_bitrev_montgomery[]; +extern uint16_t newhope_psis_inv_montgomery[]; + +void newhope_poly_frombytes(NEWHOPE_POLY* r, const uint8_t* a) { + int i; + for (i = 0; i < PARAM_N / 4; i++) { + r->coeffs[4 * i + 0] = + a[7 * i + 0] | (((uint16_t)a[7 * i + 1] & 0x3f) << 8); + r->coeffs[4 * i + 1] = (a[7 * i + 1] >> 6) | + (((uint16_t)a[7 * i + 2]) << 2) | + (((uint16_t)a[7 * i + 3] & 0x0f) << 10); + r->coeffs[4 * i + 2] = (a[7 * i + 3] >> 4) | + (((uint16_t)a[7 * i + 4]) << 4) | + (((uint16_t)a[7 * i + 5] & 0x03) << 12); + r->coeffs[4 * i + 3] = + (a[7 * i + 5] >> 2) | (((uint16_t)a[7 * i + 6]) << 6); + } +} + +void newhope_poly_tobytes(uint8_t* r, const NEWHOPE_POLY* p) { + int i; + uint16_t t0, t1, t2, t3, m; + int16_t c; + for (i = 0; i < PARAM_N / 4; i++) { + t0 = newhope_barrett_reduce( + p->coeffs[4 * i + 0]); /* Make sure that coefficients + have only 14 bits */ + t1 = newhope_barrett_reduce(p->coeffs[4 * i + 1]); + t2 = newhope_barrett_reduce(p->coeffs[4 * i + 2]); + t3 = newhope_barrett_reduce(p->coeffs[4 * i + 3]); + + m = t0 - PARAM_Q; + c = m; + c >>= 15; + t0 = m ^ ((t0 ^ m) & c); /* Make sure that coefficients are in [0,q] */ + + m = t1 - PARAM_Q; + c = m; + c >>= 15; + t1 = m ^ ((t1 ^ m) & c); /* >= 15; + t2 = m ^ ((t2 ^ m) & c); /* >= 15; + t3 = m ^ ((t3 ^ m) & c); /* Make sure that coefficients are in [0,q] */ + + r[7 * i + 0] = t0 & 0xff; + r[7 * i + 1] = (t0 >> 8) | (t1 << 6); + r[7 * i + 2] = (t1 >> 2); + r[7 * i + 3] = (t1 >> 10) | (t2 << 4); + r[7 * i + 4] = (t2 >> 4); + r[7 * i + 5] = (t2 >> 12) | (t3 << 2); + r[7 * i + 6] = (t3 >> 6); + } +} + +void newhope_poly_uniform(NEWHOPE_POLY* a, const uint8_t* seed) { +/* The reference implementation uses SHAKE-128 here; this implementation uses + * AES-CTR. Use half the seed for the initialization vector and half for the + * key. */ +#if SEED_LENGTH != 2 * AES_BLOCK_SIZE +#error "2 * seed length != AES_BLOCK_SIZE" +#endif + uint8_t ivec[AES_BLOCK_SIZE]; + memcpy(ivec, &seed[SEED_LENGTH / 2], SEED_LENGTH / 2); + AES_KEY key; + AES_set_encrypt_key(seed, 8 * SEED_LENGTH / 2, &key); + + /* AES state. */ + uint8_t ecount[AES_BLOCK_SIZE]; + memset(ecount, 0, AES_BLOCK_SIZE); + + /* Encrypt a block of zeros just to get the random bytes. With luck, 2688 + * bytes is enough. */ + static size_t kBlocks = 168; + uint8_t buf[AES_BLOCK_SIZE * kBlocks]; + memset(buf, 0, sizeof(buf)); + + unsigned int block_num = 0; + AES_ctr128_encrypt(buf, buf, sizeof(buf), &key, ivec, ecount, &block_num); + + size_t pos = 0, coeff_num = 0; + while (coeff_num < PARAM_N) { + /* Specialized for q = 12889 */ + uint16_t val = (buf[pos] | ((uint16_t)buf[pos + 1] << 8)) & 0x3fff; + if (val < PARAM_Q) { + a->coeffs[coeff_num++] = val; + } + + pos += 2; + if (pos > sizeof(buf) - 2) { + memset(buf, 0, sizeof(buf)); + AES_ctr128_encrypt(buf, buf, sizeof(buf), &key, ivec, ecount, &block_num); + pos = 0; + } + } +} + +void newhope_poly_getnoise(NEWHOPE_POLY* r) { +#if PARAM_K != 16 +#error "poly_getnoise in poly.c only supports k=16" +#endif + + uint32_t tp[PARAM_N]; + + /* The reference implementation calls ChaCha20 here. */ + RAND_bytes((uint8_t *) tp, sizeof(tp)); + + size_t i; + for (i = 0; i < PARAM_N; i++) { + const uint32_t t = tp[i]; + + size_t j; + uint32_t d = 0; + for (j = 0; j < 8; j++) { + d += (t >> j) & 0x01010101; + } + + const uint32_t a = ((d >> 8) & 0xff) + (d & 0xff); + const uint32_t b = (d >> 24) + ((d >> 16) & 0xff); + r->coeffs[i] = a + PARAM_Q - b; + } +} + +void newhope_poly_pointwise(NEWHOPE_POLY* r, const NEWHOPE_POLY* a, + const NEWHOPE_POLY* b) { + size_t i; + for (i = 0; i < PARAM_N; i++) { + uint16_t t = newhope_montgomery_reduce(3186 * b->coeffs[i]); + /* t is now in Montgomery domain */ + r->coeffs[i] = newhope_montgomery_reduce(a->coeffs[i] * t); + /* r->coeffs[i] is back in normal domain */ + } +} + +void newhope_poly_add(NEWHOPE_POLY* r, const NEWHOPE_POLY* a, + const NEWHOPE_POLY* b) { + size_t i; + for (i = 0; i < PARAM_N; i++) { + r->coeffs[i] = newhope_barrett_reduce(a->coeffs[i] + b->coeffs[i]); + } +} + +void newhope_poly_ntt(NEWHOPE_POLY* r) { + newhope_mul_coefficients(r->coeffs, newhope_psis_bitrev_montgomery); + newhope_ntt((uint16_t *) r->coeffs, newhope_omegas_montgomery); +} + +void newhope_poly_invntt(NEWHOPE_POLY* r) { + newhope_bitrev_vector(r->coeffs); + newhope_ntt((uint16_t *) r->coeffs, newhope_omegas_inv_montgomery); + newhope_mul_coefficients(r->coeffs, newhope_psis_inv_montgomery); +} diff --git a/crypto/newhope/precomp.c b/crypto/newhope/precomp.c new file mode 100644 index 00000000..d0c478ee --- /dev/null +++ b/crypto/newhope/precomp.c @@ -0,0 +1,306 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 "internal.h" + + +uint16_t newhope_omegas_montgomery[PARAM_N / 2] = { + 4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041, + 8775, 2344, 11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118, + 2683, 1190, 4789, 7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973, + 382, 3988, 468, 6843, 5339, 6196, 3710, 11316, 1254, 5435, 10930, + 3998, 10256, 10367, 3879, 11889, 1728, 6137, 4948, 5862, 6136, 3643, + 6874, 8724, 654, 10302, 1702, 7083, 6760, 56, 3199, 9987, 605, + 11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689, 4080, + 11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142, + 241, 12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968, + 12097, 7591, 5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821, + 11502, 8807, 12138, 2127, 2839, 3957, 431, 1579, 6383, 9784, 5874, + 677, 3336, 6234, 2766, 1323, 9115, 12237, 2031, 6956, 6413, 2281, + 3969, 3991, 12133, 9522, 4737, 10996, 4774, 5429, 11871, 3772, 453, + 5908, 2882, 1805, 2051, 1954, 11713, 3963, 2447, 6142, 8174, 3030, + 1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796, 2057, 5369, 11939, + 1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789, 5942, 10706, + 10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551, 9634, + 6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459, + 64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065, + 835, 3570, 4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922, + 7967, 1958, 10211, 1112, 3728, 4049, 11130, 5990, 1404, 325, 948, + 11143, 6190, 295, 11637, 5766, 8212, 8273, 2919, 8527, 6119, 6992, + 8333, 1360, 2555, 6167, 1200, 7105, 7991, 3329, 9597, 12121, 5106, + 5961, 10695, 10327, 3051, 9923, 4896, 9326, 81, 3091, 1000, 7969, + 4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062, 2294, 3553, + 4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088, + 1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479, + 1, 8246, 7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961, + 4591, 5728, 6461, 5023, 9650, 7468, 949, 9664, 2975, 11726, 2744, + 9283, 10092, 5067, 12171, 2476, 3748, 11336, 6522, 827, 9452, 5374, + 12159, 7935, 3296, 3949, 9893, 4452, 10908, 2525, 3584, 8112, 8011, + 10616, 4989, 6958, 11809, 9447, 12280, 1022, 11950, 9821, 11745, 5791, + 5092, 2089, 9005, 2881, 3289, 2013, 9048, 729, 7901, 1260, 5755, + 4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932, 9558, 8830, 3637, + 5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741, 1207, + 9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952, + 4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302, + 6022, 7278, 1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045, + 2481, 5012, 7428, 354, 6591, 9377, 11847, 2401, 1067, 7188, 11516, + 390, 8511, 8456, 7270, 545, 8585, 9611, 12047, 1537, 4143, 4714, + 4885, 1017, 5084, 1632, 3066, 27, 1440, 8526, 9273, 12046, 11618, + 9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985, 11869, 6730, + 