Coverage Report

Created: 2025-07-01 06:54

/work/mbedtls-2.28.8/library/ecp.c
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1
/*
2
 *  Elliptic curves over GF(p): generic functions
3
 *
4
 *  Copyright The Mbed TLS Contributors
5
 *  SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
6
 */
7
8
/*
9
 * References:
10
 *
11
 * SEC1 https://www.secg.org/sec1-v2.pdf
12
 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
13
 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
14
 * RFC 4492 for the related TLS structures and constants
15
 * - https://www.rfc-editor.org/rfc/rfc4492
16
 * RFC 7748 for the Curve448 and Curve25519 curve definitions
17
 * - https://www.rfc-editor.org/rfc/rfc7748
18
 *
19
 * [Curve25519] https://cr.yp.to/ecdh/curve25519-20060209.pdf
20
 *
21
 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
22
 *     for elliptic curve cryptosystems. In : Cryptographic Hardware and
23
 *     Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
24
 *     <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
25
 *
26
 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
27
 *     render ECC resistant against Side Channel Attacks. IACR Cryptology
28
 *     ePrint Archive, 2004, vol. 2004, p. 342.
29
 *     <http://eprint.iacr.org/2004/342.pdf>
30
 */
31
32
#include "common.h"
33
34
/**
35
 * \brief Function level alternative implementation.
36
 *
37
 * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
38
 * replace certain functions in this module. The alternative implementations are
39
 * typically hardware accelerators and need to activate the hardware before the
40
 * computation starts and deactivate it after it finishes. The
41
 * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
42
 * this purpose.
43
 *
44
 * To preserve the correct functionality the following conditions must hold:
45
 *
46
 * - The alternative implementation must be activated by
47
 *   mbedtls_internal_ecp_init() before any of the replaceable functions is
48
 *   called.
49
 * - mbedtls_internal_ecp_free() must \b only be called when the alternative
50
 *   implementation is activated.
51
 * - mbedtls_internal_ecp_init() must \b not be called when the alternative
52
 *   implementation is activated.
53
 * - Public functions must not return while the alternative implementation is
54
 *   activated.
55
 * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
56
 *   before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
57
 *   \endcode ensures that the alternative implementation supports the current
58
 *   group.
59
 */
60
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
61
#endif
62
63
#if defined(MBEDTLS_ECP_C)
64
65
#include "mbedtls/ecp.h"
66
#include "mbedtls/threading.h"
67
#include "mbedtls/platform_util.h"
68
#include "mbedtls/error.h"
69
#include "mbedtls/bn_mul.h"
70
71
#include "ecp_invasive.h"
72
73
#include <string.h>
74
75
#if !defined(MBEDTLS_ECP_ALT)
76
77
/* Parameter validation macros based on platform_util.h */
78
#define ECP_VALIDATE_RET(cond)    \
79
0
    MBEDTLS_INTERNAL_VALIDATE_RET(cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA)
80
#define ECP_VALIDATE(cond)        \
81
0
    MBEDTLS_INTERNAL_VALIDATE(cond)
82
83
#include "mbedtls/platform.h"
84
85
#include "mbedtls/ecp_internal.h"
86
87
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
88
#if defined(MBEDTLS_HMAC_DRBG_C)
89
#include "mbedtls/hmac_drbg.h"
90
#elif defined(MBEDTLS_CTR_DRBG_C)
91
#include "mbedtls/ctr_drbg.h"
92
#else
93
#error \
94
    "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
95
#endif
96
#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
97
98
#if defined(MBEDTLS_SELF_TEST)
99
/*
100
 * Counts of point addition and doubling, and field multiplications.
101
 * Used to test resistance of point multiplication to simple timing attacks.
102
 */
103
static unsigned long add_count, dbl_count, mul_count;
104
#endif
105
106
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
107
/*
108
 * Currently ecp_mul() takes a RNG function as an argument, used for
109
 * side-channel protection, but it can be NULL. The initial reasoning was
110
 * that people will pass non-NULL RNG when they care about side-channels, but
111
 * unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with
112
 * no opportunity for the user to do anything about it.
113
 *
114
 * The obvious strategies for addressing that include:
115
 * - change those APIs so that they take RNG arguments;
116
 * - require a global RNG to be available to all crypto modules.
117
 *
118
 * Unfortunately those would break compatibility. So what we do instead is
119
 * have our own internal DRBG instance, seeded from the secret scalar.
120
 *
121
 * The following is a light-weight abstraction layer for doing that with
122
 * HMAC_DRBG (first choice) or CTR_DRBG.
123
 */
124
125
#if defined(MBEDTLS_HMAC_DRBG_C)
126
127
/* DRBG context type */
128
typedef mbedtls_hmac_drbg_context ecp_drbg_context;
129
130
/* DRBG context init */
131
static inline void ecp_drbg_init(ecp_drbg_context *ctx)
132
0
{
133
0
    mbedtls_hmac_drbg_init(ctx);
134
0
}
135
136
/* DRBG context free */
137
static inline void ecp_drbg_free(ecp_drbg_context *ctx)
138
0
{
139
0
    mbedtls_hmac_drbg_free(ctx);
140
0
}
141
142
/* DRBG function */
143
static inline int ecp_drbg_random(void *p_rng,
144
                                  unsigned char *output, size_t output_len)
145
0
{
146
0
    return mbedtls_hmac_drbg_random(p_rng, output, output_len);
147
0
}
148
149
/* DRBG context seeding */
150
static int ecp_drbg_seed(ecp_drbg_context *ctx,
151
                         const mbedtls_mpi *secret, size_t secret_len)
152
0
{
153
0
    int ret;
154
0
    unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
155
    /* The list starts with strong hashes */
156
0
    const mbedtls_md_type_t md_type =
157
0
        (mbedtls_md_type_t) (mbedtls_md_list()[0]);
158
0
    const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type(md_type);
159
160
0
    if (secret_len > MBEDTLS_ECP_MAX_BYTES) {
161
0
        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
162
0
        goto cleanup;
163
0
    }
164
165
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(secret,
166
0
                                             secret_bytes, secret_len));
167
168
0
    ret = mbedtls_hmac_drbg_seed_buf(ctx, md_info, secret_bytes, secret_len);
169
170
0
cleanup:
171
0
    mbedtls_platform_zeroize(secret_bytes, secret_len);
172
173
0
    return ret;
174
0
}
175
176
#elif defined(MBEDTLS_CTR_DRBG_C)
177
178
/* DRBG context type */
179
typedef mbedtls_ctr_drbg_context ecp_drbg_context;
180
181
/* DRBG context init */
182
static inline void ecp_drbg_init(ecp_drbg_context *ctx)
183
{
184
    mbedtls_ctr_drbg_init(ctx);
185
}
186
187
/* DRBG context free */
188
static inline void ecp_drbg_free(ecp_drbg_context *ctx)
189
{
190
    mbedtls_ctr_drbg_free(ctx);
191
}
192
193
/* DRBG function */
194
static inline int ecp_drbg_random(void *p_rng,
195
                                  unsigned char *output, size_t output_len)
196
{
197
    return mbedtls_ctr_drbg_random(p_rng, output, output_len);
198
}
199
200
/*
201
 * Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does,
202
 * we need to pass an entropy function when seeding. So we use a dummy
203
 * function for that, and pass the actual entropy as customisation string.
204
 * (During seeding of CTR_DRBG the entropy input and customisation string are
205
 * concatenated before being used to update the secret state.)
206
 */
207
static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len)
208
{
209
    (void) ctx;
210
    memset(out, 0, len);
211
    return 0;
212
}
213
214
/* DRBG context seeding */
215
static int ecp_drbg_seed(ecp_drbg_context *ctx,
216
                         const mbedtls_mpi *secret, size_t secret_len)
217
{
218
    int ret;
219
    unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES];
220
221
    if (secret_len > MBEDTLS_ECP_MAX_BYTES) {
222
        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
223
        goto cleanup;
224
    }
225
226
    MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(secret,
227
                                             secret_bytes, secret_len));
228
229
    ret = mbedtls_ctr_drbg_seed(ctx, ecp_ctr_drbg_null_entropy, NULL,
230
                                secret_bytes, secret_len);
231
232
cleanup:
233
    mbedtls_platform_zeroize(secret_bytes, secret_len);
234
235
    return ret;
236
}
237
238
#else
239
#error \
240
    "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid."
241
#endif /* DRBG modules */
242
#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */
243
244
#if defined(MBEDTLS_ECP_RESTARTABLE)
245
/*
246
 * Maximum number of "basic operations" to be done in a row.
247
 *
248
 * Default value 0 means that ECC operations will not yield.
249
 * Note that regardless of the value of ecp_max_ops, always at
250
 * least one step is performed before yielding.
251
 *
252
 * Setting ecp_max_ops=1 can be suitable for testing purposes
253
 * as it will interrupt computation at all possible points.
254
 */
255
static unsigned ecp_max_ops = 0;
256
257
/*
258
 * Set ecp_max_ops
259
 */
260
void mbedtls_ecp_set_max_ops(unsigned max_ops)
261
{
262
    ecp_max_ops = max_ops;
263
}
264
265
/*
266
 * Check if restart is enabled
267
 */
268
int mbedtls_ecp_restart_is_enabled(void)
269
{
270
    return ecp_max_ops != 0;
271
}
272
273
/*
274
 * Restart sub-context for ecp_mul_comb()
275
 */
276
struct mbedtls_ecp_restart_mul {
277
    mbedtls_ecp_point R;    /* current intermediate result                  */
278
    size_t i;               /* current index in various loops, 0 outside    */
279
    mbedtls_ecp_point *T;   /* table for precomputed points                 */
280
    unsigned char T_size;   /* number of points in table T                  */
281
    enum {                  /* what were we doing last time we returned?    */
282
        ecp_rsm_init = 0,       /* nothing so far, dummy initial state      */
283
        ecp_rsm_pre_dbl,        /* precompute 2^n multiples                 */
284
        ecp_rsm_pre_norm_dbl,   /* normalize precomputed 2^n multiples      */
285
        ecp_rsm_pre_add,        /* precompute remaining points by adding    */
286
        ecp_rsm_pre_norm_add,   /* normalize all precomputed points         */
287
        ecp_rsm_comb_core,      /* ecp_mul_comb_core()                      */
288
        ecp_rsm_final_norm,     /* do the final normalization               */
289
    } state;
290
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
291
    ecp_drbg_context drbg_ctx;
292
    unsigned char drbg_seeded;
293
#endif
294
};
295
296
/*
297
 * Init restart_mul sub-context
298
 */
299
static void ecp_restart_rsm_init(mbedtls_ecp_restart_mul_ctx *ctx)
300
{
301
    mbedtls_ecp_point_init(&ctx->R);
302
    ctx->i = 0;
303
    ctx->T = NULL;
304
    ctx->T_size = 0;
305
    ctx->state = ecp_rsm_init;
306
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
307
    ecp_drbg_init(&ctx->drbg_ctx);
308
    ctx->drbg_seeded = 0;
309
#endif
310
}
311
312
/*
313
 * Free the components of a restart_mul sub-context
314
 */
315
static void ecp_restart_rsm_free(mbedtls_ecp_restart_mul_ctx *ctx)
316
{
317
    unsigned char i;
318
319
    if (ctx == NULL) {
320
        return;
321
    }
322
323
    mbedtls_ecp_point_free(&ctx->R);
324
325
    if (ctx->T != NULL) {
326
        for (i = 0; i < ctx->T_size; i++) {
327
            mbedtls_ecp_point_free(ctx->T + i);
328
        }
329
        mbedtls_free(ctx->T);
330
    }
331
332
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
333
    ecp_drbg_free(&ctx->drbg_ctx);
334
#endif
335
336
    ecp_restart_rsm_init(ctx);
337
}
338
339
/*
340
 * Restart context for ecp_muladd()
341
 */
342
struct mbedtls_ecp_restart_muladd {
343
    mbedtls_ecp_point mP;       /* mP value                             */
344
    mbedtls_ecp_point R;        /* R intermediate result                */
345
    enum {                      /* what should we do next?              */
346
        ecp_rsma_mul1 = 0,      /* first multiplication                 */
347
        ecp_rsma_mul2,          /* second multiplication                */
348
        ecp_rsma_add,           /* addition                             */
349
        ecp_rsma_norm,          /* normalization                        */
350
    } state;
351
};
352
353
/*
354
 * Init restart_muladd sub-context
355
 */
356
static void ecp_restart_ma_init(mbedtls_ecp_restart_muladd_ctx *ctx)
357
{
358
    mbedtls_ecp_point_init(&ctx->mP);
359
    mbedtls_ecp_point_init(&ctx->R);
360
    ctx->state = ecp_rsma_mul1;
361
}
362
363
/*
364
 * Free the components of a restart_muladd sub-context
365
 */
366
static void ecp_restart_ma_free(mbedtls_ecp_restart_muladd_ctx *ctx)
367
{
368
    if (ctx == NULL) {
369
        return;
370
    }
371
372
    mbedtls_ecp_point_free(&ctx->mP);
373
    mbedtls_ecp_point_free(&ctx->R);
374
375
    ecp_restart_ma_init(ctx);
376
}
377
378
/*
379
 * Initialize a restart context
380
 */
381
void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx *ctx)
382
{
383
    ECP_VALIDATE(ctx != NULL);
384
    ctx->ops_done = 0;
385
    ctx->depth = 0;
386
    ctx->rsm = NULL;
387
    ctx->ma = NULL;
388
}
389
390
/*
391
 * Free the components of a restart context
392
 */
393
void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx *ctx)
394
{
395
    if (ctx == NULL) {
396
        return;
397
    }
398
399
    ecp_restart_rsm_free(ctx->rsm);
400
    mbedtls_free(ctx->rsm);
401
402
    ecp_restart_ma_free(ctx->ma);
403
    mbedtls_free(ctx->ma);
404
405
    mbedtls_ecp_restart_init(ctx);
406
}
407
408
/*
409
 * Check if we can do the next step
410
 */
411
int mbedtls_ecp_check_budget(const mbedtls_ecp_group *grp,
412
                             mbedtls_ecp_restart_ctx *rs_ctx,
413
                             unsigned ops)
414
{
415
    ECP_VALIDATE_RET(grp != NULL);
416
417
    if (rs_ctx != NULL && ecp_max_ops != 0) {
418
        /* scale depending on curve size: the chosen reference is 256-bit,
419
         * and multiplication is quadratic. Round to the closest integer. */
420
        if (grp->pbits >= 512) {
421
            ops *= 4;
422
        } else if (grp->pbits >= 384) {
423
            ops *= 2;
424
        }
425
426
        /* Avoid infinite loops: always allow first step.
427
         * Because of that, however, it's not generally true
428
         * that ops_done <= ecp_max_ops, so the check
429
         * ops_done > ecp_max_ops below is mandatory. */
430
        if ((rs_ctx->ops_done != 0) &&
431
            (rs_ctx->ops_done > ecp_max_ops ||
432
             ops > ecp_max_ops - rs_ctx->ops_done)) {
433
            return MBEDTLS_ERR_ECP_IN_PROGRESS;
434
        }
435
436
        /* update running count */
437
        rs_ctx->ops_done += ops;
438
    }
439
440
    return 0;
441
}
442
443
/* Call this when entering a function that needs its own sub-context */
444
#define ECP_RS_ENTER(SUB)   do {                                      \
445
        /* reset ops count for this call if top-level */                    \
446
        if (rs_ctx != NULL && rs_ctx->depth++ == 0)                        \
447
        rs_ctx->ops_done = 0;                                           \
448
                                                                        \
449
        /* set up our own sub-context if needed */                          \
450
        if (mbedtls_ecp_restart_is_enabled() &&                             \
451
            rs_ctx != NULL && rs_ctx->SUB == NULL)                         \
452
        {                                                                   \
453
            rs_ctx->SUB = mbedtls_calloc(1, sizeof(*rs_ctx->SUB));      \
454
            if (rs_ctx->SUB == NULL)                                       \
455
            return MBEDTLS_ERR_ECP_ALLOC_FAILED;                     \
456
                                                                      \
457
            ecp_restart_## SUB ##_init(rs_ctx->SUB);                      \
458
        }                                                                   \
459
} while (0)
460
461
/* Call this when leaving a function that needs its own sub-context */
462
#define ECP_RS_LEAVE(SUB)   do {                                      \
463
        /* clear our sub-context when not in progress (done or error) */    \
464
        if (rs_ctx != NULL && rs_ctx->SUB != NULL &&                        \
465
            ret != MBEDTLS_ERR_ECP_IN_PROGRESS)                            \
466
        {                                                                   \
467
            ecp_restart_## SUB ##_free(rs_ctx->SUB);                      \
468
            mbedtls_free(rs_ctx->SUB);                                    \
469
            rs_ctx->SUB = NULL;                                             \
470
        }                                                                   \
471
                                                                        \
472
        if (rs_ctx != NULL)                                                \
473
        rs_ctx->depth--;                                                \
474
} while (0)
475
476
#else /* MBEDTLS_ECP_RESTARTABLE */
477
478
0
#define ECP_RS_ENTER(sub)     (void) rs_ctx;
479
0
#define ECP_RS_LEAVE(sub)     (void) rs_ctx;
480
481
#endif /* MBEDTLS_ECP_RESTARTABLE */
482
483
/*
484
 * List of supported curves:
485
 *  - internal ID
486
 *  - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7)
487
 *  - size in bits
488
 *  - readable name
489
 *
490
 * Curves are listed in order: largest curves first, and for a given size,
491
 * fastest curves first. This provides the default order for the SSL module.
