1 /*
2 * Copyright 2017-2021 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 */
25 typedef struct {
26 gf a, b, c;
27 } niels_s, niels_t[1];
28 typedef struct {
29 niels_t n;
30 gf z;
31 } pniels_t[1];
32
33 /* Precomputed base */
34 struct 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 */
56 typedef 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. */
61 struct curve448_precomputed_s;
62
63 /* Precomputed table based on a point. Can be trivial implementation. */
64 typedef struct curve448_precomputed_s curve448_precomputed_s;
65
66 /* Scalar is stored packed, because we don't need the speed. */
67 typedef struct curve448_scalar_s {
68 c448_word_t limb[C448_SCALAR_LIMBS];
69 } curve448_scalar_t[1];
70
71 /* A scalar equal to 1. */
72 extern const curve448_scalar_t ossl_curve448_scalar_one;
73
74 /* A scalar equal to 0. */
75 extern const curve448_scalar_t ossl_curve448_scalar_zero;
76
77 /* The identity point on the curve. */
78 extern const curve448_point_t ossl_curve448_point_identity;
79
80 /* Precomputed table for the base point on the curve. */
81 extern const struct curve448_precomputed_s *ossl_curve448_precomputed_base;
82 extern const niels_t *ossl_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 */
95 c448_error_t
96 ossl_curve448_scalar_decode(curve448_scalar_t out,
97 const unsigned char ser[C448_SCALAR_BYTES]);
98
99 /*
100 * Read a scalar from wire format or from bytes. Reduces mod scalar prime.
101 *
102 * ser (in): Serialized form of a scalar.
103 * ser_len (in): Length of serialized form.
104 * out (out): Deserialized form.
105 */
106 void
107 ossl_curve448_scalar_decode_long(curve448_scalar_t out,
108 const unsigned char *ser, size_t ser_len);
109
110 /*
111 * Serialize a scalar to wire format.
112 *
113 * ser (out): Serialized form of a scalar.
114 * s (in): Deserialized scalar.
115 */
116 void
117 ossl_curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
118 const curve448_scalar_t s);
119
120 /*
121 * Add two scalars. |a|, |b| and |out| may alias each other.
122 *
123 * a (in): One scalar.
124 * b (in): Another scalar.
125 * out (out): a+b.
126 */
127 void
128 ossl_curve448_scalar_add(curve448_scalar_t out,
129 const curve448_scalar_t a, const curve448_scalar_t b);
130
131 /*
132 * Subtract two scalars. |a|, |b| and |out| may alias each other.
133 * a (in): One scalar.
134 * b (in): Another scalar.
135 * out (out): a-b.
136 */
137 void
138 ossl_curve448_scalar_sub(curve448_scalar_t out,
139 const curve448_scalar_t a, const curve448_scalar_t b);
140
141 /*
142 * Multiply two scalars. |a|, |b| and |out| may alias each other.
143 *
144 * a (in): One scalar.
145 * b (in): Another scalar.
146 * out (out): a*b.
147 */
148 void
149 ossl_curve448_scalar_mul(curve448_scalar_t out,
150 const curve448_scalar_t a, const curve448_scalar_t b);
151
152 /*
153 * Halve a scalar. |a| and |out| may alias each other.
154 *
155 * a (in): A scalar.
156 * out (out): a/2.
157 */
158 void
159 ossl_curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
160
161 /*
162 * Copy a scalar. The scalars may alias each other, in which case this
163 * function does nothing.
164 *
165 * a (in): A scalar.
166 * out (out): Will become a copy of a.
167 */
curve448_scalar_copy(curve448_scalar_t out,const curve448_scalar_t a)168 static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
169 const curve448_scalar_t a)
170 {
171 *out = *a;
172 }
173
174 /*
175 * Copy a point. The input and output may alias, in which case this function
176 * does nothing.
177 *
178 * a (out): A copy of the point.
179 * b (in): Any point.
180 */
curve448_point_copy(curve448_point_t a,const curve448_point_t b)181 static ossl_inline void curve448_point_copy(curve448_point_t a,
182 const curve448_point_t b)
183 {
184 *a = *b;
185 }
186
187 /*
188 * Test whether two points are equal. If yes, return C448_TRUE, else return
189 * C448_FALSE.