10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407, 2686, + 9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863, + 7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852, + 12286, 4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364, + 3271, 4057, 4414, 9442, 7917, 2174}; + +uint16_t newhope_omegas_inv_montgomery[PARAM_N / 2] = { + 4075, 5315, 4324, 4916, 10120, 11767, 7210, 9027, 10316, 6715, 1278, + 9945, 3514, 11248, 11271, 5925, 147, 8500, 7840, 6833, 5537, 4749, + 4467, 7500, 11099, 9606, 6171, 8471, 8429, 5445, 11239, 7753, 9090, + 12233, 5529, 5206, 10587, 1987, 11635, 3565, 5415, 8646, 6153, 6427, + 7341, 6152, 10561, 400, 8410, 1922, 2033, 8291, 1359, 6854, 11035, + 973, 8579, 6093, 6950, 5446, 11821, 8301, 11907, 316, 52, 3174, + 10966, 9523, 6055, 8953, 11612, 6415, 2505, 5906, 10710, 11858, 8332, + 9450, 10162, 151, 3482, 787, 5468, 1010, 4169, 9162, 5241, 9369, + 7509, 8844, 7232, 4698, 192, 1321, 10240, 4912, 885, 6281, 10333, + 7280, 8757, 11286, 58, 12048, 12147, 11184, 8812, 6608, 2844, 3438, + 4212, 11314, 8687, 6068, 421, 8209, 3600, 3263, 7665, 6077, 7507, + 5886, 3029, 6695, 4213, 504, 11684, 2302, 1962, 1594, 6328, 7183, + 168, 2692, 8960, 4298, 5184, 11089, 6122, 9734, 10929, 3956, 5297, + 6170, 3762, 9370, 4016, 4077, 6523, 652, 11994, 6099, 1146, 11341, + 11964, 10885, 6299, 1159, 8240, 8561, 11177, 2078, 10331, 4322, 11367, + 441, 4079, 11231, 3150, 1319, 8243, 709, 8049, 8719, 11454, 6224, + 3054, 6803, 3123, 10542, 4433, 6370, 7032, 3834, 8633, 12225, 9830, + 683, 1566, 5782, 9786, 9341, 12115, 723, 3009, 1693, 5735, 2655, + 2738, 6421, 11942, 2925, 1975, 8532, 3315, 11863, 4754, 1858, 1583, + 6347, 2500, 10800, 6374, 1483, 12240, 1263, 1815, 5383, 10777, 350, + 6920, 10232, 4493, 9087, 8855, 8760, 9381, 218, 9928, 10446, 9259, + 4115, 6147, 9842, 8326, 576, 10335, 10238, 10484, 9407, 6381, 11836, + 8517, 418, 6860, 7515, 1293, 7552, 2767, 156, 8298, 8320, 10008, + 5876, 5333, 10258, 10115, 4372, 2847, 7875, 8232, 9018, 8925, 1689, + 8236, 2645, 5042, 9984, 7094, 9509, 1484, 7394, 3, 4437, 160, + 3149, 113, 7370, 10123, 3915, 6998, 2704, 8653, 4938, 1426, 7635, + 10512, 1663, 6957, 3510, 2370, 2865, 3978, 9320, 3247, 9603, 6882, + 3186, 10659, 10163, 1153, 9405, 8241, 10040, 2178, 1544, 5559, 420, + 8304, 4905, 476, 3531, 5191, 9153, 2399, 8889, 3000, 671, 243, + 3016, 3763, 10849, 12262, 9223, 10657, 7205, 11272, 7404, 7575, 8146, + 10752, 242, 2678, 3704, 11744, 5019, 3833, 3778, 11899, 773, 5101, + 11222, 9888, 442, 2912, 5698, 11935, 4861, 7277, 9808, 11244, 2859, + 3780, 11414, 4976, 10682, 7201, 8005, 11287, 5011, 6267, 2987, 2437, + 3646, 2566, 10102, 9867, 6250, 5444, 2381, 11796, 8193, 4337, 11854, + 1912, 1378, 404, 7644, 1065, 2143, 11121, 5277, 3248, 11082, 2548, + 8058, 8907, 11934, 1759, 8582, 3694, 7110, 12144, 6747, 8652, 3459, + 2731, 8357, 6378, 7399, 10861, 1696, 9863, 334, 7657, 6534, 11029, + 4388, 11560, 3241, 10276, 9000, 9408, 3284, 10200, 7197, 6498, 544, + 2468, 339, 11267, 9, 2842, 480, 5331, 7300, 1673, 4278, 4177, + 8705, 9764, 1381, 7837, 2396, 8340, 8993, 4354, 130, 6915, 2837, + 11462, 5767, 953, 8541, 9813, 118, 7222, 2197, 3006, 9545, 563, + 9314, 2625, 11340, 4821, 2639, 7266, 5828, 6561, 7698, 3328, 6512, + 1351, 7311, 6553, 8155, 1305, 722, 5146, 4043, 12288, 10810, 2545, + 3621, 8747, 8785, 1646, 1212, 5860, 3195, 7203, 10963, 3201, 3014, + 955, 11499, 9970, 11119, 3135, 3712, 7443, 9542, 7484, 8736, 9995, + 11227, 1635, 9521, 1177, 8034, 140, 10436, 11563, 7678, 4320, 11289, + 9198, 12208, 2963, 7393, 2366, 9238}; + +uint16_t newhope_psis_bitrev_montgomery[PARAM_N] = { + 4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041, + 8775, 2344, 11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118, + 2683, 1190, 4789, 7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973, + 