492
 *
493
 * Reminder: update profiles in x509_crt.c when adding a new curves!
494
 */
495
static const mbedtls_ecp_curve_info ecp_supported_curves[] =
496
{
497
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
498
    { MBEDTLS_ECP_DP_SECP521R1,    25,     521,    "secp521r1"         },
499
#endif
500
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
501
    { MBEDTLS_ECP_DP_BP512R1,      28,     512,    "brainpoolP512r1"   },
502
#endif
503
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
504
    { MBEDTLS_ECP_DP_SECP384R1,    24,     384,    "secp384r1"         },
505
#endif
506
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
507
    { MBEDTLS_ECP_DP_BP384R1,      27,     384,    "brainpoolP384r1"   },
508
#endif
509
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
510
    { MBEDTLS_ECP_DP_SECP256R1,    23,     256,    "secp256r1"         },
511
#endif
512
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
513
    { MBEDTLS_ECP_DP_SECP256K1,    22,     256,    "secp256k1"         },
514
#endif
515
#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
516
    { MBEDTLS_ECP_DP_BP256R1,      26,     256,    "brainpoolP256r1"   },
517
#endif
518
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
519
    { MBEDTLS_ECP_DP_SECP224R1,    21,     224,    "secp224r1"         },
520
#endif
521
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
522
    { MBEDTLS_ECP_DP_SECP224K1,    20,     224,    "secp224k1"         },
523
#endif
524
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
525
    { MBEDTLS_ECP_DP_SECP192R1,    19,     192,    "secp192r1"         },
526
#endif
527
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
528
    { MBEDTLS_ECP_DP_SECP192K1,    18,     192,    "secp192k1"         },
529
#endif
530
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
531
    { MBEDTLS_ECP_DP_CURVE25519,   29,     256,    "x25519"            },
532
#endif
533
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
534
    { MBEDTLS_ECP_DP_CURVE448,     30,     448,    "x448"              },
535
#endif
536
    { MBEDTLS_ECP_DP_NONE,          0,     0,      NULL                },
537
};
538
539
#define ECP_NB_CURVES   sizeof(ecp_supported_curves) /    \
540
    sizeof(ecp_supported_curves[0])
541
542
static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
543
544
/*
545
 * List of supported curves and associated info
546
 */
547
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list(void)
548
0
{
549
0
    return ecp_supported_curves;
550
0
}
551
552
/*
553
 * List of supported curves, group ID only
554
 */
555
const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list(void)
556
0
{
557
0
    static int init_done = 0;
558
559
0
    if (!init_done) {
560
0
        size_t i = 0;
561
0
        const mbedtls_ecp_curve_info *curve_info;
562
563
0
        for (curve_info = mbedtls_ecp_curve_list();
564
0
             curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
565
0
             curve_info++) {
566
0
            ecp_supported_grp_id[i++] = curve_info->grp_id;
567
0
        }
568
0
        ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
569
570
0
        init_done = 1;
571
0
    }
572
573
0
    return ecp_supported_grp_id;
574
0
}
575
576
/*
577
 * Get the curve info for the internal identifier
578
 */
579
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id)
580
0
{
581
0
    const mbedtls_ecp_curve_info *curve_info;
582
583
0
    for (curve_info = mbedtls_ecp_curve_list();
584
0
         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
585
0
         curve_info++) {
586
0
        if (curve_info->grp_id == grp_id) {
587
0
            return curve_info;
588
0
        }
589
0
    }
590
591
0
    return NULL;
592
0
}
593
594
/*
595
 * Get the curve info from the TLS identifier
596
 */
597
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id)
598
0
{
599
0
    const mbedtls_ecp_curve_info *curve_info;
600
601
0
    for (curve_info = mbedtls_ecp_curve_list();
602
0
         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
603
0
         curve_info++) {
604
0
        if (curve_info->tls_id == tls_id) {
605
0
            return curve_info;
606
0
        }
607
0
    }
608
609
0
    return NULL;
610
0
}
611
612
/*
613
 * Get the curve info from the name
614
 */
615
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name(const char *name)
616
0
{
617
0
    const mbedtls_ecp_curve_info *curve_info;
618
619
0
    if (name == NULL) {
620
0
        return NULL;
621
0
    }
622
623
0
    for (curve_info = mbedtls_ecp_curve_list();
624
0
         curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
625
0
         curve_info++) {
626
0
        if (strcmp(curve_info->name, name) == 0) {
627
0
            return curve_info;
628
0
        }
629
0
    }
630
631
0
    return NULL;
632
0
}
633
634
/*
635
 * Get the type of a curve
636
 */
637
mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group *grp)
638
0
{
639
0
    if (grp->G.X.p == NULL) {
640
0
        return MBEDTLS_ECP_TYPE_NONE;
641
0
    }
642
643
0
    if (grp->G.Y.p == NULL) {
644
0
        return MBEDTLS_ECP_TYPE_MONTGOMERY;
645
0
    } else {
646
0
        return MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS;
647
0
    }
648
0
}
649
650
/*
651
 * Initialize (the components of) a point
652
 */
653
void mbedtls_ecp_point_init(mbedtls_ecp_point *pt)
654
0
{
655
0
    ECP_VALIDATE(pt != NULL);
656
657
0
    mbedtls_mpi_init(&pt->X);
658
0
    mbedtls_mpi_init(&pt->Y);
659
0
    mbedtls_mpi_init(&pt->Z);
660
0
}
661
662
/*
663
 * Initialize (the components of) a group
664
 */
665
void mbedtls_ecp_group_init(mbedtls_ecp_group *grp)
666
0
{
667
0
    ECP_VALIDATE(grp != NULL);
668
669
0
    grp->id = MBEDTLS_ECP_DP_NONE;
670
0
    mbedtls_mpi_init(&grp->P);
671
0
    mbedtls_mpi_init(&grp->A);
672
0
    mbedtls_mpi_init(&grp->B);
673
0
    mbedtls_ecp_point_init(&grp->G);
674
0
    mbedtls_mpi_init(&grp->N);
675
0
    grp->pbits = 0;
676
0
    grp->nbits = 0;
677
0
    grp->h = 0;
678
0
    grp->modp = NULL;
679
0
    grp->t_pre = NULL;
680
0
    grp->t_post = NULL;
681
0
    grp->t_data = NULL;
682
0
    grp->T = NULL;
683
0
    grp->T_size = 0;
684
0
}
685
686
/*
687
 * Initialize (the components of) a key pair
688
 */
689
void mbedtls_ecp_keypair_init(mbedtls_ecp_keypair *key)
690
0
{
691
0
    ECP_VALIDATE(key != NULL);
692
693
0
    mbedtls_ecp_group_init(&key->grp);
694
0
    mbedtls_mpi_init(&key->d);
695
0
    mbedtls_ecp_point_init(&key->Q);
696
0
}
697
698
/*
699
 * Unallocate (the components of) a point
700
 */
701
void mbedtls_ecp_point_free(mbedtls_ecp_point *pt)
702
0
{
703
0
    if (pt == NULL) {
704
0
        return;
705
0
    }
706
707
0
    mbedtls_mpi_free(&(pt->X));
708
0
    mbedtls_mpi_free(&(pt->Y));
709
0
    mbedtls_mpi_free(&(pt->Z));
710
0
}
711
712
/*
713
 * Unallocate (the components of) a group
714
 */
715
void mbedtls_ecp_group_free(mbedtls_ecp_group *grp)
716
0
{
717
0
    size_t i;
718
719
0
    if (grp == NULL) {
720
0
        return;
721
0
    }
722
723
0
    if (grp->h != 1) {
724
0
        mbedtls_mpi_free(&grp->P);
725
0
        mbedtls_mpi_free(&grp->A);
726
0
        mbedtls_mpi_free(&grp->B);
727
0
        mbedtls_ecp_point_free(&grp->G);
728
0
        mbedtls_mpi_free(&grp->N);
729
0
    }
730
731
0
    if (grp->T != NULL) {
732
0
        for (i = 0; i < grp->T_size; i++) {
733
0
            mbedtls_ecp_point_free(&grp->T[i]);
734
0
        }
735
0
        mbedtls_free(grp->T);
736
0
    }
737
738
0
    mbedtls_platform_zeroize(grp, sizeof(mbedtls_ecp_group));
739
0
}
740
741
/*
742
 * Unallocate (the components of) a key pair
743
 */
744
void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair *key)
745
0
{
746
0
    if (key == NULL) {
747
0
        return;
748
0
    }
749
750
0
    mbedtls_ecp_group_free(&key->grp);
751
0
    mbedtls_mpi_free(&key->d);
752
0
    mbedtls_ecp_point_free(&key->Q);
753
0
}
754
755
/*
756
 * Copy the contents of a point
757
 */
758
int mbedtls_ecp_copy(mbedtls_ecp_point *P, const mbedtls_ecp_point *Q)
759
0
{
760
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
761
0
    ECP_VALIDATE_RET(P != NULL);
762
0
    ECP_VALIDATE_RET(Q != NULL);
763
764
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->X, &Q->X));
765
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Y, &Q->Y));
766
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&P->Z, &Q->Z));
767
768
0
cleanup:
769
0
    return ret;
770
0
}
771
772
/*
773
 * Copy the contents of a group object
774
 */
775
int mbedtls_ecp_group_copy(mbedtls_ecp_group *dst, const mbedtls_ecp_group *src)
776
0
{
777
0
    ECP_VALIDATE_RET(dst != NULL);
778
0
    ECP_VALIDATE_RET(src != NULL);
779
780
0
    return mbedtls_ecp_group_load(dst, src->id);
781
0
}
782
783
/*
784
 * Set point to zero
785
 */
786
int mbedtls_ecp_set_zero(mbedtls_ecp_point *pt)
787
0
{
788
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
789
0
    ECP_VALIDATE_RET(pt != NULL);
790
791
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->X, 1));
792
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Y, 1));
793
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 0));
794
795
0
cleanup:
796
0
    return ret;
797
0
}
798
799
/*
800
 * Tell if a point is zero
801
 */
802
int mbedtls_ecp_is_zero(mbedtls_ecp_point *pt)
803
0
{
804
0
    ECP_VALIDATE_RET(pt != NULL);
805
806
0
    return mbedtls_mpi_cmp_int(&pt->Z, 0) == 0;
807
0
}
808
809
/*
810
 * Compare two points lazily
811
 */
812
int mbedtls_ecp_point_cmp(const mbedtls_ecp_point *P,
813
                          const mbedtls_ecp_point *Q)
814
0
{
815
0
    ECP_VALIDATE_RET(P != NULL);
816
0
    ECP_VALIDATE_RET(Q != NULL);
817
818
0
    if (mbedtls_mpi_cmp_mpi(&P->X, &Q->X) == 0 &&
819
0
        mbedtls_mpi_cmp_mpi(&P->Y, &Q->Y) == 0 &&
820
0
        mbedtls_mpi_cmp_mpi(&P->Z, &Q->Z) == 0) {
821
0
        return 0;
822
0
    }
823
824
0
    return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
825
0
}
826
827
/*
828
 * Import a non-zero point from ASCII strings
829
 */
830
int mbedtls_ecp_point_read_string(mbedtls_ecp_point *P, int radix,
831
                                  const char *x, const char *y)
832
0
{
833
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
834
0
    ECP_VALIDATE_RET(P != NULL);
835
0
    ECP_VALIDATE_RET(x != NULL);
836
0
    ECP_VALIDATE_RET(y != NULL);
837
838
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->X, radix, x));
839
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&P->Y, radix, y));
840
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1));
841
842
0
cleanup:
843
0
    return ret;
844
0
}
845
846
/*
847
 * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748)
848
 */
849
int mbedtls_ecp_point_write_binary(const mbedtls_ecp_group *grp,
850
                                   const mbedtls_ecp_point *P,
851
                                   int format, size_t *olen,
852
                                   unsigned char *buf, size_t buflen)
853
0
{
854
0
    int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
855
0
    size_t plen;
856
0
    ECP_VALIDATE_RET(grp  != NULL);
857
0
    ECP_VALIDATE_RET(P    != NULL);
858
0
    ECP_VALIDATE_RET(olen != NULL);
859
0
    ECP_VALIDATE_RET(buf  != NULL);
860
0
    ECP_VALIDATE_RET(format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
861
0
                     format == MBEDTLS_ECP_PF_COMPRESSED);
862
863
0
    plen = mbedtls_mpi_size(&grp->P);
864
865
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
866
0
    (void) format; /* Montgomery curves always use the same point format */
867
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
868
0
        *olen = plen;
869
0
        if (buflen < *olen) {
870
0
            return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
871
0
        }
872
873
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&P->X, buf, plen));
874
0
    }
875
0
#endif
876
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
877
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
878
        /*
879
         * Common case: P == 0
880
         */
881
0
        if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) {
882
0
            if (buflen < 1) {
883
0
                return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
884
0
            }
885
886
0
            buf[0] = 0x00;
887
0
            *olen = 1;
888
889
0
            return 0;
890
0
        }
891
892
0
        if (format == MBEDTLS_ECP_PF_UNCOMPRESSED) {
893
0
            *olen = 2 * plen + 1;
894
895
0
            if (buflen < *olen) {
896
0
                return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
897
0
            }
898
899
0
            buf[0] = 0x04;
900
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen));
901
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->Y, buf + 1 + plen, plen));
902
0
        } else if (format == MBEDTLS_ECP_PF_COMPRESSED) {
903
0
            *olen = plen + 1;
904
905
0
            if (buflen < *olen) {
906
0
                return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
907
0
            }
908
909
0
            buf[0] = 0x02 + mbedtls_mpi_get_bit(&P->Y, 0);
910
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&P->X, buf + 1, plen));
911
0
        }
912
0
    }
913
0
#endif
914
915
0
cleanup:
916
0
    return ret;
917
0
}
918
919
/*
920
 * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
921
 */
922
int mbedtls_ecp_point_read_binary(const mbedtls_ecp_group *grp,
923
                                  mbedtls_ecp_point *pt,
924
                                  const unsigned char *buf, size_t ilen)
925
0
{
926
0
    int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
927
0
    size_t plen;
928
0
    ECP_VALIDATE_RET(grp != NULL);
929
0
    ECP_VALIDATE_RET(pt  != NULL);
930
0
    ECP_VALIDATE_RET(ilen == 0 || buf != NULL);
931
932
0
    if (ilen < 1) {
933
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
934
0
    }
935
936
0
    plen = mbedtls_mpi_size(&grp->P);
937
938
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
939
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
940
0
        if (plen != ilen) {
941
0
            return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
942
0
        }
943
944
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&pt->X, buf, plen));
945
0
        mbedtls_mpi_free(&pt->Y);
946
947
0
        if (grp->id == MBEDTLS_ECP_DP_CURVE25519) {
948
            /* Set most significant bit to 0 as prescribed in RFC7748 §5 */
949
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&pt->X, plen * 8 - 1, 0));
950
0
        }
951
952
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1));
953
0
    }
954
0
#endif
955
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
956
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
957
0
        if (buf[0] == 0x00) {
958
0
            if (ilen == 1) {
959
0
                return mbedtls_ecp_set_zero(pt);
960
0
            } else {
961
0
                return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
962
0
            }
963
0
        }
964
965
0
        if (buf[0] != 0x04) {
966
0
            return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
967
0
        }
968
969
0
        if (ilen != 2 * plen + 1) {
970
0
            return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
971
0
        }
972
973
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->X, buf + 1, plen));
974
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&pt->Y,
975
0
                                                buf + 1 + plen, plen));
976
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1));
977
0
    }
978
0
#endif
979
980
0
cleanup:
981
0
    return ret;
982
0
}
983
984
/*
985
 * Import a point from a TLS ECPoint record (RFC 4492)
986
 *      struct {
987
 *          opaque point <1..2^8-1>;
988
 *      } ECPoint;
989
 */
990
int mbedtls_ecp_tls_read_point(const mbedtls_ecp_group *grp,
991
                               mbedtls_ecp_point *pt,
992
                               const unsigned char **buf, size_t buf_len)
993
0
{
994
0
    unsigned char data_len;
995
0
    const unsigned char *buf_start;
996
0
    ECP_VALIDATE_RET(grp != NULL);
997
0
    ECP_VALIDATE_RET(pt  != NULL);
998
0
    ECP_VALIDATE_RET(buf != NULL);
999
0
    ECP_VALIDATE_RET(buf_len == 0 || *buf != NULL);
1000
1001
    /*
1002
     * We must have at least two bytes (1 for length, at least one for data)
1003
     */
1004
0
    if (buf_len < 2) {
1005
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1006
0
    }
1007
1008
0
    data_len = *(*buf)++;
1009
0
    if (data_len < 1 || data_len > buf_len - 1) {
1010
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1011
0
    }
1012
1013
    /*
1014
     * Save buffer start for read_binary and update buf
1015
     */
1016
0
    buf_start = *buf;
1017
0
    *buf += data_len;
1018
1019
0
    return mbedtls_ecp_point_read_binary(grp, pt, buf_start, data_len);
1020
0
}
1021
1022
/*
1023
 * Export a point as a TLS ECPoint record (RFC 4492)
1024
 *      struct {
1025
 *          opaque point <1..2^8-1>;
1026
 *      } ECPoint;
1027
 */
1028
int mbedtls_ecp_tls_write_point(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
1029
                                int format, size_t *olen,
1030
                                unsigned char *buf, size_t blen)
1031
0
{
1032
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1033
0
    ECP_VALIDATE_RET(grp  != NULL);
1034
0
    ECP_VALIDATE_RET(pt   != NULL);
1035
0
    ECP_VALIDATE_RET(olen != NULL);
1036
0
    ECP_VALIDATE_RET(buf  != NULL);
1037
0
    ECP_VALIDATE_RET(format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
1038
0
                     format == MBEDTLS_ECP_PF_COMPRESSED);
1039
1040
    /*
1041
     * buffer length must be at least one, for our length byte
1042
     */
1043
0
    if (blen < 1) {
1044
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1045
0
    }
1046
1047
0
    if ((ret = mbedtls_ecp_point_write_binary(grp, pt, format,
1048
0
                                              olen, buf + 1, blen - 1)) != 0) {
1049
0
        return ret;
1050
0
    }
1051
1052
    /*
1053
     * write length to the first byte and update total length
1054
     */
1055
0
    buf[0] = (unsigned char) *olen;
1056
0
    ++*olen;
1057
1058
0
    return 0;
1059
0
}
1060
1061
/*
1062
 * Set a group from an ECParameters record (RFC 4492)
1063
 */
1064
int mbedtls_ecp_tls_read_group(mbedtls_ecp_group *grp,
1065
                               const unsigned char **buf, size_t len)
1066
0
{
1067
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1068
0
    mbedtls_ecp_group_id grp_id;
1069
0
    ECP_VALIDATE_RET(grp  != NULL);
1070
0
    ECP_VALIDATE_RET(buf  != NULL);
1071
0
    ECP_VALIDATE_RET(len == 0 || *buf != NULL);
1072
1073
0
    if ((ret = mbedtls_ecp_tls_read_group_id(&grp_id, buf, len)) != 0) {
1074
0
        return ret;
1075
0
    }
1076
1077
0
    return mbedtls_ecp_group_load(grp, grp_id);
1078
0
}
1079
1080
/*
1081
 * Read a group id from an ECParameters record (RFC 4492) and convert it to
1082
 * mbedtls_ecp_group_id.
