Outline ![]()
Files ![]()
loading (3/5)...
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
/*
* Multi-precision integer library
* ESP-IDF hardware accelerated parts based on mbedTLS implementation
*
* SPDX-FileCopyrightText: The Mbed TLS Contributors
*
* SPDX-License-Identifier: Apache-2.0
*
* SPDX-FileContributor: 2016-2024 Espressif Systems (Shanghai) CO LTD
*/
#include <stdio.h>
#include <string.h>
#include <malloc.h>
#include <limits.h>
#include <assert.h>
#include <stdlib.h>
#include <sys/param.h>
#include "esp_system.h"
#include "esp_log.h"
#include "esp_attr.h"
#include "esp_intr_alloc.h"
#if CONFIG_PM_ENABLE
#include "esp_pm.h"
#endif
#include "esp_private/periph_ctrl.h"
#include "freertos/FreeRTOS.h"
#include "freertos/semphr.h"
#include "bignum_impl.h"
#include "mbedtls/bignum.h"
#include "hal/mpi_hal.h"
/* Some implementation notes:
*
* - Naming convention x_words, y_words, z_words for number of words (limbs) used in a particular
* bignum. This number may be less than the size of the bignum
*
* - Naming convention hw_words for the hardware length of the operation. This number maybe be rounded up
* for targets that requires this (e.g. ESP32), and may be larger than any of the numbers
* involved in the calculation.
*
* - Timing behaviour of these functions will depend on the length of the inputs. This is fundamentally
* the same constraint as the software mbedTLS implementations, and relies on the same
* countermeasures (exponent blinding, etc) which are used in mbedTLS.
*/
static const __attribute__((unused)) char *TAG = "bignum";
#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
#define biL (ciL << 3) /* bits in limb */
#if defined(CONFIG_MBEDTLS_MPI_USE_INTERRUPT)
static SemaphoreHandle_t op_complete_sem;
#if defined(CONFIG_PM_ENABLE)
static esp_pm_lock_handle_t s_pm_cpu_lock;
static esp_pm_lock_handle_t s_pm_sleep_lock;
#endif
static IRAM_ATTR void esp_mpi_complete_isr(void *arg)
{
BaseType_t higher_woken;
mpi_hal_clear_interrupt();
xSemaphoreGiveFromISR(op_complete_sem, &higher_woken);
if (higher_woken) {
portYIELD_FROM_ISR();
}
}
static esp_err_t esp_mpi_isr_initialise(void)
{
mpi_hal_clear_interrupt();
mpi_hal_interrupt_enable(true);
if (op_complete_sem == NULL) {
static StaticSemaphore_t op_sem_buf;
op_complete_sem = xSemaphoreCreateBinaryStatic(&op_sem_buf);
if (op_complete_sem == NULL) {
ESP_LOGE(TAG, "Failed to create intr semaphore");
return ESP_FAIL;
}
const int isr_flags = esp_intr_level_to_flags(CONFIG_MBEDTLS_MPI_INTERRUPT_LEVEL);
esp_err_t ret;
ret = esp_intr_alloc(ETS_RSA_INTR_SOURCE, isr_flags, esp_mpi_complete_isr, NULL, NULL);
if (ret != ESP_OK) {
ESP_LOGE(TAG, "Failed to allocate RSA interrupt %d", ret);
// This should be treated as fatal error as this API would mostly
// be invoked within mbedTLS interface. There is no way for the system
// to proceed if the MPI interrupt allocation fails here.