382, 3988, 468, 6843, 5339, 6196, 3710, 11316, 1254, 5435, 10930, + 3998, 10256, 10367, 3879, 11889, 1728, 6137, 4948, 5862, 6136, 3643, + 6874, 8724, 654, 10302, 1702, 7083, 6760, 56, 3199, 9987, 605, + 11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689, 4080, + 11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142, + 241, 12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968, + 12097, 7591, 5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821, + 11502, 8807, 12138, 2127, 2839, 3957, 431, 1579, 6383, 9784, 5874, + 677, 3336, 6234, 2766, 1323, 9115, 12237, 2031, 6956, 6413, 2281, + 3969, 3991, 12133, 9522, 4737, 10996, 4774, 5429, 11871, 3772, 453, + 5908, 2882, 1805, 2051, 1954, 11713, 3963, 2447, 6142, 8174, 3030, + 1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796, 2057, 5369, 11939, + 1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789, 5942, 10706, + 10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551, 9634, + 6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459, + 64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065, + 835, 3570, 4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922, + 7967, 1958, 10211, 1112, 3728, 4049, 11130, 5990, 1404, 325, 948, + 11143, 6190, 295, 11637, 5766, 8212, 8273, 2919, 8527, 6119, 6992, + 8333, 1360, 2555, 6167, 1200, 7105, 7991, 3329, 9597, 12121, 5106, + 5961, 10695, 10327, 3051, 9923, 4896, 9326, 81, 3091, 1000, 7969, + 4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062, 2294, 3553, + 4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088, + 1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479, + 1, 8246, 7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961, + 4591, 5728, 6461, 5023, 9650, 7468, 949, 9664, 2975, 11726, 2744, + 9283, 10092, 5067, 12171, 2476, 3748, 11336, 6522, 827, 9452, 5374, + 12159, 7935, 3296, 3949, 9893, 4452, 10908, 2525, 3584, 8112, 8011, + 10616, 4989, 6958, 11809, 9447, 12280, 1022, 11950, 9821, 11745, 5791, + 5092, 2089, 9005, 2881, 3289, 2013, 9048, 729, 7901, 1260, 5755, + 4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932, 9558, 8830, 3637, + 5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741, 1207, + 9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952, + 4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302, + 6022, 7278, 1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045, + 2481, 5012, 7428, 354, 6591, 9377, 11847, 2401, 1067, 7188, 11516, + 390, 8511, 8456, 7270, 545, 8585, 9611, 12047, 1537, 4143, 4714, + 4885, 1017, 5084, 1632, 3066, 27, 1440, 8526, 9273, 12046, 11618, + 9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985, 11869, 6730, + 10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407, 2686, + 9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863, + 7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852, + 12286, 4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364, + 3271, 4057, 4414, 9442, 7917, 2174, 3947, 11951, 2455, 6599, 10545, + 10975, 3654, 2894, 7681, 7126, 7287, 12269, 4119, 3343, 2151, 1522, + 7174, 7350, 11041, 2442, 2148, 5959, 6492, 8330, 8945, 5598, 3624, + 10397, 1325, 6565, 1945, 11260, 10077, 2674, 3338, 3276, 11034, 506, + 6505, 1392, 5478, 8778, 1178, 2776, 3408, 10347, 11124, 2575, 9489, + 12096, 6092, 10058, 4167, 6085, 923, 11251, 11912, 4578, 10669, 11914, + 425, 10453, 392, 10104, 8464, 4235, 8761, 7376, 2291, 3375, 7954, + 8896, 6617, 7790, 1737, 11667, 3982, 9342, 6680, 636, 6825, 7383, + 512, 4670, 2900, 12050, 7735, 994, 1687, 11883, 7021, 146, 10485, + 1403, 5189, 6094, 2483, 2054, 3042, 10945, 3981, 10821, 11826, 8882, + 8151, 180, 9600, 7684, 5219, 10880, 6780, 204, 11232, 2600, 7584, + 3121, 3017, 11053, 7814, 7043, 4251, 4739, 11063, 6771, 7073, 9261, + 2360, 11925, 1928, 11825, 8024, 3678, 3205, 