1083
 */
1084
int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id *grp,
1085
                                  const unsigned char **buf, size_t len)
1086
0
{
1087
0
    uint16_t tls_id;
1088
0
    const mbedtls_ecp_curve_info *curve_info;
1089
0
    ECP_VALIDATE_RET(grp  != NULL);
1090
0
    ECP_VALIDATE_RET(buf  != NULL);
1091
0
    ECP_VALIDATE_RET(len == 0 || *buf != NULL);
1092
1093
    /*
1094
     * We expect at least three bytes (see below)
1095
     */
1096
0
    if (len < 3) {
1097
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1098
0
    }
1099
1100
    /*
1101
     * First byte is curve_type; only named_curve is handled
1102
     */
1103
0
    if (*(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE) {
1104
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1105
0
    }
1106
1107
    /*
1108
     * Next two bytes are the namedcurve value
1109
     */
1110
0
    tls_id = *(*buf)++;
1111
0
    tls_id <<= 8;
1112
0
    tls_id |= *(*buf)++;
1113
1114
0
    if ((curve_info = mbedtls_ecp_curve_info_from_tls_id(tls_id)) == NULL) {
1115
0
        return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
1116
0
    }
1117
1118
0
    *grp = curve_info->grp_id;
1119
1120
0
    return 0;
1121
0
}
1122
1123
/*
1124
 * Write the ECParameters record corresponding to a group (RFC 4492)
1125
 */
1126
int mbedtls_ecp_tls_write_group(const mbedtls_ecp_group *grp, size_t *olen,
1127
                                unsigned char *buf, size_t blen)
1128
0
{
1129
0
    const mbedtls_ecp_curve_info *curve_info;
1130
0
    ECP_VALIDATE_RET(grp  != NULL);
1131
0
    ECP_VALIDATE_RET(buf  != NULL);
1132
0
    ECP_VALIDATE_RET(olen != NULL);
1133
1134
0
    if ((curve_info = mbedtls_ecp_curve_info_from_grp_id(grp->id)) == NULL) {
1135
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1136
0
    }
1137
1138
    /*
1139
     * We are going to write 3 bytes (see below)
1140
     */
1141
0
    *olen = 3;
1142
0
    if (blen < *olen) {
1143
0
        return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
1144
0
    }
1145
1146
    /*
1147
     * First byte is curve_type, always named_curve
1148
     */
1149
0
    *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
1150
1151
    /*
1152
     * Next two bytes are the namedcurve value
1153
     */
1154
0
    MBEDTLS_PUT_UINT16_BE(curve_info->tls_id, buf, 0);
1155
1156
0
    return 0;
1157
0
}
1158
1159
/*
1160
 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
1161
 * See the documentation of struct mbedtls_ecp_group.
1162
 *
1163
 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
1164
 */
1165
static int ecp_modp(mbedtls_mpi *N, const mbedtls_ecp_group *grp)
1166
0
{
1167
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1168
1169
0
    if (grp->modp == NULL) {
1170
0
        return mbedtls_mpi_mod_mpi(N, N, &grp->P);
1171
0
    }
1172
1173
    /* N->s < 0 is a much faster test, which fails only if N is 0 */
1174
0
    if ((N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) ||
1175
0
        mbedtls_mpi_bitlen(N) > 2 * grp->pbits) {
1176
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1177
0
    }
1178
1179
0
    MBEDTLS_MPI_CHK(grp->modp(N));
1180
1181
    /* N->s < 0 is a much faster test, which fails only if N is 0 */
1182
0
    while (N->s < 0 && mbedtls_mpi_cmp_int(N, 0) != 0) {
1183
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(N, N, &grp->P));
1184
0
    }
1185
1186
0
    while (mbedtls_mpi_cmp_mpi(N, &grp->P) >= 0) {
1187
        /* we known P, N and the result are positive */
1188
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(N, N, &grp->P));
1189
0
    }
1190
1191
0
cleanup:
1192
0
    return ret;
1193
0
}
1194
1195
/*
1196
 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
1197
 *
1198
 * In order to guarantee that, we need to ensure that operands of
1199
 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
1200
 * bring the result back to this range.
1201
 *
1202
 * The following macros are shortcuts for doing that.
1203
 */
1204
1205
/*
1206
 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
1207
 */
1208
#if defined(MBEDTLS_SELF_TEST)
1209
0
#define INC_MUL_COUNT   mul_count++;
1210
#else
1211
#define INC_MUL_COUNT
1212
#endif
1213
1214
#define MOD_MUL(N)                                                    \
1215
0
    do                                                                  \
1216
0
    {                                                                   \
1217
0
        MBEDTLS_MPI_CHK(ecp_modp(&(N), grp));                       \
1218
0
        INC_MUL_COUNT                                                   \
1219
0
    } while (0)
1220
1221
static inline int mbedtls_mpi_mul_mod(const mbedtls_ecp_group *grp,
1222
                                      mbedtls_mpi *X,
1223
                                      const mbedtls_mpi *A,
1224
                                      const mbedtls_mpi *B)
1225
0
{
1226
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1227
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(X, A, B));
1228
0
    MOD_MUL(*X);
1229
0
cleanup:
1230
0
    return ret;
1231
0
}
1232
1233
/*
1234
 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
1235
 * N->s < 0 is a very fast test, which fails only if N is 0
1236
 */
1237
#define MOD_SUB(N)                                                    \
1238
0
    while ((N).s < 0 && mbedtls_mpi_cmp_int(&(N), 0) != 0)           \
1239
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&(N), &(N), &grp->P))
1240
1241
#if (defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
1242
    !(defined(MBEDTLS_ECP_NO_FALLBACK) && \
1243
    defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
1244
    defined(MBEDTLS_ECP_ADD_MIXED_ALT))) || \
1245
    (defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \
1246
    !(defined(MBEDTLS_ECP_NO_FALLBACK) && \
1247
    defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)))
1248
static inline int mbedtls_mpi_sub_mod(const mbedtls_ecp_group *grp,
1249
                                      mbedtls_mpi *X,
1250
                                      const mbedtls_mpi *A,
1251
                                      const mbedtls_mpi *B)
1252
0
{
1253
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1254
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(X, A, B));
1255
0
    MOD_SUB(*X);
1256
0
cleanup:
1257
0
    return ret;
1258
0
}
1259
#endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */
1260
1261
/*
1262
 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
1263
 * We known P, N and the result are positive, so sub_abs is correct, and
1264
 * a bit faster.
1265
 */
1266
#define MOD_ADD(N)                                                    \
1267
0
    while (mbedtls_mpi_cmp_mpi(&(N), &grp->P) >= 0)                  \
1268
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&(N), &(N), &grp->P))
1269
1270
static inline int mbedtls_mpi_add_mod(const mbedtls_ecp_group *grp,
1271
                                      mbedtls_mpi *X,
1272
                                      const mbedtls_mpi *A,
1273
                                      const mbedtls_mpi *B)
1274
0
{
1275
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1276
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, A, B));
1277
0
    MOD_ADD(*X);
1278
0
cleanup:
1279
0
    return ret;
1280
0
}
1281
1282
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
1283
    !(defined(MBEDTLS_ECP_NO_FALLBACK) && \
1284
    defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
1285
    defined(MBEDTLS_ECP_ADD_MIXED_ALT))
1286
static inline int mbedtls_mpi_shift_l_mod(const mbedtls_ecp_group *grp,
1287
                                          mbedtls_mpi *X,
1288
                                          size_t count)
1289
0
{
1290
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1291
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, count));
1292
0
    MOD_ADD(*X);
1293
0
cleanup:
1294
0
    return ret;
1295
0
}
1296
#endif \
1297
    /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */
1298
1299
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
1300
/*
1301
 * For curves in short Weierstrass form, we do all the internal operations in
1302
 * Jacobian coordinates.
1303
 *
1304
 * For multiplication, we'll use a comb method with countermeasures against
1305
 * SPA, hence timing attacks.
1306
 */
1307
1308
/*
1309
 * Normalize jacobian coordinates so that Z == 0 || Z == 1  (GECC 3.2.1)
1310
 * Cost: 1N := 1I + 3M + 1S
1311
 */
1312
static int ecp_normalize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt)
1313
0
{
1314
0
    if (mbedtls_mpi_cmp_int(&pt->Z, 0) == 0) {
1315
0
        return 0;
1316
0
    }
1317
1318
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
1319
    if (mbedtls_internal_ecp_grp_capable(grp)) {
1320
        return mbedtls_internal_ecp_normalize_jac(grp, pt);
1321
    }
1322
#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
1323
1324
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
1325
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
1326
#else
1327
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1328
0
    mbedtls_mpi Zi, ZZi;
1329
0
    mbedtls_mpi_init(&Zi); mbedtls_mpi_init(&ZZi);
1330
1331
    /*
1332
     * X = X / Z^2  mod p
1333
     */
1334
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&Zi,      &pt->Z,     &grp->P));
1335
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ZZi,     &Zi,        &Zi));
1336
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->X,   &pt->X,     &ZZi));
1337
1338
    /*
1339
     * Y = Y / Z^3  mod p
1340
     */
1341
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y,   &pt->Y,     &ZZi));
1342
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y,   &pt->Y,     &Zi));
1343
1344
    /*
1345
     * Z = 1
1346
     */
1347
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&pt->Z, 1));
1348
1349
0
cleanup:
1350
1351
0
    mbedtls_mpi_free(&Zi); mbedtls_mpi_free(&ZZi);
1352
1353
0
    return ret;
1354
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */
1355
0
}
1356
1357
/*
1358
 * Normalize jacobian coordinates of an array of (pointers to) points,
1359
 * using Montgomery's trick to perform only one inversion mod P.
1360
 * (See for example Cohen's "A Course in Computational Algebraic Number
1361
 * Theory", Algorithm 10.3.4.)
1362
 *
1363
 * Warning: fails (returning an error) if one of the points is zero!
1364
 * This should never happen, see choice of w in ecp_mul_comb().
1365
 *
1366
 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
1367
 */
1368
static int ecp_normalize_jac_many(const mbedtls_ecp_group *grp,
1369
                                  mbedtls_ecp_point *T[], size_t T_size)
1370
0
{
1371
0
    if (T_size < 2) {
1372
0
        return ecp_normalize_jac(grp, *T);
1373
0
    }
1374
1375
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
1376
    if (mbedtls_internal_ecp_grp_capable(grp)) {
1377
        return mbedtls_internal_ecp_normalize_jac_many(grp, T, T_size);
1378
    }
1379
#endif
1380
1381
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
1382
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
1383
#else
1384
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1385
0
    size_t i;
1386
0
    mbedtls_mpi *c, u, Zi, ZZi;
1387
1388
0
    if ((c = mbedtls_calloc(T_size, sizeof(mbedtls_mpi))) == NULL) {
1389
0
        return MBEDTLS_ERR_ECP_ALLOC_FAILED;
1390
0
    }
1391
1392
0
    for (i = 0; i < T_size; i++) {
1393
0
        mbedtls_mpi_init(&c[i]);
1394
0
    }
1395
1396
0
    mbedtls_mpi_init(&u); mbedtls_mpi_init(&Zi); mbedtls_mpi_init(&ZZi);
1397
1398
    /*
1399
     * c[i] = Z_0 * ... * Z_i
1400
     */
1401
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&c[0], &T[0]->Z));
1402
0
    for (i = 1; i < T_size; i++) {
1403
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &c[i], &c[i-1], &T[i]->Z));
1404
0
    }
1405
1406
    /*
1407
     * u = 1 / (Z_0 * ... * Z_n) mod P
1408
     */
1409
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&u, &c[T_size-1], &grp->P));
1410
1411
0
    for (i = T_size - 1;; i--) {
1412
        /*
1413
         * Zi = 1 / Z_i mod p
1414
         * u = 1 / (Z_0 * ... * Z_i) mod P
1415
         */
1416
0
        if (i == 0) {
1417
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Zi, &u));
1418
0
        } else {
1419
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &Zi, &u, &c[i-1]));
1420
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &u,  &u, &T[i]->Z));
1421
0
        }
1422
1423
        /*
1424
         * proceed as in normalize()
1425
         */
1426
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ZZi,     &Zi,      &Zi));
1427
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->X, &T[i]->X, &ZZi));
1428
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->Y, &T[i]->Y, &ZZi));
1429
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T[i]->Y, &T[i]->Y, &Zi));
1430
1431
        /*
1432
         * Post-precessing: reclaim some memory by shrinking coordinates
1433
         * - not storing Z (always 1)
1434
         * - shrinking other coordinates, but still keeping the same number of
1435
         *   limbs as P, as otherwise it will too likely be regrown too fast.