abort();
}
}
/* MPI is clocked proportionally to CPU clock, take power management lock */
#ifdef CONFIG_PM_ENABLE
if (s_pm_cpu_lock == NULL) {
if (esp_pm_lock_create(ESP_PM_NO_LIGHT_SLEEP, 0, "mpi_sleep", &s_pm_sleep_lock) != ESP_OK) {
ESP_LOGE(TAG, "Failed to create PM sleep lock");
return ESP_FAIL;
}
if (esp_pm_lock_create(ESP_PM_CPU_FREQ_MAX, 0, "mpi_cpu", &s_pm_cpu_lock) != ESP_OK) {
ESP_LOGE(TAG, "Failed to create PM CPU lock");
return ESP_FAIL;
}
}
esp_pm_lock_acquire(s_pm_cpu_lock);
esp_pm_lock_acquire(s_pm_sleep_lock);
#endif
return ESP_OK;
}
static int esp_mpi_wait_intr(void)
{
if (!xSemaphoreTake(op_complete_sem, 2000 / portTICK_PERIOD_MS)) {
ESP_LOGE("MPI", "Timed out waiting for completion of MPI Interrupt");
return -1;
}
#ifdef CONFIG_PM_ENABLE
esp_pm_lock_release(s_pm_cpu_lock);
esp_pm_lock_release(s_pm_sleep_lock);
#endif // CONFIG_PM_ENABLE
mpi_hal_interrupt_enable(false);
return 0;
}
#endif // CONFIG_MBEDTLS_MPI_USE_INTERRUPT
/* Convert bit count to word count
*/
static inline size_t bits_to_words(size_t bits)
{
return (bits + 31) / 32;
}
/* Return the number of words actually used to represent an mpi
number.
*/
#if defined(MBEDTLS_MPI_EXP_MOD_ALT) || defined(MBEDTLS_MPI_EXP_MOD_ALT_FALLBACK)
static size_t mpi_words(const mbedtls_mpi *mpi)
{
for (size_t i = mpi->MBEDTLS_PRIVATE(n); i > 0; i--) {
if (mpi->MBEDTLS_PRIVATE(p[i - 1]) != 0) {
return i;
}
}
return 0;
}
#endif //(MBEDTLS_MPI_EXP_MOD_ALT || MBEDTLS_MPI_EXP_MOD_ALT_FALLBACK)
/**
*
* There is a need for the value of integer N' such that B^-1(B-1)-N^-1N'=1,
* where B^-1(B-1) mod N=1. Actually, only the least significant part of
* N' is needed, hence the definition N0'=N' mod b. We reproduce below the
* simple algorithm from an article by Dusse and Kaliski to efficiently
* find N0' from N0 and b
*/
static mbedtls_mpi_uint modular_inverse(const mbedtls_mpi *M)
{
int i;
uint64_t t = 1;
uint64_t two_2_i_minus_1 = 2; /* 2^(i-1) */
uint64_t two_2_i = 4; /* 2^i */
uint64_t N = M->MBEDTLS_PRIVATE(p[0]);
for (i = 2; i <= 32; i++) {
if ((mbedtls_mpi_uint) N * t % two_2_i >= two_2_i_minus_1) {
t += two_2_i_minus_1;
}
two_2_i_minus_1 <<= 1;
two_2_i <<= 1;
}
return (mbedtls_mpi_uint)(UINT32_MAX - t + 1);
}
/* Calculate Rinv = RR^2 mod M, where:
*
* R = b^n where b = 2^32, n=num_words,
* R = 2^N (where N=num_bits)
* RR = R^2 = 2^(2*N) (where N=num_bits=num_words*32)
*
* This calculation is computationally expensive (mbedtls_mpi_mod_mpi)
* so caller should cache the result where possible.
*
* DO NOT call this function while holding esp_mpi_enable_hardware_hw_op().