3359, 11197, 5209, 8581, + 3238, 8840, 1136, 9363, 1826, 3171, 4489, 7885, 346, 2068, 1389, + 8257, 3163, 4840, 6127, 8062, 8921, 612, 4238, 10763, 8067, 125, + 11749, 10125, 5416, 2110, 716, 9839, 10584, 11475, 11873, 3448, 343, + 1908, 4538, 10423, 7078, 4727, 1208, 11572, 3589, 2982, 1373, 1721, + 10753, 4103, 2429, 4209, 5412, 5993, 9011, 438, 3515, 7228, 1218, + 8347, 5232, 8682, 1327, 7508, 4924, 448, 1014, 10029, 12221, 4566, + 5836, 12229, 2717, 1535, 3200, 5588, 5845, 412, 5102, 7326, 3744, + 3056, 2528, 7406, 8314, 9202, 6454, 6613, 1417, 10032, 7784, 1518, + 3765, 4176, 5063, 9828, 2275, 6636, 4267, 6463, 2065, 7725, 3495, + 8328, 8755, 8144, 10533, 5966, 12077, 9175, 9520, 5596, 6302, 8400, + 579, 6781, 11014, 5734, 11113, 11164, 4860, 1131, 10844, 9068, 8016, + 9694, 3837, 567, 9348, 7000, 6627, 7699, 5082, 682, 11309, 5207, + 4050, 7087, 844, 7434, 3769, 293, 9057, 6940, 9344, 10883, 2633, + 8190, 3944, 5530, 5604, 3480, 2171, 9282, 11024, 2213, 8136, 3805, + 767, 12239, 216, 11520, 6763, 10353, 7, 8566, 845, 7235, 3154, + 4360, 3285, 10268, 2832, 3572, 1282, 7559, 3229, 8360, 10583, 6105, + 3120, 6643, 6203, 8536, 8348, 6919, 3536, 9199, 10891, 11463, 5043, + 1658, 5618, 8787, 5789, 4719, 751, 11379, 6389, 10783, 3065, 7806, + 6586, 2622, 5386, 510, 7628, 6921, 578, 10345, 11839, 8929, 4684, + 12226, 7154, 9916, 7302, 8481, 3670, 11066, 2334, 1590, 7878, 10734, + 1802, 1891, 5103, 6151, 8820, 3418, 7846, 9951, 4693, 417, 9996, + 9652, 4510, 2946, 5461, 365, 881, 1927, 1015, 11675, 11009, 1371, + 12265, 2485, 11385, 5039, 6742, 8449, 1842, 12217, 8176, 9577, 4834, + 7937, 9461, 2643, 11194, 3045, 6508, 4094, 3451, 7911, 11048, 5406, + 4665, 3020, 6616, 11345, 7519, 3669, 5287, 1790, 7014, 5410, 11038, + 11249, 2035, 6125, 10407, 4565, 7315, 5078, 10506, 2840, 2478, 9270, + 4194, 9195, 4518, 7469, 1160, 6878, 2730, 10421, 10036, 1734, 3815, + 10939, 5832, 10595, 10759, 4423, 8420, 9617, 7119, 11010, 11424, 9173, + 189, 10080, 10526, 3466, 10588, 7592, 3578, 11511, 7785, 9663, 530, + 12150, 8957, 2532, 3317, 9349, 10243, 1481, 9332, 3454, 3758, 7899, + 4218, 2593, 11410, 2276, 982, 6513, 1849, 8494, 9021, 4523, 7988, + 8, 457, 648, 150, 8000, 2307, 2301, 874, 5650, 170, 9462, + 2873, 9855, 11498, 2535, 11169, 5808, 12268, 9687, 1901, 7171, 11787, + 3846, 1573, 6063, 3793, 466, 11259, 10608, 3821, 6320, 4649, 6263, + 2929}; + +uint16_t newhope_psis_inv_montgomery[PARAM_N] = { + 256, 10570, 1510, 7238, 1034, 7170, 6291, 7921, 11665, 3422, 4000, + 2327, 2088, 5565, 795, 10647, 1521, 5484, 2539, 7385, 1055, 7173, + 8047, 11683, 1669, 1994, 3796, 5809, 4341, 9398, 11876, 12230, 10525, + 12037, 12253, 3506, 4012, 9351, 4847, 2448, 7372, 9831, 3160, 2207, + 5582, 2553, 7387, 6322, 9681, 1383, 10731, 1533, 219, 5298, 4268, + 7632, 6357, 9686, 8406, 4712, 9451, 10128, 4958, 5975, 11387, 8649, + 11769, 6948, 11526, 12180, 1740, 10782, 6807, 2728, 7412, 4570, 4164, + 4106, 11120, 12122, 8754, 11784, 3439, 5758, 11356, 6889, 9762, 11928, + 1704, 1999, 10819, 12079, 12259, 7018, 11536, 1648, 1991, 2040, 2047, + 2048, 10826, 12080, 8748, 8272, 8204, 1172, 1923, 7297, 2798, 7422, + 6327, 4415, 7653, 6360, 11442, 12168, 7005, 8023, 9924, 8440, 8228, + 2931, 7441, 1063, 3663, 5790, 9605, 10150, 1450, 8985, 11817, 10466, + 10273, 12001, 3470, 7518, 1074, 1909, 7295, 9820, 4914, 702, 5367, + 7789, 8135, 9940, 1420, 3714, 11064, 12114, 12264, 1752, 5517, 9566, + 11900, 1700, 3754, 5803, 829, 1874, 7290, 2797, 10933, 5073, 7747, + 8129, 6428, 6185, 11417, 1631, 233, 5300, 9535, 10140, 11982, 8734, + 8270, 2937, 10953, 8587, 8249, 2934, 9197, 4825, 5956, 4362, 9401, + 1343, 3703, 529, 10609, 12049, 6988, 6265, 895, 3639, 4031, 4087, + 4095, 585, 10617, 8539, 4731, 4187, 9376, 3095, 9220, 10095, 10220, + 1460, 10742, 12068, 1724, 5513, 11321, 6884, 2739, 5658, 6075, 