1436
         */
1437
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->X, grp->P.n));
1438
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(&T[i]->Y, grp->P.n));
1439
0
        mbedtls_mpi_free(&T[i]->Z);
1440
1441
0
        if (i == 0) {
1442
0
            break;
1443
0
        }
1444
0
    }
1445
1446
0
cleanup:
1447
1448
0
    mbedtls_mpi_free(&u); mbedtls_mpi_free(&Zi); mbedtls_mpi_free(&ZZi);
1449
0
    for (i = 0; i < T_size; i++) {
1450
0
        mbedtls_mpi_free(&c[i]);
1451
0
    }
1452
0
    mbedtls_free(c);
1453
1454
0
    return ret;
1455
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */
1456
0
}
1457
1458
/*
1459
 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
1460
 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
1461
 */
1462
static int ecp_safe_invert_jac(const mbedtls_ecp_group *grp,
1463
                               mbedtls_ecp_point *Q,
1464
                               unsigned char inv)
1465
0
{
1466
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1467
0
    unsigned char nonzero;
1468
0
    mbedtls_mpi mQY;
1469
1470
0
    mbedtls_mpi_init(&mQY);
1471
1472
    /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
1473
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mQY, &grp->P, &Q->Y));
1474
0
    nonzero = mbedtls_mpi_cmp_int(&Q->Y, 0) != 0;
1475
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&Q->Y, &mQY, inv & nonzero));
1476
1477
0
cleanup:
1478
0
    mbedtls_mpi_free(&mQY);
1479
1480
0
    return ret;
1481
0
}
1482
1483
/*
1484
 * Point doubling R = 2 P, Jacobian coordinates
1485
 *
1486
 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
1487
 *
1488
 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
1489
 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
1490
 *
1491
 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
1492
 *
1493
 * Cost: 1D := 3M + 4S          (A ==  0)
1494
 *             4M + 4S          (A == -3)
1495
 *             3M + 6S + 1a     otherwise
1496
 */
1497
static int ecp_double_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1498
                          const mbedtls_ecp_point *P)
1499
0
{
1500
0
#if defined(MBEDTLS_SELF_TEST)
1501
0
    dbl_count++;
1502
0
#endif
1503
1504
#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
1505
    if (mbedtls_internal_ecp_grp_capable(grp)) {
1506
        return mbedtls_internal_ecp_double_jac(grp, R, P);
1507
    }
1508
#endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
1509
1510
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
1511
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
1512
#else
1513
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1514
0
    mbedtls_mpi M, S, T, U;
1515
1516
0
    mbedtls_mpi_init(&M); mbedtls_mpi_init(&S); mbedtls_mpi_init(&T); mbedtls_mpi_init(&U);
1517
1518
    /* Special case for A = -3 */
1519
0
    if (grp->A.p == NULL) {
1520
        /* M = 3(X + Z^2)(X - Z^2) */
1521
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &P->Z,  &P->Z));
1522
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &T,  &P->X,  &S));
1523
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &U,  &P->X,  &S));
1524
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &T,     &U));
1525
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&M,  &S,     3)); MOD_ADD(M);
1526
0
    } else {
1527
        /* M = 3.X^2 */
1528
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &P->X,  &P->X));
1529
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&M,  &S,     3)); MOD_ADD(M);
1530
1531
        /* Optimize away for "koblitz" curves with A = 0 */
1532
0
        if (mbedtls_mpi_cmp_int(&grp->A, 0) != 0) {
1533
            /* M += A.Z^4 */
1534
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &P->Z,  &P->Z));
1535
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T,  &S,     &S));
1536
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &T,     &grp->A));
1537
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &M,  &M,     &S));
1538
0
        }
1539
0
    }
1540
1541
    /* S = 4.X.Y^2 */
1542
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T,  &P->Y,  &P->Y));
1543
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &T,  1));
1544
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &P->X,  &T));
1545
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &S,  1));
1546
1547
    /* U = 8.Y^4 */
1548
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &U,  &T,     &T));
1549
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &U,  1));
1550
1551
    /* T = M^2 - 2.S */
1552
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T,  &M,     &M));
1553
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T,  &T,     &S));
1554
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T,  &T,     &S));
1555
1556
    /* S = M(S - T) - U */
1557
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S,  &S,     &T));
1558
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S,  &S,     &M));
1559
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S,  &S,     &U));
1560
1561
    /* U = 2.Y.Z */
1562
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &U,  &P->Y,  &P->Z));
1563
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &U,  1));
1564
1565
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->X, &T));
1566
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Y, &S));
1567
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Z, &U));
1568
1569
0
cleanup:
1570
0
    mbedtls_mpi_free(&M); mbedtls_mpi_free(&S); mbedtls_mpi_free(&T); mbedtls_mpi_free(&U);
1571
1572
0
    return ret;
1573
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */
1574
0
}
1575
1576
/*
1577
 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
1578
 *
1579
 * The coordinates of Q must be normalized (= affine),
1580
 * but those of P don't need to. R is not normalized.
1581
 *
1582
 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
1583
 * None of these cases can happen as intermediate step in ecp_mul_comb():
1584
 * - at each step, P, Q and R are multiples of the base point, the factor
1585
 *   being less than its order, so none of them is zero;
1586
 * - Q is an odd multiple of the base point, P an even multiple,
1587
 *   due to the choice of precomputed points in the modified comb method.
1588
 * So branches for these cases do not leak secret information.
1589
 *
1590
 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
1591
 *
1592
 * Cost: 1A := 8M + 3S
1593
 */
1594
static int ecp_add_mixed(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1595
                         const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q)
1596
0
{
1597
0
#if defined(MBEDTLS_SELF_TEST)
1598
0
    add_count++;
1599
0
#endif
1600
1601
#if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1602
    if (mbedtls_internal_ecp_grp_capable(grp)) {
1603
        return mbedtls_internal_ecp_add_mixed(grp, R, P, Q);
1604
    }
1605
#endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
1606
1607
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT)
1608
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
1609
#else
1610
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1611
0
    mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
1612
1613
    /*
1614
     * Trivial cases: P == 0 or Q == 0 (case 1)
1615
     */
1616
0
    if (mbedtls_mpi_cmp_int(&P->Z, 0) == 0) {
1617
0
        return mbedtls_ecp_copy(R, Q);
1618
0
    }
1619
1620
0
    if (Q->Z.p != NULL && mbedtls_mpi_cmp_int(&Q->Z, 0) == 0) {
1621
0
        return mbedtls_ecp_copy(R, P);
1622
0
    }
1623
1624
    /*
1625
     * Make sure Q coordinates are normalized
1626
     */
1627
0
    if (Q->Z.p != NULL && mbedtls_mpi_cmp_int(&Q->Z, 1) != 0) {
1628
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
1629
0
    }
1630
1631
0
    mbedtls_mpi_init(&T1); mbedtls_mpi_init(&T2); mbedtls_mpi_init(&T3); mbedtls_mpi_init(&T4);
1632
0
    mbedtls_mpi_init(&X); mbedtls_mpi_init(&Y); mbedtls_mpi_init(&Z);
1633
1634
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T1,  &P->Z,  &P->Z));
1635
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T2,  &T1,    &P->Z));
1636
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T1,  &T1,    &Q->X));
1637
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T2,  &T2,    &Q->Y));
1638
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T1,  &T1,    &P->X));
1639
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T2,  &T2,    &P->Y));
1640
1641
    /* Special cases (2) and (3) */
1642
0
    if (mbedtls_mpi_cmp_int(&T1, 0) == 0) {
1643
0
        if (mbedtls_mpi_cmp_int(&T2, 0) == 0) {
1644
0
            ret = ecp_double_jac(grp, R, P);
1645
0
            goto cleanup;
1646
0
        } else {
1647
0
            ret = mbedtls_ecp_set_zero(R);
1648
0
            goto cleanup;
1649
0
        }
1650
0
    }
1651
1652
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &Z,   &P->Z,  &T1));
1653
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3,  &T1,    &T1));
1654
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T4,  &T3,    &T1));
1655
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3,  &T3,    &P->X));
1656
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &T3));
1657
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l_mod(grp, &T1,  1));
1658
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &X,   &T2,    &T2));
1659
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &X,   &X,     &T1));
1660
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &X,   &X,     &T4));
1661
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &T3,  &T3,    &X));
1662
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T3,  &T3,    &T2));
1663
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &T4,  &T4,    &P->Y));
1664
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &Y,   &T3,    &T4));
1665
1666
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->X, &X));
1667
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Y, &Y));
1668
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R->Z, &Z));
1669
1670
0
cleanup:
1671
1672
0
    mbedtls_mpi_free(&T1); mbedtls_mpi_free(&T2); mbedtls_mpi_free(&T3); mbedtls_mpi_free(&T4);
1673
0
    mbedtls_mpi_free(&X); mbedtls_mpi_free(&Y); mbedtls_mpi_free(&Z);
1674
1675
0
    return ret;
1676
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */
1677
0
}
1678
1679
/*
1680
 * Randomize jacobian coordinates:
1681
 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
1682
 * This is sort of the reverse operation of ecp_normalize_jac().
1683
 *
1684
 * This countermeasure was first suggested in [2].
1685
 */
1686
static int ecp_randomize_jac(const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
1687
                             int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
1688
0
{
1689
#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1690
    if (mbedtls_internal_ecp_grp_capable(grp)) {
1691
        return mbedtls_internal_ecp_randomize_jac(grp, pt, f_rng, p_rng);
1692
    }
1693
#endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
1694
1695
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
1696
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
1697
#else
1698
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1699
0
    mbedtls_mpi l, ll;
1700
1701
0
    mbedtls_mpi_init(&l); mbedtls_mpi_init(&ll);
1702
1703
    /* Generate l such that 1 < l < p */
1704
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_random(&l, 2, &grp->P, f_rng, p_rng));
1705
1706
    /* Z = l * Z */
1707
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Z,   &pt->Z,     &l));
1708
1709
    /* X = l^2 * X */
1710
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ll,      &l,         &l));
1711
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->X,   &pt->X,     &ll));
1712
1713
    /* Y = l^3 * Y */
1714
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &ll,      &ll,        &l));
1715
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &pt->Y,   &pt->Y,     &ll));
1716
1717
0
cleanup:
1718
0
    mbedtls_mpi_free(&l); mbedtls_mpi_free(&ll);
1719
1720
0
    if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) {
1721
0
        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
1722
0
    }
1723
0
    return ret;
1724
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */
1725
0
}
1726
1727
/*
1728
 * Check and define parameters used by the comb method (see below for details)
1729
 */
1730
#if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
1731
#error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
1732
#endif
1733
1734
/* d = ceil( n / w ) */
1735
#define COMB_MAX_D      (MBEDTLS_ECP_MAX_BITS + 1) / 2
1736
1737
/* number of precomputed points */
1738
#define COMB_MAX_PRE    (1 << (MBEDTLS_ECP_WINDOW_SIZE - 1))
1739
1740
/*
1741
 * Compute the representation of m that will be used with our comb method.
1742
 *
1743
 * The basic comb method is described in GECC 3.44 for example. We use a
1744
 * modified version that provides resistance to SPA by avoiding zero
1745
 * digits in the representation as in [3]. We modify the method further by
1746
 * requiring that all K_i be odd, which has the small cost that our
1747
 * representation uses one more K_i, due to carries, but saves on the size of
1748
 * the precomputed table.
1749
 *
1750
 * Summary of the comb method and its modifications:
1751
 *
1752
 * - The goal is to compute m*P for some w*d-bit integer m.
1753
 *
1754
 * - The basic comb method splits m into the w-bit integers
1755
 *   x[0] .. x[d-1] where x[i] consists of the bits in m whose
1756
 *   index has residue i modulo d, and computes m * P as
1757
 *   S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
1758
 *   S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
1759
 *
1760
 * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
1761
 *    .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] ..,
1762
 *   thereby successively converting it into a form where all summands
1763
 *   are nonzero, at the cost of negative summands. This is the basic idea of [3].
1764
 *
1765
 * - More generally, even if x[i+1] != 0, we can first transform the sum as
1766
 *   .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
1767
 *   and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
1768
 *   Performing and iterating this procedure for those x[i] that are even
1769
 *   (keeping track of carry), we can transform the original sum into one of the form
1770
 *   S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
1771
 *   with all x'[i] odd. It is therefore only necessary to know S at odd indices,
1772
 *   which is why we are only computing half of it in the first place in
1773
 *   ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
1774
 *
1775
 * - For the sake of compactness, only the seven low-order bits of x[i]
1776
 *   are used to represent its absolute value (K_i in the paper), and the msb
1777
 *   of x[i] encodes the sign (s_i in the paper): it is set if and only if
1778
 *   if s_i == -1;
1779
 *
1780
 * Calling conventions:
1781
 * - x is an array of size d + 1
1782
 * - w is the size, ie number of teeth, of the comb, and must be between
1783
 *   2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
1784
 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
1785
 *   (the result will be incorrect if these assumptions are not satisfied)
1786
 */
1787
static void ecp_comb_recode_core(unsigned char x[], size_t d,
1788
                                 unsigned char w, const mbedtls_mpi *m)
1789
0
{
1790
0
    size_t i, j;
1791
0
    unsigned char c, cc, adjust;
1792
1793
0
    memset(x, 0, d+1);
1794
1795
    /* First get the classical comb values (except for x_d = 0) */
1796
0
    for (i = 0; i < d; i++) {
1797
0
        for (j = 0; j < w; j++) {
1798
0
            x[i] |= mbedtls_mpi_get_bit(m, i + d * j) << j;
1799
0
        }
1800
0
    }
1801
1802
    /* Now make sure x_1 .. x_d are odd */
1803
0
    c = 0;
1804
0
    for (i = 1; i <= d; i++) {
1805
        /* Add carry and update it */
1806
0
        cc   = x[i] & c;
1807
0
        x[i] = x[i] ^ c;
1808
0
        c = cc;
1809
1810
        /* Adjust if needed, avoiding branches */
1811
0
        adjust = 1 - (x[i] & 0x01);
1812
0
        c   |= x[i] & (x[i-1] * adjust);
1813
0
        x[i] = x[i] ^ (x[i-1] * adjust);
1814
0
        x[i-1] |= adjust << 7;
1815
0
    }
1816
0
}
1817
1818
/*
1819
 * Precompute points for the adapted comb method
1820
 *
1821
 * Assumption: T must be able to hold 2^{w - 1} elements.
1822
 *
1823
 * Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
1824
 *            sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
1825
 *
1826
 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
1827
 *
1828
 * Note: Even comb values (those where P would be omitted from the
1829
 *       sum defining T[i] above) are not needed in our adaption
1830
 *       the comb method. See ecp_comb_recode_core().
1831
 *
1832
 * This function currently works in four steps:
1833
 * (1) [dbl]      Computation of intermediate T[i] for 2-power values of i
1834
 * (2) [norm_dbl] Normalization of coordinates of these T[i]
1835
 * (3) [add]      Computation of all T[i]
1836
 * (4) [norm_add] Normalization of all T[i]
1837
 *
1838
 * Step 1 can be interrupted but not the others; together with the final
1839
 * coordinate normalization they are the largest steps done at once, depending
1840
 * on the window size. Here are operation counts for P-256:
1841
 *
1842
 * step     (2)     (3)     (4)
1843
 * w = 5    142     165     208
1844
 * w = 4    136      77     160
1845
 * w = 3    130      33     136
1846
 * w = 2    124      11     124
1847
 *
1848
 * So if ECC operations are blocking for too long even with a low max_ops
1849
 * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
1850
 * to minimize maximum blocking time.
1851
 */
1852
static int ecp_precompute_comb(const mbedtls_ecp_group *grp,
1853
                               mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
1854
                               unsigned char w, size_t d,
1855
                               mbedtls_ecp_restart_ctx *rs_ctx)
1856
0
{
1857
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
1858
0
    unsigned char i;
1859
0
    size_t j = 0;
1860
0
    const unsigned char T_size = 1U << (w - 1);
1861
0
    mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
1862
1863
#if defined(MBEDTLS_ECP_RESTARTABLE)
1864
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
1865
        if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) {
1866
            goto dbl;
1867
        }
1868
        if (rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl) {
1869
            goto norm_dbl;
1870
        }
1871
        if (rs_ctx->rsm->state == ecp_rsm_pre_add) {
1872
            goto add;
1873
        }
1874
        if (rs_ctx->rsm->state == ecp_rsm_pre_norm_add) {
1875
            goto norm_add;
1876
        }
1877
    }
1878
#else
1879
0
    (void) rs_ctx;
1880
0
#endif
1881
1882
#if defined(MBEDTLS_ECP_RESTARTABLE)
1883
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
1884
        rs_ctx->rsm->state = ecp_rsm_pre_dbl;
1885
1886
        /* initial state for the loop */
1887
        rs_ctx->rsm->i = 0;
1888
    }
1889
1890
dbl:
1891
#endif
1892
    /*
1893
     * Set T[0] = P and
1894
     * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
1895
     */
1896
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&T[0], P));
1897
1898
#if defined(MBEDTLS_ECP_RESTARTABLE)
1899
    if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) {
1900
        j = rs_ctx->rsm->i;
1901
    } else
1902
#endif
1903
0
    j = 0;
1904
1905
0
    for (; j < d * (w - 1); j++) {
1906
0
        MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL);
1907
1908
0
        i = 1U << (j / d);
1909
0
        cur = T + i;
1910
1911
0
        if (j % d == 0) {
1912
0
            MBEDTLS_MPI_CHK(mbedtls_ecp_copy(cur, T + (i >> 1)));
1913
0
        }
1914
1915
0
        MBEDTLS_MPI_CHK(ecp_double_jac(grp, cur, cur));
1916
0
    }
1917
1918
#if defined(MBEDTLS_ECP_RESTARTABLE)
1919
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
1920
        rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
1921
    }
1922
1923
norm_dbl:
1924
#endif
1925
    /*
1926
     * Normalize current elements in T. As T has holes,
1927
     * use an auxiliary array of pointers to elements in T.