*
*/
static int calculate_rinv(mbedtls_mpi *Rinv, const mbedtls_mpi *M, int num_words)
{
int ret;
size_t num_bits = num_words * 32;
mbedtls_mpi RR;
mbedtls_mpi_init(&RR);
MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&RR, num_bits * 2, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(Rinv, &RR, M));
cleanup:
mbedtls_mpi_free(&RR);
return ret;
}
/* Z = (X * Y) mod M
Not an mbedTLS function
*/
int esp_mpi_mul_mpi_mod(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M)
{
int ret = 0;
size_t x_bits = mbedtls_mpi_bitlen(X);
size_t y_bits = mbedtls_mpi_bitlen(Y);
size_t m_bits = mbedtls_mpi_bitlen(M);
size_t z_bits = MIN(m_bits, x_bits + y_bits);
size_t x_words = bits_to_words(x_bits);
size_t y_words = bits_to_words(y_bits);
size_t m_words = bits_to_words(m_bits);
size_t z_words = bits_to_words(z_bits);
size_t hw_words = mpi_hal_calc_hardware_words(MAX(x_words, MAX(y_words, m_words))); /* longest operand */
mbedtls_mpi Rinv;
mbedtls_mpi_uint Mprime;
/* Calculate and load the first stage montgomery multiplication */
mbedtls_mpi_init(&Rinv);
MBEDTLS_MPI_CHK(calculate_rinv(&Rinv, M, hw_words));
Mprime = modular_inverse(M);
esp_mpi_enable_hardware_hw_op();
/* Load and start a (X * Y) mod M calculation */
esp_mpi_mul_mpi_mod_hw_op(X, Y, M, &Rinv, Mprime, hw_words);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Z, z_words));
/* Read back the result */
mpi_hal_read_result_hw_op(Z->MBEDTLS_PRIVATE(p), Z->MBEDTLS_PRIVATE(n), z_words);
Z->MBEDTLS_PRIVATE(s) = X->MBEDTLS_PRIVATE(s) * Y->MBEDTLS_PRIVATE(s);
cleanup:
mbedtls_mpi_free(&Rinv);
esp_mpi_disable_hardware_hw_op();
return ret;
}
#if defined(MBEDTLS_MPI_EXP_MOD_ALT) || defined(MBEDTLS_MPI_EXP_MOD_ALT_FALLBACK)
#ifdef ESP_MPI_USE_MONT_EXP
/*
* Return the most significant one-bit.
*/
static size_t mbedtls_mpi_msb( const mbedtls_mpi *X )
{
int i, j;
if (X != NULL && X->MBEDTLS_PRIVATE(n) != 0) {
for (i = X->MBEDTLS_PRIVATE(n) - 1; i >= 0; i--) {
if (X->MBEDTLS_PRIVATE(p[i]) != 0) {
for (j = biL - 1; j >= 0; j--) {
if ((X->MBEDTLS_PRIVATE(p[i]) & (1 << j)) != 0) {
return (i * biL) + j;
}
}
}
}
}
return 0;
}
/*
* Montgomery exponentiation: Z = X ^ Y mod M (HAC 14.94)
*/
static int mpi_montgomery_exp_calc( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M,
mbedtls_mpi *Rinv,
size_t hw_words,
mbedtls_mpi_uint Mprime )
{
int ret = 0;
mbedtls_mpi X_, one;
mbedtls_mpi_init(&X_);
mbedtls_mpi_init(&one);
if ( ( ( ret = mbedtls_mpi_grow(&one, hw_words) ) != 0 ) ||
( ( ret = mbedtls_mpi_set_bit(&one, 0, 1) ) != 0 ) ) {
goto cleanup2;
}
// Algorithm from HAC 14.94
{
// 0 determine t (highest bit set in y)
int t = mbedtls_mpi_msb(Y);
esp_mpi_enable_hardware_hw_op();
// 1.1 x_ = mont(x, R^2 mod m)
// = mont(x, rb)
MBEDTLS_MPI_CHK( esp_mont_hw_op(&X_, X, Rinv, M, Mprime, hw_words, false) );
// 1.2 z = R mod m
// now z = R mod m = Mont (R^2 mod m, 1) mod M (as Mont(x) = X&R^-1 mod M)
MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Rinv, &one, M, Mprime, hw_words, true) );
// 2 for i from t down to 0
for (int i = t; i >= 0; i--) {
// 2.1 z = mont(z,z)
if (i != t) { // skip on the first iteration as is still unity
MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Z, Z, M, Mprime, hw_words, true) );
}
// 2.2 if y[i] = 1 then z = mont(A, x_)
if (mbedtls_mpi_get_bit(Y, i)) {
MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Z, &X_, M, Mprime, hw_words, true) );
}
}
// 3 z = Mont(z, 1)
MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Z, &one, M, Mprime, hw_words, true) );
}
cleanup:
esp_mpi_disable_hardware_hw_op();
cleanup2:
mbedtls_mpi_free(&X_);
mbedtls_mpi_free(&one);
return ret;
}
#endif //USE_MONT_EXPONENATIATION
/*
* Z = X ^ Y mod M
*
* _Rinv is optional pre-calculated version of Rinv (via calculate_rinv()).
