1/*
2 * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright 2015-2016 Cryptography Research, Inc.
4 *
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 *
10 * Originally written by Mike Hamburg
11 */
12
13#ifndef OSSL_CRYPTO_EC_CURVE448_POINT_448_H
14# define OSSL_CRYPTO_EC_CURVE448_POINT_448_H
15
16# include "curve448utils.h"
17# include "field.h"
18
19/* Comb config: number of combs, n, t, s. */
20#define COMBS_N 5
21#define COMBS_T 5
22#define COMBS_S 18
23
24/* Projective Niels coordinates */
25typedef struct {
26 gf a, b, c;
27} niels_s, niels_t[1];
28typedef struct {
29 niels_t n;
30 gf z;
31} pniels_t[1];
32
33/* Precomputed base */
34struct curve448_precomputed_s {
35 niels_t table[COMBS_N << (COMBS_T - 1)];
36};
37
38# define C448_SCALAR_LIMBS ((446-1)/C448_WORD_BITS+1)
39
40/* The number of bits in a scalar */
41# define C448_SCALAR_BITS 446
42
43/* Number of bytes in a serialized scalar. */
44# define C448_SCALAR_BYTES 56
45
46/* X448 encoding ratio. */
47# define X448_ENCODE_RATIO 2
48
49/* Number of bytes in an x448 public key */
50# define X448_PUBLIC_BYTES 56
51
52/* Number of bytes in an x448 private key */
53# define X448_PRIVATE_BYTES 56
54
55/* Twisted Edwards extended homogeneous coordinates */
56typedef struct curve448_point_s {
57 gf x, y, z, t;
58} curve448_point_t[1];
59
60/* Precomputed table based on a point. Can be trivial implementation. */
61struct curve448_precomputed_s;
62
63/* Precomputed table based on a point. Can be trivial implementation. */
64typedef struct curve448_precomputed_s curve448_precomputed_s;
65
66/* Scalar is stored packed, because we don't need the speed. */
67typedef struct curve448_scalar_s {
68 c448_word_t limb[C448_SCALAR_LIMBS];
69} curve448_scalar_t[1];
70
71/* A scalar equal to 1. */
72extern const curve448_scalar_t curve448_scalar_one;
73
74/* A scalar equal to 0. */
75extern const curve448_scalar_t curve448_scalar_zero;
76
77/* The identity point on the curve. */
78extern const curve448_point_t curve448_point_identity;
79
80/* Precomputed table for the base point on the curve. */
81extern const struct curve448_precomputed_s *curve448_precomputed_base;
82extern const niels_t *curve448_wnaf_base;
83
84/*
85 * Read a scalar from wire format or from bytes.
86 *
87 * ser (in): Serialized form of a scalar.
88 * out (out): Deserialized form.
89 *
90 * Returns:
91 * C448_SUCCESS: The scalar was correctly encoded.
92 * C448_FAILURE: The scalar was greater than the modulus, and has been reduced
93 * modulo that modulus.
94 */
95c448_error_t curve448_scalar_decode(curve448_scalar_t out,
96 const unsigned char ser[C448_SCALAR_BYTES]);
97
98/*
99 * Read a scalar from wire format or from bytes. Reduces mod scalar prime.
100 *
101 * ser (in): Serialized form of a scalar.
102 * ser_len (in): Length of serialized form.
103 * out (out): Deserialized form.
104 */
105void curve448_scalar_decode_long(curve448_scalar_t out,
106 const unsigned char *ser, size_t ser_len);
107
108/*
109 * Serialize a scalar to wire format.
110 *
111 * ser (out): Serialized form of a scalar.
112 * s (in): Deserialized scalar.
113 */
114void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
115 const curve448_scalar_t s);
116
117/*
118 * Add two scalars. |a|, |b| and |out| may alias each other.
119 *
120 * a (in): One scalar.
121 * b (in): Another scalar.
122 * out (out): a+b.
123 */
124void curve448_scalar_add(curve448_scalar_t out,
125 const curve448_scalar_t a, const curve448_scalar_t b);
126
127/*
128 * Subtract two scalars. |a|, |b| and |out| may alias each other.
129 * a (in): One scalar.
130 * b (in): Another scalar.
131 * out (out): a-b.
132 */
133void curve448_scalar_sub(curve448_scalar_t out,
134 const curve448_scalar_t a, const curve448_scalar_t b);
135
136/*
137 * Multiply two scalars. |a|, |b| and |out| may alias each other.
138 *
139 * a (in): One scalar.
140 * b (in): Another scalar.
141 * out (out): a*b.
142 */
143void curve448_scalar_mul(curve448_scalar_t out,
144 const curve448_scalar_t a, const curve448_scalar_t b);
145
146/*
147* Halve a scalar. |a| and |out| may alias each other.
148*
149* a (in): A scalar.
150* out (out): a/2.