1928
     */
1929
0
    j = 0;
1930
0
    for (i = 1; i < T_size; i <<= 1) {
1931
0
        TT[j++] = T + i;
1932
0
    }
1933
1934
0
    MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2);
1935
1936
0
    MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j));
1937
1938
#if defined(MBEDTLS_ECP_RESTARTABLE)
1939
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
1940
        rs_ctx->rsm->state = ecp_rsm_pre_add;
1941
    }
1942
1943
add:
1944
#endif
1945
    /*
1946
     * Compute the remaining ones using the minimal number of additions
1947
     * Be careful to update T[2^l] only after using it!
1948
     */
1949
0
    MBEDTLS_ECP_BUDGET((T_size - 1) * MBEDTLS_ECP_OPS_ADD);
1950
1951
0
    for (i = 1; i < T_size; i <<= 1) {
1952
0
        j = i;
1953
0
        while (j--) {
1954
0
            MBEDTLS_MPI_CHK(ecp_add_mixed(grp, &T[i + j], &T[j], &T[i]));
1955
0
        }
1956
0
    }
1957
1958
#if defined(MBEDTLS_ECP_RESTARTABLE)
1959
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
1960
        rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
1961
    }
1962
1963
norm_add:
1964
#endif
1965
    /*
1966
     * Normalize final elements in T. Even though there are no holes now, we
1967
     * still need the auxiliary array for homogeneity with the previous
1968
     * call. Also, skip T[0] which is already normalised, being a copy of P.
1969
     */
1970
0
    for (j = 0; j + 1 < T_size; j++) {
1971
0
        TT[j] = T + j + 1;
1972
0
    }
1973
1974
0
    MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV + 6 * j - 2);
1975
1976
0
    MBEDTLS_MPI_CHK(ecp_normalize_jac_many(grp, TT, j));
1977
1978
0
cleanup:
1979
#if defined(MBEDTLS_ECP_RESTARTABLE)
1980
    if (rs_ctx != NULL && rs_ctx->rsm != NULL &&
1981
        ret == MBEDTLS_ERR_ECP_IN_PROGRESS) {
1982
        if (rs_ctx->rsm->state == ecp_rsm_pre_dbl) {
1983
            rs_ctx->rsm->i = j;
1984
        }
1985
    }
1986
#endif
1987
1988
0
    return ret;
1989
0
}
1990
1991
/*
1992
 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
1993
 *
1994
 * See ecp_comb_recode_core() for background
1995
 */
1996
static int ecp_select_comb(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1997
                           const mbedtls_ecp_point T[], unsigned char T_size,
1998
                           unsigned char i)
1999
0
{
2000
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2001
0
    unsigned char ii, j;
2002
2003
    /* Ignore the "sign" bit and scale down */
2004
0
    ii =  (i & 0x7Fu) >> 1;
2005
2006
    /* Read the whole table to thwart cache-based timing attacks */
2007
0
    for (j = 0; j < T_size; j++) {
2008
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&R->X, &T[j].X, j == ii));
2009
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&R->Y, &T[j].Y, j == ii));
2010
0
    }
2011
2012
    /* Safely invert result if i is "negative" */
2013
0
    MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, R, i >> 7));
2014
2015
0
cleanup:
2016
0
    return ret;
2017
0
}
2018
2019
/*
2020
 * Core multiplication algorithm for the (modified) comb method.
2021
 * This part is actually common with the basic comb method (GECC 3.44)
2022
 *
2023
 * Cost: d A + d D + 1 R
2024
 */
2025
static int ecp_mul_comb_core(const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2026
                             const mbedtls_ecp_point T[], unsigned char T_size,
2027
                             const unsigned char x[], size_t d,
2028
                             int (*f_rng)(void *, unsigned char *, size_t),
2029
                             void *p_rng,
2030
                             mbedtls_ecp_restart_ctx *rs_ctx)
2031
0
{
2032
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2033
0
    mbedtls_ecp_point Txi;
2034
0
    size_t i;
2035
2036
0
    mbedtls_ecp_point_init(&Txi);
2037
2038
0
#if !defined(MBEDTLS_ECP_RESTARTABLE)
2039
0
    (void) rs_ctx;
2040
0
#endif
2041
2042
#if defined(MBEDTLS_ECP_RESTARTABLE)
2043
    if (rs_ctx != NULL && rs_ctx->rsm != NULL &&
2044
        rs_ctx->rsm->state != ecp_rsm_comb_core) {
2045
        rs_ctx->rsm->i = 0;
2046
        rs_ctx->rsm->state = ecp_rsm_comb_core;
2047
    }
2048
2049
    /* new 'if' instead of nested for the sake of the 'else' branch */
2050
    if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0) {
2051
        /* restore current index (R already pointing to rs_ctx->rsm->R) */
2052
        i = rs_ctx->rsm->i;
2053
    } else
2054
#endif
2055
0
    {
2056
0
        int have_rng = 1;
2057
2058
        /* Start with a non-zero point and randomize its coordinates */
2059
0
        i = d;
2060
0
        MBEDTLS_MPI_CHK(ecp_select_comb(grp, R, T, T_size, x[i]));
2061
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->Z, 1));
2062
2063
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2064
        if (f_rng == NULL) {
2065
            have_rng = 0;
2066
        }
2067
#endif
2068
0
        if (have_rng) {
2069
0
            MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, R, f_rng, p_rng));
2070
0
        }
2071
0
    }
2072
2073
0
    while (i != 0) {
2074
0
        MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD);
2075
0
        --i;
2076
2077
0
        MBEDTLS_MPI_CHK(ecp_double_jac(grp, R, R));
2078
0
        MBEDTLS_MPI_CHK(ecp_select_comb(grp, &Txi, T, T_size, x[i]));
2079
0
        MBEDTLS_MPI_CHK(ecp_add_mixed(grp, R, R, &Txi));
2080
0
    }
2081
2082
0
cleanup:
2083
2084
0
    mbedtls_ecp_point_free(&Txi);
2085
2086
#if defined(MBEDTLS_ECP_RESTARTABLE)
2087
    if (rs_ctx != NULL && rs_ctx->rsm != NULL &&
2088
        ret == MBEDTLS_ERR_ECP_IN_PROGRESS) {
2089
        rs_ctx->rsm->i = i;
2090
        /* no need to save R, already pointing to rs_ctx->rsm->R */
2091
    }
2092
#endif
2093
2094
0
    return ret;
2095
0
}
2096
2097
/*
2098
 * Recode the scalar to get constant-time comb multiplication
2099
 *
2100
 * As the actual scalar recoding needs an odd scalar as a starting point,
2101
 * this wrapper ensures that by replacing m by N - m if necessary, and
2102
 * informs the caller that the result of multiplication will be negated.
2103
 *
2104
 * This works because we only support large prime order for Short Weierstrass
2105
 * curves, so N is always odd hence either m or N - m is.
2106
 *
2107
 * See ecp_comb_recode_core() for background.
2108
 */
2109
static int ecp_comb_recode_scalar(const mbedtls_ecp_group *grp,
2110
                                  const mbedtls_mpi *m,
2111
                                  unsigned char k[COMB_MAX_D + 1],
2112
                                  size_t d,
2113
                                  unsigned char w,
2114
                                  unsigned char *parity_trick)
2115
0
{
2116
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2117
0
    mbedtls_mpi M, mm;
2118
2119
0
    mbedtls_mpi_init(&M);
2120
0
    mbedtls_mpi_init(&mm);
2121
2122
    /* N is always odd (see above), just make extra sure */
2123
0
    if (mbedtls_mpi_get_bit(&grp->N, 0) != 1) {
2124
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2125
0
    }
2126
2127
    /* do we need the parity trick? */
2128
0
    *parity_trick = (mbedtls_mpi_get_bit(m, 0) == 0);
2129
2130
    /* execute parity fix in constant time */
2131
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&M, m));
2132
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&mm, &grp->N, m));
2133
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(&M, &mm, *parity_trick));
2134
2135
    /* actual scalar recoding */
2136
0
    ecp_comb_recode_core(k, d, w, &M);
2137
2138
0
cleanup:
2139
0
    mbedtls_mpi_free(&mm);
2140
0
    mbedtls_mpi_free(&M);
2141
2142
0
    return ret;
2143
0
}
2144
2145
/*
2146
 * Perform comb multiplication (for short Weierstrass curves)
2147
 * once the auxiliary table has been pre-computed.
2148
 *
2149
 * Scalar recoding may use a parity trick that makes us compute -m * P,
2150
 * if that is the case we'll need to recover m * P at the end.
2151
 */
2152
static int ecp_mul_comb_after_precomp(const mbedtls_ecp_group *grp,
2153
                                      mbedtls_ecp_point *R,
2154
                                      const mbedtls_mpi *m,
2155
                                      const mbedtls_ecp_point *T,
2156
                                      unsigned char T_size,
2157
                                      unsigned char w,
2158
                                      size_t d,
2159
                                      int (*f_rng)(void *, unsigned char *, size_t),
2160
                                      void *p_rng,
2161
                                      mbedtls_ecp_restart_ctx *rs_ctx)
2162
0
{
2163
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2164
0
    unsigned char parity_trick;
2165
0
    unsigned char k[COMB_MAX_D + 1];
2166
0
    mbedtls_ecp_point *RR = R;
2167
0
    int have_rng = 1;
2168
2169
#if defined(MBEDTLS_ECP_RESTARTABLE)
2170
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
2171
        RR = &rs_ctx->rsm->R;
2172
2173
        if (rs_ctx->rsm->state == ecp_rsm_final_norm) {
2174
            goto final_norm;
2175
        }
2176
    }
2177
#endif
2178
2179
0
    MBEDTLS_MPI_CHK(ecp_comb_recode_scalar(grp, m, k, d, w,
2180
0
                                           &parity_trick));
2181
0
    MBEDTLS_MPI_CHK(ecp_mul_comb_core(grp, RR, T, T_size, k, d,
2182
0
                                      f_rng, p_rng, rs_ctx));
2183
0
    MBEDTLS_MPI_CHK(ecp_safe_invert_jac(grp, RR, parity_trick));
2184
2185
#if defined(MBEDTLS_ECP_RESTARTABLE)
2186
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
2187
        rs_ctx->rsm->state = ecp_rsm_final_norm;
2188
    }
2189
2190
final_norm:
2191
    MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV);
2192
#endif
2193
    /*
2194
     * Knowledge of the jacobian coordinates may leak the last few bits of the
2195
     * scalar [1], and since our MPI implementation isn't constant-flow,
2196
     * inversion (used for coordinate normalization) may leak the full value
2197
     * of its input via side-channels [2].
2198
     *
2199
     * [1] https://eprint.iacr.org/2003/191
2200
     * [2] https://eprint.iacr.org/2020/055
2201
     *
2202
     * Avoid the leak by randomizing coordinates before we normalize them.
2203
     */
2204
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2205
    if (f_rng == NULL) {
2206
        have_rng = 0;
2207
    }
2208
#endif
2209
0
    if (have_rng) {
2210
0
        MBEDTLS_MPI_CHK(ecp_randomize_jac(grp, RR, f_rng, p_rng));
2211
0
    }
2212
2213
0
    MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, RR));
2214
2215
#if defined(MBEDTLS_ECP_RESTARTABLE)
2216
    if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
2217
        MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, RR));
2218
    }
2219
#endif
2220
2221
0
cleanup:
2222
0
    return ret;
2223
0
}
2224
2225
/*
2226
 * Pick window size based on curve size and whether we optimize for base point
2227
 */
2228
static unsigned char ecp_pick_window_size(const mbedtls_ecp_group *grp,
2229
                                          unsigned char p_eq_g)
2230
0
{
2231
0
    unsigned char w;
2232
2233
    /*
2234
     * Minimize the number of multiplications, that is minimize
2235
     * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
2236
     * (see costs of the various parts, with 1S = 1M)
2237
     */
2238
0
    w = grp->nbits >= 384 ? 5 : 4;
2239
2240
    /*
2241
     * If P == G, pre-compute a bit more, since this may be re-used later.
2242
     * Just adding one avoids upping the cost of the first mul too much,
2243
     * and the memory cost too.
2244
     */
2245
0
    if (p_eq_g) {
2246
0
        w++;
2247
0
    }
2248
2249
    /*
2250
     * Make sure w is within bounds.
2251
     * (The last test is useful only for very small curves in the test suite.)
2252
     */
2253
0
#if (MBEDTLS_ECP_WINDOW_SIZE < 6)
2254
0
    if (w > MBEDTLS_ECP_WINDOW_SIZE) {
2255
0
        w = MBEDTLS_ECP_WINDOW_SIZE;
2256
0
    }
2257
0
#endif
2258
0
    if (w >= grp->nbits) {
2259
0
        w = 2;
2260
0
    }
2261
2262
0
    return w;
2263
0
}
2264
2265
/*
2266
 * Multiplication using the comb method - for curves in short Weierstrass form
2267
 *
2268
 * This function is mainly responsible for administrative work:
2269
 * - managing the restart context if enabled
2270
 * - managing the table of precomputed points (passed between the below two
2271
 *   functions): allocation, computation, ownership transfer, freeing.
2272
 *
2273
 * It delegates the actual arithmetic work to:
2274
 *      ecp_precompute_comb() and ecp_mul_comb_with_precomp()
2275
 *
2276
 * See comments on ecp_comb_recode_core() regarding the computation strategy.