*
* (See RSA Accelerator section in Technical Reference for more about Mprime, Rinv)
*
*/
static int esp_mpi_exp_mod( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M, mbedtls_mpi *_Rinv )
{
int ret = 0;
mbedtls_mpi Rinv_new; /* used if _Rinv == NULL */
mbedtls_mpi *Rinv; /* points to _Rinv (if not NULL) otherwise &RR_new */
mbedtls_mpi_uint Mprime;
size_t x_words = mpi_words(X);
size_t y_words = mpi_words(Y);
size_t m_words = mpi_words(M);
/* "all numbers must be the same length", so choose longest number
as cardinal length of operation...
*/
size_t num_words = mpi_hal_calc_hardware_words(MAX(m_words, MAX(x_words, y_words)));
if (num_words * 32 > SOC_RSA_MAX_BIT_LEN) {
return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
}
if (mbedtls_mpi_cmp_int(M, 0) <= 0 || (M->MBEDTLS_PRIVATE(p[0]) & 1) == 0) {
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
}
if (mbedtls_mpi_cmp_int(Y, 0) < 0) {
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
}
if (mbedtls_mpi_cmp_int(Y, 0) == 0) {
return mbedtls_mpi_lset(Z, 1);
}
/* Determine RR pointer, either _RR for cached value
or local RR_new */
if (_Rinv == NULL) {
mbedtls_mpi_init(&Rinv_new);
Rinv = &Rinv_new;
} else {
Rinv = _Rinv;
}
if (Rinv->MBEDTLS_PRIVATE(p) == NULL) {
MBEDTLS_MPI_CHK(calculate_rinv(Rinv, M, num_words));
}
Mprime = modular_inverse(M);
// Montgomery exponentiation: Z = X ^ Y mod M (HAC 14.94)
#ifdef ESP_MPI_USE_MONT_EXP
ret = mpi_montgomery_exp_calc(Z, X, Y, M, Rinv, num_words, Mprime) ;
MBEDTLS_MPI_CHK(ret);
#else
esp_mpi_enable_hardware_hw_op();
#if defined (CONFIG_MBEDTLS_MPI_USE_INTERRUPT)
if (esp_mpi_isr_initialise() != ESP_OK) {
ret = -1;
esp_mpi_disable_hardware_hw_op();
goto cleanup;
}
#endif
esp_mpi_exp_mpi_mod_hw_op(X, Y, M, Rinv, Mprime, num_words);
ret = mbedtls_mpi_grow(Z, m_words);
if (ret != 0) {
esp_mpi_disable_hardware_hw_op();
goto cleanup;
}
#if defined(CONFIG_MBEDTLS_MPI_USE_INTERRUPT)
ret = esp_mpi_wait_intr();
if (ret != 0) {
esp_mpi_disable_hardware_hw_op();
goto cleanup;
}
#endif //CONFIG_MBEDTLS_MPI_USE_INTERRUPT
/* Read back the result */
mpi_hal_read_result_hw_op(Z->MBEDTLS_PRIVATE(p), Z->MBEDTLS_PRIVATE(n), m_words);
esp_mpi_disable_hardware_hw_op();
#endif
// Compensate for negative X
if (X->MBEDTLS_PRIVATE(s) == -1 && (Y->MBEDTLS_PRIVATE(p[0]) & 1) != 0) {
Z->MBEDTLS_PRIVATE(s) = -1;
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(Z, M, Z));
} else {
Z->MBEDTLS_PRIVATE(s) = 1;
}
cleanup:
if (_Rinv == NULL) {
mbedtls_mpi_free(&Rinv_new);
}
return ret;
}
#endif /* (MBEDTLS_MPI_EXP_MOD_ALT || MBEDTLS_MPI_EXP_MOD_ALT_FALLBACK) */
/*
* Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
*/
int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *E, const mbedtls_mpi *N,
mbedtls_mpi *_RR )
{
int ret;
#if defined(MBEDTLS_MPI_EXP_MOD_ALT_FALLBACK)
/* Try hardware API first and then fallback to software */
ret = esp_mpi_exp_mod( X, A, E, N, _RR );
if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) {
ret = mbedtls_mpi_exp_mod_soft( X, A, E, N, _RR );
}
#else
/* Hardware approach */
ret = esp_mpi_exp_mod( X, A, E, N, _RR );
#endif
/* Note: For software only approach, it gets handled in mbedTLS library.