151*/
152void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
153
154/*
155 * Copy a scalar. The scalars may alias each other, in which case this
156 * function does nothing.
157 *
158 * a (in): A scalar.
159 * out (out): Will become a copy of a.
160 */
161static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
162 const curve448_scalar_t a)
163{
164 *out = *a;
165}
166
167/*
168 * Copy a point. The input and output may alias, in which case this function
169 * does nothing.
170 *
171 * a (out): A copy of the point.
172 * b (in): Any point.
173 */
174static ossl_inline void curve448_point_copy(curve448_point_t a,
175 const curve448_point_t b)
176{
177 *a = *b;
178}
179
180/*
181 * Test whether two points are equal. If yes, return C448_TRUE, else return
182 * C448_FALSE.
183 *
184 * a (in): A point.
185 * b (in): Another point.
186 *
187 * Returns:
188 * C448_TRUE: The points are equal.
189 * C448_FALSE: The points are not equal.
190 */
191__owur c448_bool_t curve448_point_eq(const curve448_point_t a,
192 const curve448_point_t b);
193
194/*
195 * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
196 * faster.
197 *
198 * two_a (out): The sum a+a.
199 * a (in): A point.
200 */
201void curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
202
203/*
204 * RFC 7748 Diffie-Hellman scalarmul. This function uses a different
205 * (non-Decaf) encoding.
206 *
207 * out (out): The scaled point base*scalar
208 * base (in): The point to be scaled.
209 * scalar (in): The scalar to multiply by.
210 *
211 * Returns:
212 * C448_SUCCESS: The scalarmul succeeded.
213 * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a
214 * small subgroup.
215 */
216__owur c448_error_t x448_int(uint8_t out[X448_PUBLIC_BYTES],
217 const uint8_t base[X448_PUBLIC_BYTES],
218 const uint8_t scalar[X448_PRIVATE_BYTES]);
219
220/*
221 * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.
222 *
223 * This function is mainly used internally, but is exported in case
224 * it will be useful.
225 *
226 * The ratio is necessary because the internal representation doesn't
227 * track the cofactor information, so on output we must clear the cofactor.
228 * This would multiply by the cofactor, but in fact internally points are always
229 * even, so it multiplies by half the cofactor instead.
230 *
231 * As it happens, this aligns with the base point definitions; that is,
232 * if you pass the Decaf/Ristretto base point to this function, the result
233 * will be X448_ENCODE_RATIO times the X448
234 * base point.
235 *
236 * out (out): The scaled and encoded point.
237 * p (in): The point to be scaled and encoded.
238 */
239void curve448_point_mul_by_ratio_and_encode_like_x448(
240 uint8_t out[X448_PUBLIC_BYTES],
241 const curve448_point_t p);
242
243/*
244 * RFC 7748 Diffie-Hellman base point scalarmul. This function uses a different
245 * (non-Decaf) encoding.
246 *
247 * out (out): The scaled point base*scalar
248 * scalar (in): The scalar to multiply by.
249 */
250void x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],
251 const uint8_t scalar[X448_PRIVATE_BYTES]);
252
253/*
254 * Multiply a precomputed base point by a scalar: out = scalar*base.
255 *
256 * scaled (out): The scaled point base*scalar
257 * base (in): The point to be scaled.
258 * scalar (in): The scalar to multiply by.
259 */
260void curve448_precomputed_scalarmul(curve448_point_t scaled,
261 const curve448_precomputed_s * base,
262 const curve448_scalar_t scalar);
263
264/*
265 * Multiply two base points by two scalars:
266 * combo = scalar1*curve448_point_base + scalar2*base2.
267 *
268 * Otherwise equivalent to curve448_point_double_scalarmul, but may be
269 * faster at the expense of being variable time.
270 *
271 * combo (out): The linear combination scalar1*base + scalar2*base2.
272 * scalar1 (in): A first scalar to multiply by.
273 * base2 (in): A second point to be scaled.
274 * scalar2 (in) A second scalar to multiply by.
275 *
276 * Warning: This function takes variable time, and may leak the scalars used.
277 * It is designed for signature verification.
278 */
279void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
280 const curve448_scalar_t scalar1,
281 const curve448_point_t base2,
282 const curve448_scalar_t scalar2);
283
284/*
285 * Test that a point is valid, for debugging purposes.
286 *
287 * to_test (in): The point to test.
288 *
289 * Returns:
290 * C448_TRUE The point is valid.
291 * C448_FALSE The point is invalid.
292 */
293__owur c448_bool_t curve448_point_valid(const curve448_point_t to_test);
294
295/* Overwrite scalar with zeros. */
296void curve448_scalar_destroy(curve448_scalar_t scalar);
297
298/* Overwrite point with zeros. */
299void curve448_point_destroy(curve448_point_t point);
300
301#endif /* OSSL_CRYPTO_EC_CURVE448_POINT_448_H */
302