2277
 */
2278
static int ecp_mul_comb(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2279
                        const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2280
                        int (*f_rng)(void *, unsigned char *, size_t),
2281
                        void *p_rng,
2282
                        mbedtls_ecp_restart_ctx *rs_ctx)
2283
0
{
2284
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2285
0
    unsigned char w, p_eq_g, i;
2286
0
    size_t d;
2287
0
    unsigned char T_size = 0, T_ok = 0;
2288
0
    mbedtls_ecp_point *T = NULL;
2289
0
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2290
0
    ecp_drbg_context drbg_ctx;
2291
2292
0
    ecp_drbg_init(&drbg_ctx);
2293
0
#endif
2294
2295
0
    ECP_RS_ENTER(rsm);
2296
2297
0
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2298
0
    if (f_rng == NULL) {
2299
        /* Adjust pointers */
2300
0
        f_rng = &ecp_drbg_random;
2301
#if defined(MBEDTLS_ECP_RESTARTABLE)
2302
        if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
2303
            p_rng = &rs_ctx->rsm->drbg_ctx;
2304
        } else
2305
#endif
2306
0
        p_rng = &drbg_ctx;
2307
2308
        /* Initialize internal DRBG if necessary */
2309
#if defined(MBEDTLS_ECP_RESTARTABLE)
2310
        if (rs_ctx == NULL || rs_ctx->rsm == NULL ||
2311
            rs_ctx->rsm->drbg_seeded == 0)
2312
#endif
2313
0
        {
2314
0
            const size_t m_len = (grp->nbits + 7) / 8;
2315
0
            MBEDTLS_MPI_CHK(ecp_drbg_seed(p_rng, m, m_len));
2316
0
        }
2317
#if defined(MBEDTLS_ECP_RESTARTABLE)
2318
        if (rs_ctx != NULL && rs_ctx->rsm != NULL) {
2319
            rs_ctx->rsm->drbg_seeded = 1;
2320
        }
2321
#endif
2322
0
    }
2323
0
#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2324
2325
    /* Is P the base point ? */
2326
0
#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
2327
0
    p_eq_g = (mbedtls_mpi_cmp_mpi(&P->Y, &grp->G.Y) == 0 &&
2328
0
              mbedtls_mpi_cmp_mpi(&P->X, &grp->G.X) == 0);
2329
#else
2330
    p_eq_g = 0;
2331
#endif
2332
2333
    /* Pick window size and deduce related sizes */
2334
0
    w = ecp_pick_window_size(grp, p_eq_g);
2335
0
    T_size = 1U << (w - 1);
2336
0
    d = (grp->nbits + w - 1) / w;
2337
2338
    /* Pre-computed table: do we have it already for the base point? */
2339
0
    if (p_eq_g && grp->T != NULL) {
2340
        /* second pointer to the same table, will be deleted on exit */
2341
0
        T = grp->T;
2342
0
        T_ok = 1;
2343
0
    } else
2344
#if defined(MBEDTLS_ECP_RESTARTABLE)
2345
    /* Pre-computed table: do we have one in progress? complete? */
2346
    if (rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL) {
2347
        /* transfer ownership of T from rsm to local function */
2348
        T = rs_ctx->rsm->T;
2349
        rs_ctx->rsm->T = NULL;
2350
        rs_ctx->rsm->T_size = 0;
2351
2352
        /* This effectively jumps to the call to mul_comb_after_precomp() */
2353
        T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
2354
    } else
2355
#endif
2356
    /* Allocate table if we didn't have any */
2357
0
    {
2358
0
        T = mbedtls_calloc(T_size, sizeof(mbedtls_ecp_point));
2359
0
        if (T == NULL) {
2360
0
            ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
2361
0
            goto cleanup;
2362
0
        }
2363
2364
0
        for (i = 0; i < T_size; i++) {
2365
0
            mbedtls_ecp_point_init(&T[i]);
2366
0
        }
2367
2368
0
        T_ok = 0;
2369
0
    }
2370
2371
    /* Compute table (or finish computing it) if not done already */
2372
0
    if (!T_ok) {
2373
0
        MBEDTLS_MPI_CHK(ecp_precompute_comb(grp, T, P, w, d, rs_ctx));
2374
2375
0
        if (p_eq_g) {
2376
            /* almost transfer ownership of T to the group, but keep a copy of
2377
             * the pointer to use for calling the next function more easily */
2378
0
            grp->T = T;
2379
0
            grp->T_size = T_size;
2380
0
        }
2381
0
    }
2382
2383
    /* Actual comb multiplication using precomputed points */
2384
0
    MBEDTLS_MPI_CHK(ecp_mul_comb_after_precomp(grp, R, m,
2385
0
                                               T, T_size, w, d,
2386
0
                                               f_rng, p_rng, rs_ctx));
2387
2388
0
cleanup:
2389
2390
0
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2391
0
    ecp_drbg_free(&drbg_ctx);
2392
0
#endif
2393
2394
    /* does T belong to the group? */
2395
0
    if (T == grp->T) {
2396
0
        T = NULL;
2397
0
    }
2398
2399
    /* does T belong to the restart context? */
2400
#if defined(MBEDTLS_ECP_RESTARTABLE)
2401
    if (rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL) {
2402
        /* transfer ownership of T from local function to rsm */
2403
        rs_ctx->rsm->T_size = T_size;
2404
        rs_ctx->rsm->T = T;
2405
        T = NULL;
2406
    }
2407
#endif
2408
2409
    /* did T belong to us? then let's destroy it! */
2410
0
    if (T != NULL) {
2411
0
        for (i = 0; i < T_size; i++) {
2412
0
            mbedtls_ecp_point_free(&T[i]);
2413
0
        }
2414
0
        mbedtls_free(T);
2415
0
    }
2416
2417
    /* prevent caller from using invalid value */
2418
0
    int should_free_R = (ret != 0);
2419
#if defined(MBEDTLS_ECP_RESTARTABLE)
2420
    /* don't free R while in progress in case R == P */
2421
    if (ret == MBEDTLS_ERR_ECP_IN_PROGRESS) {
2422
        should_free_R = 0;
2423
    }
2424
#endif
2425
0
    if (should_free_R) {
2426
0
        mbedtls_ecp_point_free(R);
2427
0
    }
2428
2429
0
    ECP_RS_LEAVE(rsm);
2430
2431
0
    return ret;
2432
0
}
2433
2434
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2435
2436
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2437
/*
2438
 * For Montgomery curves, we do all the internal arithmetic in projective
2439
 * coordinates. Import/export of points uses only the x coordinates, which is
2440
 * internally represented as X / Z.
2441
 *
2442
 * For scalar multiplication, we'll use a Montgomery ladder.
2443
 */
2444
2445
/*
2446
 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
2447
 * Cost: 1M + 1I
2448
 */
2449
static int ecp_normalize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P)
2450
0
{
2451
#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
2452
    if (mbedtls_internal_ecp_grp_capable(grp)) {
2453
        return mbedtls_internal_ecp_normalize_mxz(grp, P);
2454
    }
2455
#endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
2456
2457
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
2458
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
2459
#else
2460
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2461
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&P->Z, &P->Z, &grp->P));
2462
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->X, &P->X, &P->Z));
2463
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&P->Z, 1));
2464
2465
0
cleanup:
2466
0
    return ret;
2467
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */
2468
0
}
2469
2470
/*
2471
 * Randomize projective x/z coordinates:
2472
 * (X, Z) -> (l X, l Z) for random l
2473
 * This is sort of the reverse operation of ecp_normalize_mxz().
2474
 *
2475
 * This countermeasure was first suggested in [2].
2476
 * Cost: 2M
2477
 */
2478
static int ecp_randomize_mxz(const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
2479
                             int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
2480
0
{
2481
#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
2482
    if (mbedtls_internal_ecp_grp_capable(grp)) {
2483
        return mbedtls_internal_ecp_randomize_mxz(grp, P, f_rng, p_rng);
2484
    }
2485
#endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
2486
2487
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
2488
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
2489
#else
2490
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2491
0
    mbedtls_mpi l;
2492
0
    mbedtls_mpi_init(&l);
2493
2494
    /* Generate l such that 1 < l < p */
2495
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_random(&l, 2, &grp->P, f_rng, p_rng));
2496
2497
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->X, &P->X, &l));
2498
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &P->Z, &P->Z, &l));
2499
2500
0
cleanup:
2501
0
    mbedtls_mpi_free(&l);
2502
2503
0
    if (ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) {
2504
0
        ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
2505
0
    }
2506
0
    return ret;
2507
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */
2508
0
}
2509
2510
/*
2511
 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
2512
 * for Montgomery curves in x/z coordinates.
2513
 *
2514
 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
2515
 * with
2516
 * d =  X1
2517
 * P = (X2, Z2)
2518
 * Q = (X3, Z3)
2519
 * R = (X4, Z4)
2520
 * S = (X5, Z5)
2521
 * and eliminating temporary variables tO, ..., t4.
2522
 *
2523
 * Cost: 5M + 4S
2524
 */
2525
static int ecp_double_add_mxz(const mbedtls_ecp_group *grp,
2526
                              mbedtls_ecp_point *R, mbedtls_ecp_point *S,
2527
                              const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
2528
                              const mbedtls_mpi *d)
2529
0
{
2530
#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
2531
    if (mbedtls_internal_ecp_grp_capable(grp)) {
2532
        return mbedtls_internal_ecp_double_add_mxz(grp, R, S, P, Q, d);
2533
    }
2534
#endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
2535
2536
#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
2537
    return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
2538
#else
2539
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2540
0
    mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
2541
2542
0
    mbedtls_mpi_init(&A); mbedtls_mpi_init(&AA); mbedtls_mpi_init(&B);
2543
0
    mbedtls_mpi_init(&BB); mbedtls_mpi_init(&E); mbedtls_mpi_init(&C);
2544
0
    mbedtls_mpi_init(&D); mbedtls_mpi_init(&DA); mbedtls_mpi_init(&CB);
2545
2546
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &A,    &P->X,   &P->Z));
2547
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &AA,   &A,      &A));
2548
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &B,    &P->X,   &P->Z));
2549
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &BB,   &B,      &B));
2550
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &E,    &AA,     &BB));
2551
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &C,    &Q->X,   &Q->Z));
2552
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &D,    &Q->X,   &Q->Z));
2553
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &DA,   &D,      &A));
2554
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &CB,   &C,      &B));
2555
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &S->X, &DA,     &CB));
2556
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->X, &S->X,   &S->X));
2557
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mod(grp, &S->Z, &DA,     &CB));
2558
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->Z, &S->Z,   &S->Z));
2559
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &S->Z, d,       &S->Z));
2560
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->X, &AA,     &BB));
2561
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->Z, &grp->A, &E));
2562
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &R->Z, &BB,     &R->Z));
2563
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &R->Z, &E,      &R->Z));
2564
2565
0
cleanup:
2566
0
    mbedtls_mpi_free(&A); mbedtls_mpi_free(&AA); mbedtls_mpi_free(&B);
2567
0
    mbedtls_mpi_free(&BB); mbedtls_mpi_free(&E); mbedtls_mpi_free(&C);
2568
0
    mbedtls_mpi_free(&D); mbedtls_mpi_free(&DA); mbedtls_mpi_free(&CB);
2569
2570
0
    return ret;
2571
0
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */
2572
0
}
2573
2574
/*
2575
 * Multiplication with Montgomery ladder in x/z coordinates,
2576
 * for curves in Montgomery form
2577
 */
2578
static int ecp_mul_mxz(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2579
                       const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2580
                       int (*f_rng)(void *, unsigned char *, size_t),
2581
                       void *p_rng)
2582
0
{
2583
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2584
0
    int have_rng = 1;
2585
0
    size_t i;
2586
0
    unsigned char b;
2587
0
    mbedtls_ecp_point RP;
2588
0
    mbedtls_mpi PX;
2589
0
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2590
0
    ecp_drbg_context drbg_ctx;
2591
2592
0
    ecp_drbg_init(&drbg_ctx);
2593
0
#endif
2594
0
    mbedtls_ecp_point_init(&RP); mbedtls_mpi_init(&PX);
2595
2596
0
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2597
0
    if (f_rng == NULL) {
2598
0
        const size_t m_len = (grp->nbits + 7) / 8;
2599
0
        MBEDTLS_MPI_CHK(ecp_drbg_seed(&drbg_ctx, m, m_len));
2600
0
        f_rng = &ecp_drbg_random;
2601
0
        p_rng = &drbg_ctx;
2602
0
    }
2603
0
#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */
2604
2605
    /* Save PX and read from P before writing to R, in case P == R */
2606
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&PX, &P->X));
2607
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_copy(&RP, P));
2608
2609
    /* Set R to zero in modified x/z coordinates */
2610
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->X, 1));
2611
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&R->Z, 0));
2612
0
    mbedtls_mpi_free(&R->Y);
2613
2614
    /* RP.X might be slightly larger than P, so reduce it */
2615
0
    MOD_ADD(RP.X);
2616
2617
    /* Randomize coordinates of the starting point */
2618
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2619
    if (f_rng == NULL) {
2620
        have_rng = 0;
2621
    }
2622
#endif
2623
0
    if (have_rng) {
2624
0
        MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, &RP, f_rng, p_rng));
2625
0
    }
2626
2627
    /* Loop invariant: R = result so far, RP = R + P */
2628
0
    i = grp->nbits + 1; /* one past the (zero-based) required msb for private keys */
2629
0
    while (i-- > 0) {
2630
0
        b = mbedtls_mpi_get_bit(m, i);
2631
        /*
2632
         *  if (b) R = 2R + P else R = 2R,
2633
         * which is:
2634
         *  if (b) double_add( RP, R, RP, R )
2635
         *  else   double_add( R, RP, R, RP )
2636
         * but using safe conditional swaps to avoid leaks
2637
         */
2638
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->X, &RP.X, b));
2639
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->Z, &RP.Z, b));
2640
0
        MBEDTLS_MPI_CHK(ecp_double_add_mxz(grp, R, &RP, R, &RP, &PX));
2641
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->X, &RP.X, b));
2642
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_swap(&R->Z, &RP.Z, b));
2643
0
    }
2644
2645
    /*
2646
     * Knowledge of the projective coordinates may leak the last few bits of the
2647
     * scalar [1], and since our MPI implementation isn't constant-flow,
2648
     * inversion (used for coordinate normalization) may leak the full value
2649
     * of its input via side-channels [2].
2650
     *
2651
     * [1] https://eprint.iacr.org/2003/191
2652
     * [2] https://eprint.iacr.org/2020/055
2653
     *
2654
     * Avoid the leak by randomizing coordinates before we normalize them.
2655
     */
2656
0
    have_rng = 1;
2657
#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2658
    if (f_rng == NULL) {
2659
        have_rng = 0;
2660
    }
2661
#endif
2662
0
    if (have_rng) {
2663
0
        MBEDTLS_MPI_CHK(ecp_randomize_mxz(grp, R, f_rng, p_rng));
2664
0
    }
2665
2666
0
    MBEDTLS_MPI_CHK(ecp_normalize_mxz(grp, R));
2667
2668
0
cleanup:
2669
0
#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG)
2670
0
    ecp_drbg_free(&drbg_ctx);
2671
0
#endif
2672
2673
0
    mbedtls_ecp_point_free(&RP); mbedtls_mpi_free(&PX);
2674
2675
0
    return ret;
2676
0
}
2677
2678
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
2679
2680
/*
2681
 * Restartable multiplication R = m * P
2682
 */
2683
int mbedtls_ecp_mul_restartable(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2684
                                const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2685
                                int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
2686
                                mbedtls_ecp_restart_ctx *rs_ctx)
2687
0
{
2688
0
    int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2689
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2690
    char is_grp_capable = 0;
2691
#endif
2692
0
    ECP_VALIDATE_RET(grp != NULL);
2693
0
    ECP_VALIDATE_RET(R   != NULL);
2694
0
    ECP_VALIDATE_RET(m   != NULL);
2695
0
    ECP_VALIDATE_RET(P   != NULL);
2696
2697
#if defined(MBEDTLS_ECP_RESTARTABLE)
2698
    /* reset ops count for this call if top-level */
2699
    if (rs_ctx != NULL && rs_ctx->depth++ == 0) {
2700
        rs_ctx->ops_done = 0;
2701
    }
2702
#else
2703
0
    (void) rs_ctx;
2704
0
#endif
2705
2706
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2707
    if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) {
2708
        MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp));
2709
    }
2710
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
2711
2712
0
    int restarting = 0;
2713
#if defined(MBEDTLS_ECP_RESTARTABLE)
2714
    restarting = (rs_ctx != NULL && rs_ctx->rsm != NULL);
2715
#endif
2716
    /* skip argument check when restarting */
2717
0
    if (!restarting) {
2718
        /* check_privkey is free */
2719
0
        MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_CHK);
2720
2721
        /* Common sanity checks */
2722
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(grp, m));
2723
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P));
2724
0
    }
2725
2726
0
    ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
2727
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2728
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
2729
0
        MBEDTLS_MPI_CHK(ecp_mul_mxz(grp, R, m, P, f_rng, p_rng));
2730
0
    }
2731
0
#endif
2732
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2733
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
2734
0
        MBEDTLS_MPI_CHK(ecp_mul_comb(grp, R, m, P, f_rng, p_rng, rs_ctx));
2735
0
    }
2736
0
#endif
2737
2738
0
cleanup:
2739
2740
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2741
    if (is_grp_capable) {
2742
        mbedtls_internal_ecp_free(grp);
2743
    }
2744
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
2745
2746
#if defined(MBEDTLS_ECP_RESTARTABLE)
2747
    if (rs_ctx != NULL) {
2748
        rs_ctx->depth--;
2749
    }
2750
#endif
2751
2752
0
    return ret;
2753
0
}
2754
2755
/*
2756
 * Multiplication R = m * P
2757
 */
2758
int mbedtls_ecp_mul(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2759
                    const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2760
                    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
2761
0
{
2762
0
    ECP_VALIDATE_RET(grp != NULL);
2763
0
    ECP_VALIDATE_RET(R   != NULL);
2764
0
    ECP_VALIDATE_RET(m   != NULL);
2765
0
    ECP_VALIDATE_RET(P   != NULL);
2766
0
    return mbedtls_ecp_mul_restartable(grp, R, m, P, f_rng, p_rng, NULL);
2767
0
}
2768
2769
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2770
/*
2771
 * Check that an affine point is valid as a public key,
2772
 * short weierstrass curves (SEC1 3.2.3.1)
2773
 */
2774
static int ecp_check_pubkey_sw(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt)
2775
0
{
2776
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2777
0
    mbedtls_mpi YY, RHS;
2778
2779
    /* pt coordinates must be normalized for our checks */
2780
0
    if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0 ||
2781
0
        mbedtls_mpi_cmp_int(&pt->Y, 0) < 0 ||
2782
0
        mbedtls_mpi_cmp_mpi(&pt->X, &grp->P) >= 0 ||
2783
0
        mbedtls_mpi_cmp_mpi(&pt->Y, &grp->P) >= 0) {
2784
0
        return MBEDTLS_ERR_ECP_INVALID_KEY;
2785
0
    }
2786
2787
0
    mbedtls_mpi_init(&YY); mbedtls_mpi_init(&RHS);
2788
2789
    /*
2790
     * YY = Y^2
2791
     * RHS = X (X^2 + A) + B = X^3 + A X + B
2792
     */
2793
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &YY,  &pt->Y,   &pt->Y));
2794
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &RHS, &pt->X,   &pt->X));
2795
2796
    /* Special case for A = -3 */
2797
0
    if (grp->A.p == NULL) {
2798
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(&RHS, &RHS, 3));  MOD_SUB(RHS);
2799
0
    } else {
2800
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &RHS, &RHS, &grp->A));
2801
0
    }
2802
2803
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mod(grp, &RHS, &RHS,     &pt->X));
2804
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mod(grp, &RHS, &RHS,     &grp->B));
2805
2806
0
    if (mbedtls_mpi_cmp_mpi(&YY, &RHS) != 0) {
2807
0
        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
2808
0
    }
2809
2810
0
cleanup:
2811
2812
0
    mbedtls_mpi_free(&YY); mbedtls_mpi_free(&RHS);
2813
2814
0
    return ret;
2815
0
}
2816
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2817
2818
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
2819
/*
2820
 * R = m * P with shortcuts for m == 0, m == 1 and m == -1
2821
 * NOT constant-time - ONLY for short Weierstrass!