This file is not part of build objects for that case */
return ret;
}
#if defined(MBEDTLS_MPI_MUL_MPI_ALT) /* MBEDTLS_MPI_MUL_MPI_ALT */
static int mpi_mult_mpi_failover_mod_mult( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t z_words);
static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t y_words, size_t z_words);
/* Z = X * Y */
int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y )
{
int ret = 0;
size_t x_bits = mbedtls_mpi_bitlen(X);
size_t y_bits = mbedtls_mpi_bitlen(Y);
size_t x_words = bits_to_words(x_bits);
size_t y_words = bits_to_words(y_bits);
size_t z_words = bits_to_words(x_bits + y_bits);
size_t hw_words = mpi_hal_calc_hardware_words(MAX(x_words, y_words)); // length of one operand in hardware
/* Short-circuit eval if either argument is 0 or 1.
This is needed as the mpi modular division
argument will sometimes call in here when one
argument is too large for the hardware unit, but the other
argument is zero or one.
*/
if (x_bits == 0 || y_bits == 0) {
ret = mbedtls_mpi_lset(Z, 0);
return ret;
}
if (x_bits == 1) {
ret = mbedtls_mpi_copy(Z, Y);
Z->MBEDTLS_PRIVATE(s) *= X->MBEDTLS_PRIVATE(s);
return ret;
}
if (y_bits == 1) {
ret = mbedtls_mpi_copy(Z, X);
Z->MBEDTLS_PRIVATE(s) *= Y->MBEDTLS_PRIVATE(s);
return ret;
}
/* Grow Z to result size early, avoid interim allocations */
MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, z_words) );
/* If either factor is over 2048 bits, we can't use the standard hardware multiplier
(it assumes result is double longest factor, and result is max 4096 bits.)
However, we can fail over to mod_mult for up to 4096 bits of result (modulo
multiplication doesn't have the same restriction, so result is simply the
number of bits in X plus number of bits in in Y.)
*/
if (hw_words * 32 > SOC_RSA_MAX_BIT_LEN/2) {
if (z_words * 32 <= SOC_RSA_MAX_BIT_LEN) {
/* Note: it's possible to use mpi_mult_mpi_overlong
for this case as well, but it's very slightly
slower and requires a memory allocation.
*/
return mpi_mult_mpi_failover_mod_mult(Z, X, Y, z_words);
} else {
/* Still too long for the hardware unit... */
if (y_words > x_words) {
return mpi_mult_mpi_overlong(Z, X, Y, y_words, z_words);
} else {
return mpi_mult_mpi_overlong(Z, Y, X, x_words, z_words);
}
}
}
/* Otherwise, we can use the (faster) multiply hardware unit */
esp_mpi_enable_hardware_hw_op();
esp_mpi_mul_mpi_hw_op(X, Y, hw_words);
/* Read back the result */
mpi_hal_read_result_hw_op(Z->MBEDTLS_PRIVATE(p), Z->MBEDTLS_PRIVATE(n), z_words);
esp_mpi_disable_hardware_hw_op();
Z->MBEDTLS_PRIVATE(s) = X->MBEDTLS_PRIVATE(s) * Y->MBEDTLS_PRIVATE(s);
cleanup:
return ret;
}
int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
_B.MBEDTLS_PRIVATE(s) = 1;
_B.MBEDTLS_PRIVATE(n) = 1;
_B.MBEDTLS_PRIVATE(p) = p;
p[0] = b;
return( mbedtls_mpi_mul_mpi( X, A, &_B ) );
}
/* Deal with the case when X & Y are too long for the hardware unit, by splitting one operand
into two halves.
