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
|
/*
* Copyright (c) 2013, Google Inc.
*
* SPDX-License-Identifier: GPL-2.0+
*/
#ifndef USE_HOSTCC
#include <common.h>
#include <fdtdec.h>
#include <asm/types.h>
#include <asm/byteorder.h>
#include <asm/errno.h>
#include <asm/types.h>
#include <asm/unaligned.h>
#else
#include "fdt_host.h"
#include "mkimage.h"
#include <fdt_support.h>
#endif
#include <u-boot/rsa.h>
#include <u-boot/sha1.h>
#include <u-boot/sha256.h>
#define UINT64_MULT32(v, multby) (((uint64_t)(v)) * ((uint32_t)(multby)))
#define get_unaligned_be32(a) fdt32_to_cpu(*(uint32_t *)a)
#define put_unaligned_be32(a, b) (*(uint32_t *)(b) = cpu_to_fdt32(a))
/* Default public exponent for backward compatibility */
#define RSA_DEFAULT_PUBEXP 65537
/**
* subtract_modulus() - subtract modulus from the given value
*
* @key: Key containing modulus to subtract
* @num: Number to subtract modulus from, as little endian word array
*/
static void subtract_modulus(const struct rsa_public_key *key, uint32_t num[])
{
int64_t acc = 0;
uint i;
for (i = 0; i < key->len; i++) {
acc += (uint64_t)num[i] - key->modulus[i];
num[i] = (uint32_t)acc;
acc >>= 32;
}
}
/**
* greater_equal_modulus() - check if a value is >= modulus
*
* @key: Key containing modulus to check
* @num: Number to check against modulus, as little endian word array
* @return 0 if num < modulus, 1 if num >= modulus
*/
static int greater_equal_modulus(const struct rsa_public_key *key,
uint32_t num[])
{
uint32_t i;
for (i = key->len - 1; i >= 0; i--) {
if (num[i] < key->modulus[i])
return 0;
if (num[i] > key->modulus[i])
return 1;
}
return 1; /* equal */
}
/**
* montgomery_mul_add_step() - Perform montgomery multiply-add step
*
* Operation: montgomery result[] += a * b[] / n0inv % modulus
*
* @key: RSA key
* @result: Place to put result, as little endian word array
* @a: Multiplier
* @b: Multiplicand, as little endian word array
*/
static void montgomery_mul_add_step(const struct rsa_public_key *key,
uint32_t result[], const uint32_t a, const uint32_t b[])
{
uint64_t acc_a, acc_b;
uint32_t d0;
uint i;
acc_a = (uint64_t)a * b[0] + result[0];
d0 = (uint32_t)acc_a * key->n0inv;
acc_b = (uint64_t)d0 * key->modulus[0] + (uint32_t)acc_a;
for (i = 1; i < key->len; i++) {
acc_a = (acc_a >> 32) + (uint64_t)a * b[i] + result[i];
acc_b = (acc_b >> 32) + (uint64_t)d0 * key->modulus[i] +
(uint32_t)acc_a;
result[i - 1] = (uint32_t)acc_b;
}
acc_a = (acc_a >> 32) + (acc_b >> 32);
result[i - 1] = (uint32_t)acc_a;
if (acc_a >> 32)
subtract_modulus(key, result);
}
/**
* montgomery_mul() - Perform montgomery mutitply
*
* Operation: montgomery result[] = a[] * b[] / n0inv % modulus
*
* @key: RSA key
* @result: Place to put result, as little endian word array
* @a: Multiplier, as little endian word array
* @b: Multiplicand, as little endian word array
*/
static void montgomery_mul(const struct rsa_public_key *key,
uint32_t result[], uint32_t a[], const uint32_t b[])
{
uint i;
for (i = 0; i < key->len; ++i)
result[i] = 0;
for (i = 0; i < key->len; ++i)
montgomery_mul_add_step(key, result, a[i], b);
}
/**
* num_pub_exponent_bits() - Number of bits in the public exponent
*
* @key: RSA key
* @num_bits: Storage for the number of public exponent bits
*/
static int num_public_exponent_bits(const struct rsa_public_key *key,
int *num_bits)
{
uint64_t exponent;
int exponent_bits;
const uint max_bits = (sizeof(exponent) * 8);
exponent = key->exponent;
exponent_bits = 0;
if (!exponent) {
*num_bits = exponent_bits;
return 0;
}