2822
 */
2823
static int mbedtls_ecp_mul_shortcuts(mbedtls_ecp_group *grp,
2824
                                     mbedtls_ecp_point *R,
2825
                                     const mbedtls_mpi *m,
2826
                                     const mbedtls_ecp_point *P,
2827
                                     mbedtls_ecp_restart_ctx *rs_ctx)
2828
0
{
2829
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2830
2831
0
    if (mbedtls_mpi_cmp_int(m, 0) == 0) {
2832
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P));
2833
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_set_zero(R));
2834
0
    } else if (mbedtls_mpi_cmp_int(m, 1) == 0) {
2835
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P));
2836
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P));
2837
0
    } else if (mbedtls_mpi_cmp_int(m, -1) == 0) {
2838
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, P));
2839
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, P));
2840
0
        if (mbedtls_mpi_cmp_int(&R->Y, 0) != 0) {
2841
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&R->Y, &grp->P, &R->Y));
2842
0
        }
2843
0
    } else {
2844
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_mul_restartable(grp, R, m, P,
2845
0
                                                    NULL, NULL, rs_ctx));
2846
0
    }
2847
2848
0
cleanup:
2849
0
    return ret;
2850
0
}
2851
2852
/*
2853
 * Restartable linear combination
2854
 * NOT constant-time
2855
 */
2856
int mbedtls_ecp_muladd_restartable(
2857
    mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2858
    const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2859
    const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
2860
    mbedtls_ecp_restart_ctx *rs_ctx)
2861
0
{
2862
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
2863
0
    mbedtls_ecp_point mP;
2864
0
    mbedtls_ecp_point *pmP = &mP;
2865
0
    mbedtls_ecp_point *pR = R;
2866
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2867
    char is_grp_capable = 0;
2868
#endif
2869
0
    ECP_VALIDATE_RET(grp != NULL);
2870
0
    ECP_VALIDATE_RET(R   != NULL);
2871
0
    ECP_VALIDATE_RET(m   != NULL);
2872
0
    ECP_VALIDATE_RET(P   != NULL);
2873
0
    ECP_VALIDATE_RET(n   != NULL);
2874
0
    ECP_VALIDATE_RET(Q   != NULL);
2875
2876
0
    if (mbedtls_ecp_get_type(grp) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
2877
0
        return MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
2878
0
    }
2879
2880
0
    mbedtls_ecp_point_init(&mP);
2881
2882
0
    ECP_RS_ENTER(ma);
2883
2884
#if defined(MBEDTLS_ECP_RESTARTABLE)
2885
    if (rs_ctx != NULL && rs_ctx->ma != NULL) {
2886
        /* redirect intermediate results to restart context */
2887
        pmP = &rs_ctx->ma->mP;
2888
        pR  = &rs_ctx->ma->R;
2889
2890
        /* jump to next operation */
2891
        if (rs_ctx->ma->state == ecp_rsma_mul2) {
2892
            goto mul2;
2893
        }
2894
        if (rs_ctx->ma->state == ecp_rsma_add) {
2895
            goto add;
2896
        }
2897
        if (rs_ctx->ma->state == ecp_rsma_norm) {
2898
            goto norm;
2899
        }
2900
    }
2901
#endif /* MBEDTLS_ECP_RESTARTABLE */
2902
2903
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pmP, m, P, rs_ctx));
2904
#if defined(MBEDTLS_ECP_RESTARTABLE)
2905
    if (rs_ctx != NULL && rs_ctx->ma != NULL) {
2906
        rs_ctx->ma->state = ecp_rsma_mul2;
2907
    }
2908
2909
mul2:
2910
#endif
2911
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_mul_shortcuts(grp, pR,  n, Q, rs_ctx));
2912
2913
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2914
    if ((is_grp_capable = mbedtls_internal_ecp_grp_capable(grp))) {
2915
        MBEDTLS_MPI_CHK(mbedtls_internal_ecp_init(grp));
2916
    }
2917
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
2918
2919
#if defined(MBEDTLS_ECP_RESTARTABLE)
2920
    if (rs_ctx != NULL && rs_ctx->ma != NULL) {
2921
        rs_ctx->ma->state = ecp_rsma_add;
2922
    }
2923
2924
add:
2925
#endif
2926
0
    MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_ADD);
2927
0
    MBEDTLS_MPI_CHK(ecp_add_mixed(grp, pR, pmP, pR));
2928
#if defined(MBEDTLS_ECP_RESTARTABLE)
2929
    if (rs_ctx != NULL && rs_ctx->ma != NULL) {
2930
        rs_ctx->ma->state = ecp_rsma_norm;
2931
    }
2932
2933
norm:
2934
#endif
2935
0
    MBEDTLS_ECP_BUDGET(MBEDTLS_ECP_OPS_INV);
2936
0
    MBEDTLS_MPI_CHK(ecp_normalize_jac(grp, pR));
2937
2938
#if defined(MBEDTLS_ECP_RESTARTABLE)
2939
    if (rs_ctx != NULL && rs_ctx->ma != NULL) {
2940
        MBEDTLS_MPI_CHK(mbedtls_ecp_copy(R, pR));
2941
    }
2942
#endif
2943
2944
0
cleanup:
2945
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
2946
    if (is_grp_capable) {
2947
        mbedtls_internal_ecp_free(grp);
2948
    }
2949
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
2950
2951
0
    mbedtls_ecp_point_free(&mP);
2952
2953
0
    ECP_RS_LEAVE(ma);
2954
2955
0
    return ret;
2956
0
}
2957
2958
/*
2959
 * Linear combination
2960
 * NOT constant-time
2961
 */
2962
int mbedtls_ecp_muladd(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
2963
                       const mbedtls_mpi *m, const mbedtls_ecp_point *P,
2964
                       const mbedtls_mpi *n, const mbedtls_ecp_point *Q)
2965
0
{
2966
0
    ECP_VALIDATE_RET(grp != NULL);
2967
0
    ECP_VALIDATE_RET(R   != NULL);
2968
0
    ECP_VALIDATE_RET(m   != NULL);
2969
0
    ECP_VALIDATE_RET(P   != NULL);
2970
0
    ECP_VALIDATE_RET(n   != NULL);
2971
0
    ECP_VALIDATE_RET(Q   != NULL);
2972
0
    return mbedtls_ecp_muladd_restartable(grp, R, m, P, n, Q, NULL);
2973
0
}
2974
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
2975
2976
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
2977
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
2978
#define ECP_MPI_INIT(s, n, p) { s, (n), (mbedtls_mpi_uint *) (p) }
2979
#define ECP_MPI_INIT_ARRAY(x)   \
2980
    ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x)
2981
/*
2982
 * Constants for the two points other than 0, 1, -1 (mod p) in
2983
 * https://cr.yp.to/ecdh.html#validate
2984
 * See ecp_check_pubkey_x25519().
2985
 */
2986
static const mbedtls_mpi_uint x25519_bad_point_1[] = {
2987
    MBEDTLS_BYTES_TO_T_UINT_8(0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae),
2988
    MBEDTLS_BYTES_TO_T_UINT_8(0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a),
2989
    MBEDTLS_BYTES_TO_T_UINT_8(0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd),
2990
    MBEDTLS_BYTES_TO_T_UINT_8(0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00),
2991
};
2992
static const mbedtls_mpi_uint x25519_bad_point_2[] = {
2993
    MBEDTLS_BYTES_TO_T_UINT_8(0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24),
2994
    MBEDTLS_BYTES_TO_T_UINT_8(0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b),
2995
    MBEDTLS_BYTES_TO_T_UINT_8(0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86),
2996
    MBEDTLS_BYTES_TO_T_UINT_8(0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57),
2997
};
2998
static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY(
2999
    x25519_bad_point_1);
3000
static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY(
3001
    x25519_bad_point_2);
3002
#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
3003
3004
/*
3005
 * Check that the input point is not one of the low-order points.
3006
 * This is recommended by the "May the Fourth" paper:
3007
 * https://eprint.iacr.org/2017/806.pdf
3008
 * Those points are never sent by an honest peer.
3009
 */
3010
static int ecp_check_bad_points_mx(const mbedtls_mpi *X, const mbedtls_mpi *P,
3011
                                   const mbedtls_ecp_group_id grp_id)
3012
0
{
3013
0
    int ret;
3014
0
    mbedtls_mpi XmP;
3015
3016
0
    mbedtls_mpi_init(&XmP);
3017
3018
    /* Reduce X mod P so that we only need to check values less than P.
3019
     * We know X < 2^256 so we can proceed by subtraction. */
3020
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&XmP, X));
3021
0
    while (mbedtls_mpi_cmp_mpi(&XmP, P) >= 0) {
3022
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&XmP, &XmP, P));
3023
0
    }
3024
3025
    /* Check against the known bad values that are less than P. For Curve448
3026
     * these are 0, 1 and -1. For Curve25519 we check the values less than P
3027
     * from the following list: https://cr.yp.to/ecdh.html#validate */
3028
0
    if (mbedtls_mpi_cmp_int(&XmP, 1) <= 0) {  /* takes care of 0 and 1 */
3029
0
        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3030
0
        goto cleanup;
3031
0
    }
3032
3033
0
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3034
0
    if (grp_id == MBEDTLS_ECP_DP_CURVE25519) {
3035
0
        if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_1) == 0) {
3036
0
            ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3037
0
            goto cleanup;
3038
0
        }
3039
3040
0
        if (mbedtls_mpi_cmp_mpi(&XmP, &ecp_x25519_bad_point_2) == 0) {
3041
0
            ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3042
0
            goto cleanup;
3043
0
        }
3044
0
    }
3045
#else
3046
    (void) grp_id;
3047
#endif
3048
3049
    /* Final check: check if XmP + 1 is P (final because it changes XmP!) */
3050
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&XmP, &XmP, 1));
3051
0
    if (mbedtls_mpi_cmp_mpi(&XmP, P) == 0) {
3052
0
        ret = MBEDTLS_ERR_ECP_INVALID_KEY;
3053
0
        goto cleanup;
3054
0
    }
3055
3056
0
    ret = 0;
3057
3058
0
cleanup:
3059
0
    mbedtls_mpi_free(&XmP);
3060
3061
0
    return ret;
3062
0
}
3063
3064
/*
3065
 * Check validity of a public key for Montgomery curves with x-only schemes
3066
 */
3067
static int ecp_check_pubkey_mx(const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt)
3068
0
{
3069
    /* [Curve25519 p. 5] Just check X is the correct number of bytes */
3070
    /* Allow any public value, if it's too big then we'll just reduce it mod p
3071
     * (RFC 7748 sec. 5 para. 3). */
3072
0
    if (mbedtls_mpi_size(&pt->X) > (grp->nbits + 7) / 8) {
3073
0
        return MBEDTLS_ERR_ECP_INVALID_KEY;
3074
0
    }
3075
3076
    /* Implicit in all standards (as they don't consider negative numbers):
3077
     * X must be non-negative. This is normally ensured by the way it's
3078
     * encoded for transmission, but let's be extra sure. */
3079
0
    if (mbedtls_mpi_cmp_int(&pt->X, 0) < 0) {
3080
0
        return MBEDTLS_ERR_ECP_INVALID_KEY;
3081
0
    }
3082
3083
0
    return ecp_check_bad_points_mx(&pt->X, &grp->P, grp->id);
3084
0
}
3085
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3086
3087
/*
3088
 * Check that a point is valid as a public key
3089
 */
3090
int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group *grp,
3091
                             const mbedtls_ecp_point *pt)
3092
0
{
3093
0
    ECP_VALIDATE_RET(grp != NULL);
3094
0
    ECP_VALIDATE_RET(pt  != NULL);
3095
3096
    /* Must use affine coordinates */
3097
0
    if (mbedtls_mpi_cmp_int(&pt->Z, 1) != 0) {
3098
0
        return MBEDTLS_ERR_ECP_INVALID_KEY;
3099
0
    }
3100
3101
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3102
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
3103
0
        return ecp_check_pubkey_mx(grp, pt);
3104
0
    }
3105
0
#endif
3106
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3107
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
3108
0
        return ecp_check_pubkey_sw(grp, pt);
3109
0
    }
3110
0
#endif
3111
0
    return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3112
0
}
3113
3114
/*
3115
 * Check that an mbedtls_mpi is valid as a private key
3116
 */
3117
int mbedtls_ecp_check_privkey(const mbedtls_ecp_group *grp,
3118
                              const mbedtls_mpi *d)
3119
0
{
3120
0
    ECP_VALIDATE_RET(grp != NULL);
3121
0
    ECP_VALIDATE_RET(d   != NULL);
3122
3123
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3124
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
3125
        /* see RFC 7748 sec. 5 para. 5 */
3126
0
        if (mbedtls_mpi_get_bit(d, 0) != 0 ||
3127
0
            mbedtls_mpi_get_bit(d, 1) != 0 ||
3128
0
            mbedtls_mpi_bitlen(d) - 1 != grp->nbits) {  /* mbedtls_mpi_bitlen is one-based! */
3129
0
            return MBEDTLS_ERR_ECP_INVALID_KEY;
3130
0
        }
3131
3132
        /* see [Curve25519] page 5 */
3133
0
        if (grp->nbits == 254 && mbedtls_mpi_get_bit(d, 2) != 0) {
3134
0
            return MBEDTLS_ERR_ECP_INVALID_KEY;
3135
0
        }
3136
3137
0
        return 0;
3138
0
    }
3139
0
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3140
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3141
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
3142
        /* see SEC1 3.2 */
3143
0
        if (mbedtls_mpi_cmp_int(d, 1) < 0 ||
3144
0
            mbedtls_mpi_cmp_mpi(d, &grp->N) >= 0) {
3145
0
            return MBEDTLS_ERR_ECP_INVALID_KEY;
3146
0
        } else {
3147
0
            return 0;
3148
0
        }
3149
0
    }
3150
0
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3151
3152
0
    return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3153
0
}
3154
3155
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3156
MBEDTLS_STATIC_TESTABLE
3157
int mbedtls_ecp_gen_privkey_mx(size_t high_bit,
3158
                               mbedtls_mpi *d,
3159
                               int (*f_rng)(void *, unsigned char *, size_t),
3160
                               void *p_rng)
3161
0
{
3162
0
    int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3163
0
    size_t n_random_bytes = high_bit / 8 + 1;
3164
3165
    /* [Curve25519] page 5 */
3166
    /* Generate a (high_bit+1)-bit random number by generating just enough
3167
     * random bytes, then shifting out extra bits from the top (necessary
3168
     * when (high_bit+1) is not a multiple of 8). */
3169
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(d, n_random_bytes,
3170
0
                                            f_rng, p_rng));
3171
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(d, 8 * n_random_bytes - high_bit - 1));
3172
3173
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, high_bit, 1));
3174
3175
    /* Make sure the last two bits are unset for Curve448, three bits for
3176
       Curve25519 */
3177
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 0, 0));
3178
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 1, 0));
3179
0
    if (high_bit == 254) {
3180
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(d, 2, 0));
3181
0
    }
3182
3183
0
cleanup:
3184
0
    return ret;
3185
0
}
3186
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3187
3188
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3189
static int mbedtls_ecp_gen_privkey_sw(
3190
    const mbedtls_mpi *N, mbedtls_mpi *d,
3191
    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
3192
0
{
3193
0
    int ret = mbedtls_mpi_random(d, 1, N, f_rng, p_rng);
3194
0
    switch (ret) {
3195
0
        case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE:
3196
0
            return MBEDTLS_ERR_ECP_RANDOM_FAILED;
3197
0
        default:
3198
0
            return ret;
3199
0
    }
3200
0
}
3201
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3202
3203
/*
3204
 * Generate a private key
3205
 */
3206
int mbedtls_ecp_gen_privkey(const mbedtls_ecp_group *grp,
3207
                            mbedtls_mpi *d,
3208
                            int (*f_rng)(void *, unsigned char *, size_t),
3209
                            void *p_rng)
3210
0
{
3211
0
    ECP_VALIDATE_RET(grp   != NULL);
3212
0
    ECP_VALIDATE_RET(d     != NULL);
3213
0
    ECP_VALIDATE_RET(f_rng != NULL);
3214
3215
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3216
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
3217
0
        return mbedtls_ecp_gen_privkey_mx(grp->nbits, d, f_rng, p_rng);
3218
0
    }
3219
0
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3220
3221
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3222
0
    if (mbedtls_ecp_get_type(grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
3223
0
        return mbedtls_ecp_gen_privkey_sw(&grp->N, d, f_rng, p_rng);
3224
0
    }
3225
0
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3226
3227
0
    return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3228
0
}
3229
3230
/*
3231
 * Generate a keypair with configurable base point
3232
 */
3233
int mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group *grp,
3234
                                 const mbedtls_ecp_point *G,
3235
                                 mbedtls_mpi *d, mbedtls_ecp_point *Q,
3236
                                 int (*f_rng)(void *, unsigned char *, size_t),
3237
                                 void *p_rng)
3238
0
{
3239
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3240
0
    ECP_VALIDATE_RET(grp   != NULL);
3241
0
    ECP_VALIDATE_RET(d     != NULL);
3242
0
    ECP_VALIDATE_RET(G     != NULL);
3243
0
    ECP_VALIDATE_RET(Q     != NULL);
3244
0
    ECP_VALIDATE_RET(f_rng != NULL);
3245
3246
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_gen_privkey(grp, d, f_rng, p_rng));
3247
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, Q, d, G, f_rng, p_rng));
3248
3249
0
cleanup:
3250
0
    return ret;
3251
0
}
3252
3253
/*
3254
 * Generate key pair, wrapper for conventional base point
3255
 */
3256
int mbedtls_ecp_gen_keypair(mbedtls_ecp_group *grp,
3257
                            mbedtls_mpi *d, mbedtls_ecp_point *Q,
3258
                            int (*f_rng)(void *, unsigned char *, size_t),
3259
                            void *p_rng)
3260
0
{
3261
0
    ECP_VALIDATE_RET(grp   != NULL);
3262
0
    ECP_VALIDATE_RET(d     != NULL);
3263
0
    ECP_VALIDATE_RET(Q     != NULL);
3264
0
    ECP_VALIDATE_RET(f_rng != NULL);
3265
3266
0
    return mbedtls_ecp_gen_keypair_base(grp, &grp->G, d, Q, f_rng, p_rng);
3267
0
}
3268
3269
/*
3270
 * Generate a keypair, prettier wrapper
3271
 */
3272
int mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3273
                        int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
3274
0
{
3275
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3276
0
    ECP_VALIDATE_RET(key   != NULL);
3277
0
    ECP_VALIDATE_RET(f_rng != NULL);
3278
3279
0
    if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) {
3280
0
        return ret;
3281
0
    }
3282
3283
0
    return mbedtls_ecp_gen_keypair(&key->grp, &key->d, &key->Q, f_rng, p_rng);
3284
0
}
3285
3286
0
#define ECP_CURVE25519_KEY_SIZE 32
3287
/*
3288
 * Read a private key.