Y must be the longer operand
Slice Y into Yp, Ypp such that:
Yp = lower 'b' bits of Y
Ypp = upper 'b' bits of Y (right shifted)
Such that
Z = X * Y
Z = X * (Yp + Ypp<<b)
Z = (X * Yp) + (X * Ypp<<b)
Note that this function may recurse multiple times, if both X & Y
are too long for the hardware multiplication unit.
*/
static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t y_words, size_t z_words)
{
int ret = 0;
mbedtls_mpi Ztemp;
/* Rather than slicing in two on bits we slice on limbs (32 bit words) */
const size_t words_slice = y_words / 2;
/* Yp holds lower bits of Y (declared to reuse Y's array contents to save on copying) */
const mbedtls_mpi Yp = {
.MBEDTLS_PRIVATE(p) = Y->MBEDTLS_PRIVATE(p),
.MBEDTLS_PRIVATE(n) = words_slice,
.MBEDTLS_PRIVATE(s) = Y->MBEDTLS_PRIVATE(s)
};
/* Ypp holds upper bits of Y, right shifted (also reuses Y's array contents) */
const mbedtls_mpi Ypp = {
.MBEDTLS_PRIVATE(p) = Y->MBEDTLS_PRIVATE(p) + words_slice,
.MBEDTLS_PRIVATE(n) = y_words - words_slice,
.MBEDTLS_PRIVATE(s) = Y->MBEDTLS_PRIVATE(s)
};
mbedtls_mpi_init(&Ztemp);
/* Get result Ztemp = Yp * X (need temporary variable Ztemp) */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi(&Ztemp, X, &Yp) );
/* Z = Ypp * Y */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi(Z, X, &Ypp) );
/* Z = Z << b */
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l(Z, words_slice * 32) );
/* Z += Ztemp */
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi(Z, Z, &Ztemp) );
cleanup:
mbedtls_mpi_free(&Ztemp);
return ret;
}
static int mpi_mult_mpi_failover_mod_mult( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t z_words)
{
int ret;
size_t hw_words = mpi_hal_calc_hardware_words(z_words);
esp_mpi_enable_hardware_hw_op();
esp_mpi_mult_mpi_failover_mod_mult_hw_op(X, Y, hw_words );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, hw_words) );
/* Read back the result */
mpi_hal_read_result_hw_op(Z->MBEDTLS_PRIVATE(p), Z->MBEDTLS_PRIVATE(n), hw_words);
Z->MBEDTLS_PRIVATE(s) = X->MBEDTLS_PRIVATE(s) * Y->MBEDTLS_PRIVATE(s);
/*
* Relevant: https://github.com/espressif/esp-idf/issues/11850
*
* If z_words < mpi_words(Z) (the actual words taken by the MPI result),
* the assert fails due to unsigned arithmetic - most likely hardware
* peripheral has produced an incorrect result for MPI operation.
* This can happen if data fed to the peripheral register was incorrect.
*
* z_words is calculated as the worst-case possible size of the result
* MPI Z. The difference between z_words and the actual words taken by
* the MPI result (mpi_words(Z)) can be a maximum of 1 word.
* The value z_bits (actual bits taken by the MPI result) is calculated
* as x_bits + y_bits bits, however, in some cases, z_bits can be
* x_bits + y_bits - 1 bits (see example below).
* 0b1111 * 0b1111 = 0b11100001 -> 8 bits
* 0b1000 * 0b1000 = 0b01000000 -> 7 bits.
* The code rounds up to the nearest word size, so the maximum difference
* could be of only 1 word. The assert handles this.
*
*/
assert(z_words - mpi_words(Z) <= (size_t)1);
cleanup:
esp_mpi_disable_hardware_hw_op();
return ret;
}
#endif /* MBEDTLS_MPI_MUL_MPI_ALT */
Details ![]()
Show: from Types: Columns: ![]( "Show Project Names")
![]( "Show Locations")
![]( "Show Referring Symbols")
![]( "Show Scope")
This file uses the notable symbols shown below. Click anywhere in the file to view more details.