4379, + 11159, 10372, 8504, 4726, 9453, 3106, 7466, 11600, 10435, 8513, 9994, + 8450, 9985, 3182, 10988, 8592, 2983, 9204, 4826, 2445, 5616, 6069, + 867, 3635, 5786, 11360, 5134, 2489, 10889, 12089, 1727, 7269, 2794, + 9177, 1311, 5454, 9557, 6632, 2703, 9164, 10087, 1441, 3717, 531, + 3587, 2268, 324, 5313, 759, 1864, 5533, 2546, 7386, 9833, 8427, + 4715, 11207, 1601, 7251, 4547, 11183, 12131, 1733, 10781, 10318, 1474, + 10744, 5046, 4232, 11138, 10369, 6748, 964, 7160, 4534, 7670, 8118, + 8182, 4680, 11202, 6867, 981, 8918, 1274, 182, 26, 7026, 8026, + 11680, 12202, 10521, 1503, 7237, 4545, 5916, 9623, 8397, 11733, 10454, + 3249, 9242, 6587, 941, 1890, 270, 10572, 6777, 9746, 6659, 6218, + 6155, 6146, 878, 1881, 7291, 11575, 12187, 1741, 7271, 8061, 11685, + 6936, 4502, 9421, 4857, 4205, 7623, 1089, 10689, 1527, 8996, 10063, + 11971, 10488, 6765, 2722, 3900, 9335, 11867, 6962, 11528, 5158, 4248, + 4118, 5855, 2592, 5637, 6072, 2623, 7397, 8079, 9932, 4930, 5971, + 853, 3633, 519, 8852, 11798, 3441, 11025, 1575, 225, 8810, 11792, + 12218, 3501, 9278, 3081, 9218, 4828, 7712, 8124, 11694, 12204, 3499, + 4011, 573, 3593, 5780, 7848, 9899, 10192, 1456, 208, 7052, 2763, + 7417, 11593, 10434, 12024, 8740, 11782, 10461, 3250, 5731, 7841, 9898, + 1414, 202, 3540, 7528, 2831, 2160, 10842, 5060, 4234, 4116, 588, + 84, 12, 7024, 2759, 9172, 6577, 11473, 1639, 9012, 3043, 7457, + 6332, 11438, 1634, 1989, 9062, 11828, 8712, 11778, 12216, 10523, 6770, + 9745, 10170, 4964, 9487, 6622, 946, 8913, 6540, 6201, 4397, 9406, + 8366, 9973, 8447, 8229, 11709, 8695, 10020, 3187, 5722, 2573, 10901, + 6824, 4486, 4152, 9371, 8361, 2950, 2177, 311, 1800, 9035, 8313, + 11721, 3430, 490, 70, 10, 1757, 251, 3547, 7529, 11609, 3414, + 7510, 4584, 4166, 9373, 1339, 5458, 7802, 11648, 1664, 7260, 9815, + 10180, 6721, 9738, 10169, 8475, 8233, 9954, 1422, 8981, 1283, 5450, + 11312, 1616, 3742, 11068, 10359, 4991, 713, 3613, 9294, 8350, 4704, + 672, 96, 7036, 9783, 11931, 3460, 5761, 823, 10651, 12055, 10500, + 1500, 5481, 783, 3623, 11051, 8601, 8251, 8201, 11705, 10450, 5004, + 4226, 7626, 2845, 2162, 3820, 7568, 9859, 3164, 452, 10598, 1514, + 5483, 6050, 6131, 4387, 7649, 8115, 6426, 918, 8909, 8295, 1185, + 5436, 11310, 8638, 1234, 5443, 11311, 5127, 2488, 2111, 10835, 5059, + 7745, 2862, 3920, 560, 80, 1767, 2008, 3798, 11076, 6849, 2734, + 10924, 12094, 8750, 1250, 10712, 6797, 971, 7161, 1023, 8924, 4786, + 7706, 4612, 4170, 7618, 6355, 4419, 5898, 11376, 10403, 10264, 6733, + 4473, 639, 5358, 2521, 9138, 3061, 5704, 4326, 618, 5355, 765, + 5376, 768, 7132, 4530, 9425, 3102, 9221, 6584, 11474, 10417, 10266, + 12000, 6981, 6264, 4406, 2385, 7363, 4563, 4163, 7617, 9866, 3165, + 9230, 11852, 10471, 5007, 5982, 11388, 5138, 734, 3616, 11050, 12112, + 6997, 11533, 12181, 10518, 12036, 3475, 2252, 7344, 9827, 4915, 9480, + 6621, 4457, 7659, 9872, 6677, 4465, 4149, 7615, 4599, 657, 3605, + 515, 10607, 6782, 4480, 640, 1847, 3775, 5806, 2585, 5636, 9583, + 1369, 10729, 8555, 10000, 11962, 5220, 7768, 8132, 8184, 9947, 1421, + 203, 29, 8782, 11788, 1684, 10774, 10317, 4985, 9490, 8378, 4708, + 11206, 5112, 5997, 7879, 11659, 12199, 8765, 10030, 4944, 5973, 6120, + 6141, 6144, 7900, 11662, 1666, 238, 34, 3516, 5769, 9602, 8394, + 9977, 6692, 956, 10670, 6791, 9748, 11926, 8726, 11780, 5194, 742, + 106, 8793, 10034, 3189, 10989, 5081, 4237, 5872, 4350, 2377, 10873, + 6820, 6241, 11425, 10410, 10265, 3222, 5727, 9596, 4882, 2453, 2106, + 3812, 11078, 12116, 5242, 4260, 11142, 8614, 11764, 12214, 5256, 4262, + 4120, 11122, 5100, 11262, 5120, 2487, 5622, 9581, 8391, 8221, 2930, + 10952, 12098, 6995, 6266, 9673, 4893, 699, 3611, 4027, 5842, 11368, + 1624, 232, 8811, 8281, 1183, 169, 8802, 3013, 2186, 5579, 797, + 3625, 4029, 11109, 1587, 7249, 11569, 8675, 6506, 2685, 10917, 12093, + 12261, 