3289
 */
3290
int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
3291
                         const unsigned char *buf, size_t buflen)
3292
0
{
3293
0
    int ret = 0;
3294
3295
0
    ECP_VALIDATE_RET(key  != NULL);
3296
0
    ECP_VALIDATE_RET(buf  != NULL);
3297
3298
0
    if ((ret = mbedtls_ecp_group_load(&key->grp, grp_id)) != 0) {
3299
0
        return ret;
3300
0
    }
3301
3302
0
    ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3303
3304
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3305
0
    if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
3306
        /*
3307
         * If it is Curve25519 curve then mask the key as mandated by RFC7748
3308
         */
3309
0
        if (grp_id == MBEDTLS_ECP_DP_CURVE25519) {
3310
0
            if (buflen != ECP_CURVE25519_KEY_SIZE) {
3311
0
                return MBEDTLS_ERR_ECP_INVALID_KEY;
3312
0
            }
3313
3314
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary_le(&key->d, buf, buflen));
3315
3316
            /* Set the three least significant bits to 0 */
3317
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 0, 0));
3318
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 1, 0));
3319
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&key->d, 2, 0));
3320
3321
            /* Set the most significant bit to 0 */
3322
0
            MBEDTLS_MPI_CHK(
3323
0
                mbedtls_mpi_set_bit(&key->d,
3324
0
                                    ECP_CURVE25519_KEY_SIZE * 8 - 1, 0)
3325
0
                );
3326
3327
            /* Set the second most significant bit to 1 */
3328
0
            MBEDTLS_MPI_CHK(
3329
0
                mbedtls_mpi_set_bit(&key->d,
3330
0
                                    ECP_CURVE25519_KEY_SIZE * 8 - 2, 1)
3331
0
                );
3332
0
        } else {
3333
0
            ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3334
0
        }
3335
0
    }
3336
3337
0
#endif
3338
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3339
0
    if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
3340
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(&key->d, buf, buflen));
3341
3342
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_check_privkey(&key->grp, &key->d));
3343
0
    }
3344
3345
0
#endif
3346
0
cleanup:
3347
3348
0
    if (ret != 0) {
3349
0
        mbedtls_mpi_free(&key->d);
3350
0
    }
3351
3352
0
    return ret;
3353
0
}
3354
3355
/*
3356
 * Write a private key.
3357
 */
3358
int mbedtls_ecp_write_key(mbedtls_ecp_keypair *key,
3359
                          unsigned char *buf, size_t buflen)
3360
0
{
3361
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3362
3363
0
    ECP_VALIDATE_RET(key != NULL);
3364
0
    ECP_VALIDATE_RET(buflen == 0 || buf != NULL);
3365
3366
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3367
0
    if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_MONTGOMERY) {
3368
0
        if (key->grp.id == MBEDTLS_ECP_DP_CURVE25519) {
3369
0
            if (buflen < ECP_CURVE25519_KEY_SIZE) {
3370
0
                return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL;
3371
0
            }
3372
3373
0
            MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary_le(&key->d, buf, buflen));
3374
0
        } else {
3375
0
            ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE;
3376
0
        }
3377
0
    }
3378
3379
0
#endif
3380
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3381
0
    if (mbedtls_ecp_get_type(&key->grp) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS) {
3382
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&key->d, buf, buflen));
3383
0
    }
3384
3385
0
#endif
3386
0
cleanup:
3387
3388
0
    return ret;
3389
0
}
3390
3391
3392
/*
3393
 * Check a public-private key pair
3394
 */
3395
int mbedtls_ecp_check_pub_priv(const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv)
3396
0
{
3397
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3398
0
    mbedtls_ecp_point Q;
3399
0
    mbedtls_ecp_group grp;
3400
0
    ECP_VALIDATE_RET(pub != NULL);
3401
0
    ECP_VALIDATE_RET(prv != NULL);
3402
3403
0
    if (pub->grp.id == MBEDTLS_ECP_DP_NONE ||
3404
0
        pub->grp.id != prv->grp.id ||
3405
0
        mbedtls_mpi_cmp_mpi(&pub->Q.X, &prv->Q.X) ||
3406
0
        mbedtls_mpi_cmp_mpi(&pub->Q.Y, &prv->Q.Y) ||
3407
0
        mbedtls_mpi_cmp_mpi(&pub->Q.Z, &prv->Q.Z)) {
3408
0
        return MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3409
0
    }
3410
3411
0
    mbedtls_ecp_point_init(&Q);
3412
0
    mbedtls_ecp_group_init(&grp);
3413
3414
    /* mbedtls_ecp_mul() needs a non-const group... */
3415
0
    mbedtls_ecp_group_copy(&grp, &prv->grp);
3416
3417
    /* Also checks d is valid */
3418
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &Q, &prv->d, &prv->grp.G, NULL, NULL));
3419
3420
0
    if (mbedtls_mpi_cmp_mpi(&Q.X, &prv->Q.X) ||
3421
0
        mbedtls_mpi_cmp_mpi(&Q.Y, &prv->Q.Y) ||
3422
0
        mbedtls_mpi_cmp_mpi(&Q.Z, &prv->Q.Z)) {
3423
0
        ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
3424
0
        goto cleanup;
3425
0
    }
3426
3427
0
cleanup:
3428
0
    mbedtls_ecp_point_free(&Q);
3429
0
    mbedtls_ecp_group_free(&grp);
3430
3431
0
    return ret;
3432
0
}
3433
3434
#if defined(MBEDTLS_SELF_TEST)
3435
3436
/* Adjust the exponent to be a valid private point for the specified curve.
3437
 * This is sometimes necessary because we use a single set of exponents
3438
 * for all curves but the validity of values depends on the curve. */
3439
static int self_test_adjust_exponent(const mbedtls_ecp_group *grp,
3440
                                     mbedtls_mpi *m)
3441
0
{
3442
0
    int ret = 0;
3443
0
    switch (grp->id) {
3444
    /* If Curve25519 is available, then that's what we use for the
3445
     * Montgomery test, so we don't need the adjustment code. */
3446
#if !defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3447
#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3448
        case MBEDTLS_ECP_DP_CURVE448:
3449
            /* Move highest bit from 254 to N-1. Setting bit N-1 is
3450
             * necessary to enforce the highest-bit-set constraint. */
3451
            MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, 254, 0));
3452
            MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(m, grp->nbits, 1));
3453
            /* Copy second-highest bit from 253 to N-2. This is not
3454
             * necessary but improves the test variety a bit. */
3455
            MBEDTLS_MPI_CHK(
3456
                mbedtls_mpi_set_bit(m, grp->nbits - 1,
3457
                                    mbedtls_mpi_get_bit(m, 253)));
3458
            break;
3459
#endif
3460
#endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */
3461
0
        default:
3462
            /* Non-Montgomery curves and Curve25519 need no adjustment. */
3463
0
            (void) grp;
3464
0
            (void) m;
3465
0
            goto cleanup;
3466
0
    }
3467
0
cleanup:
3468
0
    return ret;
3469
0
}
3470
3471
/* Calculate R = m.P for each m in exponents. Check that the number of
3472
 * basic operations doesn't depend on the value of m. */
3473
static int self_test_point(int verbose,
3474
                           mbedtls_ecp_group *grp,
3475
                           mbedtls_ecp_point *R,
3476
                           mbedtls_mpi *m,
3477
                           const mbedtls_ecp_point *P,
3478
                           const char *const *exponents,
3479
                           size_t n_exponents)
3480
0
{
3481
0
    int ret = 0;
3482
0
    size_t i = 0;
3483
0
    unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
3484
0
    add_count = 0;
3485
0
    dbl_count = 0;
3486
0
    mul_count = 0;
3487
3488
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[0]));
3489
0
    MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m));
3490
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, NULL, NULL));
3491
3492
0
    for (i = 1; i < n_exponents; i++) {
3493
0
        add_c_prev = add_count;
3494
0
        dbl_c_prev = dbl_count;
3495
0
        mul_c_prev = mul_count;
3496
0
        add_count = 0;
3497
0
        dbl_count = 0;
3498
0
        mul_count = 0;
3499
3500
0
        MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(m, 16, exponents[i]));
3501
0
        MBEDTLS_MPI_CHK(self_test_adjust_exponent(grp, m));
3502
0
        MBEDTLS_MPI_CHK(mbedtls_ecp_mul(grp, R, m, P, NULL, NULL));
3503
3504
0
        if (add_count != add_c_prev ||
3505
0
            dbl_count != dbl_c_prev ||
3506
0
            mul_count != mul_c_prev) {
3507
0
            ret = 1;
3508
0
            break;
3509
0
        }
3510
0
    }
3511
3512
0
cleanup:
3513
0
    if (verbose != 0) {
3514
0
        if (ret != 0) {
3515
0
            mbedtls_printf("failed (%u)\n", (unsigned int) i);
3516
0
        } else {
3517
0
            mbedtls_printf("passed\n");
3518
0
        }
3519
0
    }
3520
0
    return ret;
3521
0
}
3522
3523
/*
3524
 * Checkup routine
3525
 */
3526
int mbedtls_ecp_self_test(int verbose)
3527
0
{
3528
0
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
3529
0
    mbedtls_ecp_group grp;
3530
0
    mbedtls_ecp_point R, P;
3531
0
    mbedtls_mpi m;
3532
3533
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3534
    /* Exponents especially adapted for secp192k1, which has the lowest
3535
     * order n of all supported curves (secp192r1 is in a slightly larger
3536
     * field but the order of its base point is slightly smaller). */
3537
0
    const char *sw_exponents[] =
3538
0
    {
3539
0
        "000000000000000000000000000000000000000000000001", /* one */
3540
0
        "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */
3541
0
        "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
3542
0
        "400000000000000000000000000000000000000000000000", /* one and zeros */
3543
0
        "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
3544
0
        "555555555555555555555555555555555555555555555555", /* 101010... */
3545
0
    };
3546
0
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3547
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3548
0
    const char *m_exponents[] =
3549
0
    {
3550
        /* Valid private values for Curve25519. In a build with Curve448
3551
         * but not Curve25519, they will be adjusted in
3552
         * self_test_adjust_exponent(). */
3553
0
        "4000000000000000000000000000000000000000000000000000000000000000",
3554
0
        "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30",
3555
0
        "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8",
3556
0
        "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460",
3557
0
        "5555555555555555555555555555555555555555555555555555555555555550",
3558
0
        "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8",
3559
0
    };
3560
0
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3561
3562
0
    mbedtls_ecp_group_init(&grp);
3563
0
    mbedtls_ecp_point_init(&R);
3564
0
    mbedtls_ecp_point_init(&P);
3565
0
    mbedtls_mpi_init(&m);
3566
3567
0
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
3568
    /* Use secp192r1 if available, or any available curve */
3569
0
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
3570
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_SECP192R1));
3571
#else
3572
    MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, mbedtls_ecp_curve_list()->grp_id));
3573
#endif
3574
3575
0
    if (verbose != 0) {
3576
0
        mbedtls_printf("  ECP SW test #1 (constant op_count, base point G): ");
3577
0
    }
3578
    /* Do a dummy multiplication first to trigger precomputation */
3579
0
    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&m, 2));
3580
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_mul(&grp, &P, &m, &grp.G, NULL, NULL));
3581
0
    ret = self_test_point(verbose,
3582
0
                          &grp, &R, &m, &grp.G,
3583
0
                          sw_exponents,
3584
0
                          sizeof(sw_exponents) / sizeof(sw_exponents[0]));
3585
0
    if (ret != 0) {
3586
0
        goto cleanup;
3587
0
    }
3588
3589
0
    if (verbose != 0) {
3590
0
        mbedtls_printf("  ECP SW test #2 (constant op_count, other point): ");
3591
0
    }
3592
    /* We computed P = 2G last time, use it */
3593
0
    ret = self_test_point(verbose,
3594
0
                          &grp, &R, &m, &P,
3595
0
                          sw_exponents,
3596
0
                          sizeof(sw_exponents) / sizeof(sw_exponents[0]));
3597
0
    if (ret != 0) {
3598
0
        goto cleanup;
3599
0
    }
3600
3601
0
    mbedtls_ecp_group_free(&grp);
3602
0
    mbedtls_ecp_point_free(&R);
3603
0
#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
3604
3605
0
#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)
3606
0
    if (verbose != 0) {
3607
0
        mbedtls_printf("  ECP Montgomery test (constant op_count): ");
3608
0
    }
3609
0
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
3610
0
    MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE25519));
3611
#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
3612
    MBEDTLS_MPI_CHK(mbedtls_ecp_group_load(&grp, MBEDTLS_ECP_DP_CURVE448));
3613
#else
3614
#error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test"
3615
#endif
3616
0
    ret = self_test_point(verbose,
3617
0
                          &grp, &R, &m, &grp.G,
3618
0
                          m_exponents,
3619
0
                          sizeof(m_exponents) / sizeof(m_exponents[0]));
3620
0
    if (ret != 0) {
3621
0
        goto cleanup;
3622
0
    }
3623
0
#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */
3624
3625
0
cleanup:
3626
3627
0
    if (ret < 0 && verbose != 0) {
3628
0
        mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret);
3629
0
    }
3630
3631
0
    mbedtls_ecp_group_free(&grp);
3632
0
    mbedtls_ecp_point_free(&R);
3633
0
    mbedtls_ecp_point_free(&P);
3634
0
    mbedtls_mpi_free(&m);
3635
3636
0
    if (verbose != 0) {
3637
0
        mbedtls_printf("\n");
3638
0
    }
3639
3640
0
    return ret;
3641
0
}
3642
3643
#endif /* MBEDTLS_SELF_TEST */
3644
3645
#endif /* !MBEDTLS_ECP_ALT */
3646
3647
#endif /* MBEDTLS_ECP_C */