for (exponent_bits = 1; exponent_bits < max_bits + 1; ++exponent_bits)
if (!(exponent >>= 1)) {
*num_bits = exponent_bits;
return 0;
}
return -EINVAL;
}
/**
* is_public_exponent_bit_set() - Check if a bit in the public exponent is set
*
* @key: RSA key
* @pos: The bit position to check
*/
static int is_public_exponent_bit_set(const struct rsa_public_key *key,
int pos)
{
return key->exponent & (1ULL << pos);
}
/**
* pow_mod() - in-place public exponentiation
*
* @key: RSA key
* @inout: Big-endian word array containing value and result
*/
static int pow_mod(const struct rsa_public_key *key, uint32_t *inout)
{
uint32_t *result, *ptr;
uint i;
int j, k;
/* Sanity check for stack size - key->len is in 32-bit words */
if (key->len > RSA_MAX_KEY_BITS / 32) {
debug("RSA key words %u exceeds maximum %d\n", key->len,
RSA_MAX_KEY_BITS / 32);
return -EINVAL;
}
uint32_t val[key->len], acc[key->len], tmp[key->len];
uint32_t a_scaled[key->len];
result = tmp; /* Re-use location. */
/* Convert from big endian byte array to little endian word array. */
for (i = 0, ptr = inout + key->len - 1; i < key->len; i++, ptr--)
val[i] = get_unaligned_be32(ptr);
if (0 != num_public_exponent_bits(key, &k))
return -EINVAL;
if (k < 2) {
debug("Public exponent is too short (%d bits, minimum 2)\n",
k);
return -EINVAL;
}
if (!is_public_exponent_bit_set(key, 0)) {
debug("LSB of RSA public exponent must be set.\n");
return -EINVAL;
}
/* the bit at e[k-1] is 1 by definition, so start with: C := M */
montgomery_mul(key, acc, val, key->rr); /* acc = a * RR / R mod n */
/* retain scaled version for intermediate use */
memcpy(a_scaled, acc, key->len * sizeof(a_scaled[0]));
for (j = k - 2; j > 0; --j) {
montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod n */
if (is_public_exponent_bit_set(key, j)) {
/* acc = tmp * val / R mod n */
montgomery_mul(key, acc, tmp, a_scaled);
} else {
/* e[j] == 0, copy tmp back to acc for next operation */
memcpy(acc, tmp, key->len * sizeof(acc[0]));
}
}
/* the bit at e[0] is always 1 */
montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod n */
montgomery_mul(key, acc, tmp, val); /* acc = tmp * a / R mod M */
memcpy(result, acc, key->len * sizeof(result[0]));
/* Make sure result < mod; result is at most 1x mod too large. */
if (greater_equal_modulus(key, result))
subtract_modulus(key, result);
/* Convert to bigendian byte array */
for (i = key->len - 1, ptr = inout; (int)i >= 0; i--, ptr++)
put_unaligned_be32(result[i], ptr);
return 0;
}
static int rsa_verify_key(const struct rsa_public_key *key, const uint8_t *sig,
const uint32_t sig_len, const uint8_t *hash,
struct checksum_algo *algo)
{
const uint8_t *padding;
int pad_len;
int ret;
if (!key || !sig || !hash || !algo)
return -EIO;
if (sig_len != (key->len * sizeof(uint32_t))) {
debug("Signature is of incorrect length %d\n", sig_len);
return -EINVAL;
}
debug("Checksum algorithm: %s", algo->name);
/* Sanity check for stack size */
if (sig_len > RSA_MAX_SIG_BITS / 8) {
debug("Signature length %u exceeds maximum %d\n", sig_len,
RSA_MAX_SIG_BITS / 8);
return -EINVAL;
}
uint32_t buf[sig_len / sizeof(uint32_t)];
memcpy(buf, sig, sig_len);
ret = pow_mod(key, buf);
if (ret)
return ret;
padding = algo->rsa_padding;
pad_len = algo->pad_len - algo->checksum_len;
/* Check pkcs1.5 padding bytes. */
if (memcmp(buf, padding, pad_len)) {
debug("In RSAVerify(): Padding check failed!\n");
return -EINVAL;
}
/* Check hash. */
if (memcmp((uint8_t *)buf + pad_len, hash, sig_len - pad_len)) {
debug("In RSAVerify(): Hash check failed!\n");