12285, 1755, 7273, 1039, 1904, 272, 3550, 9285, 3082, 5707, + 6082, 4380, 7648, 11626, 5172, 4250, 9385, 8363, 8217, 4685, 5936, + 848, 8899, 6538, 934, 1889, 3781, 9318, 10109, 10222, 6727, 961, + 5404, 772, 5377, 9546, 8386, 1198, 8949, 3034, 2189, 7335, 4559, + 5918, 2601, 10905, 5069, 9502, 3113, 7467, 8089, 11689, 5181, 9518, + 8382, 2953, 3933, 4073, 4093, 7607, 8109, 2914, 5683, 4323, 11151, + 1593, 10761, 6804, 972, 3650, 2277, 5592, 4310, 7638, 9869, 4921, + 703, 1856, 9043, 4803, 9464, 1352, 8971, 11815, 5199, 7765, 6376, + 4422, 7654, 2849, 407, 8836, 6529, 7955, 2892, 9191, 1313, 10721, + 12065, 12257, 1751, 9028, 8312, 2943, 2176, 3822, 546, 78, 8789, + 11789, 10462, 12028, 6985, 4509, 9422, 1346, 5459, 4291, 613, 10621, + 6784, 9747, 3148, 7472, 2823, 5670, 810, 7138, 8042, 4660, 7688, + 6365, 6176, 6149, 2634, 5643, 9584, 10147, 11983, 5223, 9524, 11894, + 10477, 8519, 1217, 3685, 2282, 326, 10580, 3267, 7489, 4581, 2410, + 5611, 11335, 6886, 8006, 8166, 11700, 3427, 11023, 8597, 10006, 3185, + 455, 65, 5276, 7776, 4622, 5927, 7869, 9902, 11948, 5218, 2501, + 5624, 2559, 10899, 1557, 1978, 10816, 10323, 8497, 4725, 675, 1852, + 10798, 12076, 10503, 3256, 9243, 3076, 2195, 10847, 12083, 10504, 12034, + 10497}; diff --git a/crypto/newhope/reduce.c b/crypto/newhope/reduce.c new file mode 100644 index 00000000..e7f13649 --- /dev/null +++ b/crypto/newhope/reduce.c @@ -0,0 +1,42 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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 "internal.h" + + +/* Incomplete-reduction routines; for details on allowed input ranges + * and produced output ranges, see the description in the paper: + * https://cryptojedi.org/papers/#newhope */ + +static const uint32_t kQInv = 12287; /* -inverse_mod(p,2^18) */ +static const uint32_t kRLog = 18; + +uint16_t newhope_montgomery_reduce(uint32_t a) { + uint32_t u; + + u = (a * kQInv); + u &= ((1 << kRLog) - 1); + u *= PARAM_Q; + a = a + u; + return a >> 18; +} + +uint16_t newhope_barrett_reduce(uint16_t a) { + uint32_t u; + + u = ((uint32_t)a * 5) >> 16; + u *= PARAM_Q; + a -= u; + return a; +} diff --git a/include/openssl/base.h b/include/openssl/base.h index 13787263..22119205 100644 --- a/include/openssl/base.h +++ b/include/openssl/base.h @@ -236,6 +236,7 @@ typedef struct evp_pkey_st EVP_PKEY; typedef struct hmac_ctx_st HMAC_CTX; typedef struct md4_state_st MD4_CTX; typedef struct md5_state_st MD5_CTX; +typedef struct newhope_poly_st NEWHOPE_POLY; typedef struct pkcs12_st PKCS12; typedef struct pkcs8_priv_key_info_st PKCS8_PRIV_KEY_INFO; typedef struct private_key_st X509_PKEY; diff --git a/include/openssl/newhope.h b/include/openssl/newhope.h new file mode 100644 index 00000000..af573bae --- /dev/null +++ b/include/openssl/newhope.h @@ -0,0 +1,78 @@ +/* Copyright (c) 2016, Google Inc. + * + * Permission to use, copy, modify, and/or 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. */ + +#ifndef OPENSSL_HEADER_NEWHOPE_H +#define OPENSSL_HEADER_NEWHOPE_H + +#include +#include + +#if defined(__cplusplus) +extern "C" { +#endif + + +/* Post-quantum key agreement, based upon the reference + * implementation. Note: this implementation does not interoperate + * with the reference implementation! + * + * Source: https://github.com/tpoeppelmann/newhope + * + * The authors' permission to use their code is gratefully acknowledged. */ + + +/* NEWHOPE_POLY_new returns a new |NEWHOPE_POLY| object, or NULL on error. */ +OPENSSL_EXPORT NEWHOPE_POLY *NEWHOPE_POLY_new(void); + +/* NEWHOPE_POLY_free frees |p|. */ +OPENSSL_EXPORT void NEWHOPE_POLY_free(NEWHOPE_POLY *p); + +/* NEWHOPE_SERVERMSG_LENGTH is the length of the server's message to the + * client. */ +#define NEWHOPE_SERVERMSG_LENGTH (((1024 * 14) / 8) + 32) + +/* NEWHOPE_CLIENTMSG_LENGTH is the length of the