190 *
191 * a (in): A point.
192 * b (in): Another point.
193 *
194 * Returns:
195 * C448_TRUE: The points are equal.
196 * C448_FALSE: The points are not equal.
197 */
198 __owur c448_bool_t
199 ossl_curve448_point_eq(const curve448_point_t a,
200 const curve448_point_t b);
201
202 /*
203 * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
204 * faster.
205 *
206 * two_a (out): The sum a+a.
207 * a (in): A point.
208 */
209 void
210 ossl_curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
211
212 /*
213 * RFC 7748 Diffie-Hellman scalarmul. This function uses a different
214 * (non-Decaf) encoding.
215 *
216 * out (out): The scaled point base*scalar
217 * base (in): The point to be scaled.
218 * scalar (in): The scalar to multiply by.
219 *
220 * Returns:
221 * C448_SUCCESS: The scalarmul succeeded.
222 * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a
223 * small subgroup.
224 */
225 __owur c448_error_t
226 ossl_x448_int(uint8_t out[X448_PUBLIC_BYTES],
227 const uint8_t base[X448_PUBLIC_BYTES],
228 const uint8_t scalar[X448_PRIVATE_BYTES]);
229
230 /*
231 * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.
232 *
233 * This function is mainly used internally, but is exported in case
234 * it will be useful.
235 *
236 * The ratio is necessary because the internal representation doesn't
237 * track the cofactor information, so on output we must clear the cofactor.
238 * This would multiply by the cofactor, but in fact internally points are always
239 * even, so it multiplies by half the cofactor instead.
240 *
241 * As it happens, this aligns with the base point definitions; that is,
242 * if you pass the Decaf/Ristretto base point to this function, the result
243 * will be X448_ENCODE_RATIO times the X448
244 * base point.
245 *
246 * out (out): The scaled and encoded point.
247 * p (in): The point to be scaled and encoded.
248 */
249 void
250 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(
251 uint8_t out[X448_PUBLIC_BYTES],
252 const curve448_point_t p);
253
254 /*
255 * RFC 7748 Diffie-Hellman base point scalarmul. This function uses a different
256 * (non-Decaf) encoding.
257 *
258 * out (out): The scaled point base*scalar
259 * scalar (in): The scalar to multiply by.
260 */
261 void
262 ossl_x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],
263 const uint8_t scalar[X448_PRIVATE_BYTES]);
264
265 /*
266 * Multiply a precomputed base point by a scalar: out = scalar*base.
267 *
268 * scaled (out): The scaled point base*scalar
269 * base (in): The point to be scaled.
270 * scalar (in): The scalar to multiply by.
271 */
272 void
273 ossl_curve448_precomputed_scalarmul(curve448_point_t scaled,
274 const curve448_precomputed_s * base,
275 const curve448_scalar_t scalar);
276
277 /*
278 * Multiply two base points by two scalars:
279 * combo = scalar1*curve448_point_base + scalar2*base2.
280 *
281 * Otherwise equivalent to curve448_point_double_scalarmul, but may be
282 * faster at the expense of being variable time.
283 *
284 * combo (out): The linear combination scalar1*base + scalar2*base2.
285 * scalar1 (in): A first scalar to multiply by.
286 * base2 (in): A second point to be scaled.
287 * scalar2 (in) A second scalar to multiply by.
288 *
289 * Warning: This function takes variable time, and may leak the scalars used.
290 * It is designed for signature verification.
291 */
292 void
293 ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
294 const curve448_scalar_t scalar1,
295 const curve448_point_t base2,
296 const curve448_scalar_t scalar2);
297
298 /*
299 * Test that a point is valid, for debugging purposes.
300 *
301 * to_test (in): The point to test.
302 *
303 * Returns:
304 * C448_TRUE The point is valid.
305 * C448_FALSE The point is invalid.
306 */
307 __owur c448_bool_t
308 ossl_curve448_point_valid(const curve448_point_t to_test);
309
310 /* Overwrite scalar with zeros. */
311 void ossl_curve448_scalar_destroy(curve448_scalar_t scalar);
312
313 /* Overwrite point with zeros. */
314 void ossl_curve448_point_destroy(curve448_point_t point);
315
316 #endif /* OSSL_CRYPTO_EC_CURVE448_POINT_448_H */
317