return -EACCES;
}
return 0;
}
static void rsa_convert_big_endian(uint32_t *dst, const uint32_t *src, int len)
{
int i;
for (i = 0; i < len; i++)
dst[i] = fdt32_to_cpu(src[len - 1 - i]);
}
static int rsa_verify_with_keynode(struct image_sign_info *info,
const void *hash, uint8_t *sig, uint sig_len, int node)
{
const void *blob = info->fdt_blob;
struct rsa_public_key key;
const void *modulus, *rr;
const uint64_t *public_exponent;
int length;
int ret;
if (node < 0) {
debug("%s: Skipping invalid node", __func__);
return -EBADF;
}
if (!fdt_getprop(blob, node, "rsa,n0-inverse", NULL)) {
debug("%s: Missing rsa,n0-inverse", __func__);
return -EFAULT;
}
key.len = fdtdec_get_int(blob, node, "rsa,num-bits", 0);
key.n0inv = fdtdec_get_int(blob, node, "rsa,n0-inverse", 0);
public_exponent = fdt_getprop(blob, node, "rsa,exponent", &length);
if (!public_exponent || length < sizeof(*public_exponent))
key.exponent = RSA_DEFAULT_PUBEXP;
else
key.exponent = fdt64_to_cpu(*public_exponent);
modulus = fdt_getprop(blob, node, "rsa,modulus", NULL);
rr = fdt_getprop(blob, node, "rsa,r-squared", NULL);
if (!key.len || !modulus || !rr) {
debug("%s: Missing RSA key info", __func__);
return -EFAULT;
}
/* Sanity check for stack size */
if (key.len > RSA_MAX_KEY_BITS || key.len < RSA_MIN_KEY_BITS) {
debug("RSA key bits %u outside allowed range %d..%d\n",
key.len, RSA_MIN_KEY_BITS, RSA_MAX_KEY_BITS);
return -EFAULT;
}
key.len /= sizeof(uint32_t) * 8;
uint32_t key1[key.len], key2[key.len];
key.modulus = key1;
key.rr = key2;
rsa_convert_big_endian(key.modulus, modulus, key.len);
rsa_convert_big_endian(key.rr, rr, key.len);
if (!key.modulus || !key.rr) {
debug("%s: Out of memory", __func__);
return -ENOMEM;
}
debug("key length %d\n", key.len);
ret = rsa_verify_key(&key, sig, sig_len, hash, info->algo->checksum);
if (ret) {
printf("%s: RSA failed to verify: %d\n", __func__, ret);
return ret;
}
return 0;
}
int rsa_verify(struct image_sign_info *info,
const struct image_region region[], int region_count,
uint8_t *sig, uint sig_len)
{
const void *blob = info->fdt_blob;
/* Reserve memory for maximum checksum-length */
uint8_t hash[info->algo->checksum->pad_len];
int ndepth, noffset;
int sig_node, node;
char name[100];
int ret;
/*
* Verify that the checksum-length does not exceed the
* rsa-signature-length
*/
if (info->algo->checksum->checksum_len >
info->algo->checksum->pad_len) {
debug("%s: invlaid checksum-algorithm %s for %s\n",
__func__, info->algo->checksum->name, info->algo->name);
return -EINVAL;
}
sig_node = fdt_subnode_offset(blob, 0, FIT_SIG_NODENAME);
if (sig_node < 0) {
debug("%s: No signature node found\n", __func__);
return -ENOENT;
}
/* Calculate checksum with checksum-algorithm */
info->algo->checksum->calculate(region, region_count, hash);
/* See if we must use a particular key */
if (info->required_keynode != -1) {
ret = rsa_verify_with_keynode(info, hash, sig, sig_len,
info->required_keynode);
if (!ret)
return ret;
}
/* Look for a key that matches our hint */
snprintf(name, sizeof(name), "key-%s", info->keyname);
node = fdt_subnode_offset(blob, sig_node, name);
ret = rsa_verify_with_keynode(info, hash, sig, sig_len, node);
if (!ret)
return ret;
/* No luck, so try each of the keys in turn */
for (ndepth = 0, noffset = fdt_next_node(info->fit, sig_node, &ndepth);
(noffset >= 0) && (ndepth > 0);
noffset = fdt_next_node(info->fit, noffset, &ndepth)) {
if (ndepth == 1 && noffset != node) {
ret = rsa_verify_with_keynode(info, hash, sig, sig_len,
noffset);
if (!ret)
break;
}
}
return ret;
}
|