client's message to the + * server. */ +#define NEWHOPE_CLIENTMSG_LENGTH (((1024 * 14) / 8) + 1024 / 4) + +/* NEWHOPE_keygen initializes |out_msg| and |out_sk| for a new key + * exchange. |msg| must have room for |NEWHOPE_SERVERMSG_LENGTH| bytes. Neither + * output may be cached. */ +OPENSSL_EXPORT void NEWHOPE_keygen(uint8_t out_msg[NEWHOPE_SERVERMSG_LENGTH], + NEWHOPE_POLY *out_sk); + +/* NEWHOPE_server_compute_key completes a key exchange given a client message + * |msg| and the previously generated server secret |sk|. The result of the + * key exchange is written to |out_key|, which must have space for + * |SHA256_DIGEST_LENGTH| bytes. Returns 1 on success and 0 on error. */ +OPENSSL_EXPORT int NEWHOPE_server_compute_key( + uint8_t out_key[SHA256_DIGEST_LENGTH], const NEWHOPE_POLY *sk, + const uint8_t msg[NEWHOPE_CLIENTMSG_LENGTH], size_t msg_len); + +/* NEWHOPE_client_compute_key completes a key exchange given a server message + * |msg|. The result of the key exchange is written to |out_key|, which must + * have space for |SHA256_DIGEST_LENGTH| bytes. The message to be send to the + * client is written to |out_msg|, which must have room for + * |NEWHOPE_CLIENTMSG_LENGTH| bytes. Returns 1 on success and 0 on error. */ +OPENSSL_EXPORT int NEWHOPE_client_compute_key( + uint8_t out_key[SHA256_DIGEST_LENGTH], + uint8_t out_msg[NEWHOPE_CLIENTMSG_LENGTH], + const uint8_t msg[NEWHOPE_SERVERMSG_LENGTH], size_t msg_len); + + +#if defined(__cplusplus) +} /* extern "C" */ +#endif + +#endif /* OPENSSL_HEADER_NEWHOPE_H */ diff --git a/tool/speed.cc b/tool/speed.cc index 63cb0e20..46430585 100644 --- a/tool/speed.cc +++ b/tool/speed.cc @@ -24,6 +24,7 @@ #include #include #include +#include #include #include #include @@ -514,6 +515,35 @@ static bool SpeedSPAKE2(const std::string &selected) { return true; } +static bool SpeedNewHope(const std::string &selected) { + if (!selected.empty() && selected.find("newhope") == std::string::npos) { + return true; + } + + TimeResults results; + NEWHOPE_POLY *sk = NEWHOPE_POLY_new(); + uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH]; + RAND_bytes(clientmsg, sizeof(clientmsg)); + + if (!TimeFunction(&results, [sk, clientmsg]() -> bool { + uint8_t server_key[SHA256_DIGEST_LENGTH]; + uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH]; + NEWHOPE_keygen(servermsg, sk); + if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg, + sizeof(clientmsg))) { + return false; + } + return true; + })) { + fprintf(stderr, "failed to exchange key.\n"); + return false; + } + + NEWHOPE_POLY_free(sk); + results.Print("newhope server key exchange"); + return true; +} + bool Speed(const std::vector &args) { std::string selected; if (args.size() > 1) { @@ -594,7 +624,8 @@ bool Speed(const std::vector &args) { !SpeedECDH(selected) || !SpeedECDSA(selected) || !Speed25519(selected) || - !SpeedSPAKE2(selected)) { + !SpeedSPAKE2(selected) || + !SpeedNewHope(selected)) { return false; } diff --git a/util/all_tests.json b/util/all_tests.json index bd6cbe58..3de06946 100644 --- a/util/all_tests.json +++ b/util/all_tests.json @@ -50,9 +50,10 @@ ["crypto/hmac/hmac_test", "crypto/hmac/hmac_tests.txt"], ["crypto/lhash/lhash_test"], ["crypto/modes/gcm_test"], + ["crypto/newhope/newhope_test"], ["crypto/obj/obj_test"], - ["crypto/pkcs8/pkcs8_test"], ["crypto/pkcs8/pkcs12_test"], + ["crypto/pkcs8/pkcs8_test"], ["crypto/poly1305/poly1305_test", "crypto/poly1305/poly1305_test.txt"], ["crypto/refcount_test"], ["crypto/rsa/rsa_test"], diff --git a/util/doc.config b/util/doc.config index af02029a..e7cfa82d 100644 --- a/util/doc.config +++ b/util/doc.config @@ -36,6 +36,7 @@ "include/openssl/hkdf.h", "include/openssl/hmac.h", "include/openssl/md5.h", + "include/openssl/newhope.h", "include/openssl/rc4.h", "include/openssl/rsa.h", "include/openssl/sha.h"