1 /*
2  * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
3  * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
4  *
5  * Redistribution and use in source and binary forms, with or without
6  * modification, are permitted provided that the following conditions are
7  * met:
8  *  * Redistributions of source code must retain the above copyright
9  *   notice, this list of conditions and the following disclaimer.
10  *  * Redistributions in binary form must reproduce the above copyright
11  *    notice, this list of conditions and the following disclaimer in the
12  *    documentation and/or other materials provided with the distribution.
13  *
14  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
15  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
16  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
17  * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
18  * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
19  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
20  * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
24  * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25  */
26 
27 #include <crypto/ecc_curve.h>
28 #include <linux/module.h>
29 #include <linux/random.h>
30 #include <linux/slab.h>
31 #include <linux/swab.h>
32 #include <linux/fips.h>
33 #include <crypto/ecdh.h>
34 #include <crypto/rng.h>
35 #include <crypto/internal/ecc.h>
36 #include <asm/unaligned.h>
37 #include <linux/ratelimit.h>
38 
39 #include "ecc_curve_defs.h"
40 
41 typedef struct {
42 	u64 m_low;
43 	u64 m_high;
44 } uint128_t;
45 
46 /* Returns curv25519 curve param */
ecc_get_curve25519(void)47 const struct ecc_curve *ecc_get_curve25519(void)
48 {
49 	return &ecc_25519;
50 }
51 EXPORT_SYMBOL(ecc_get_curve25519);
52 
ecc_get_curve(unsigned int curve_id)53 const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
54 {
55 	switch (curve_id) {
56 	/* In FIPS mode only allow P256 and higher */
57 	case ECC_CURVE_NIST_P192:
58 		return fips_enabled ? NULL : &nist_p192;
59 	case ECC_CURVE_NIST_P256:
60 		return &nist_p256;
61 	case ECC_CURVE_NIST_P384:
62 		return &nist_p384;
63 	default:
64 		return NULL;
65 	}
66 }
67 EXPORT_SYMBOL(ecc_get_curve);
68 
ecc_alloc_digits_space(unsigned int ndigits)69 static u64 *ecc_alloc_digits_space(unsigned int ndigits)
70 {
71 	size_t len = ndigits * sizeof(u64);
72 
73 	if (!len)
74 		return NULL;
75 
76 	return kmalloc(len, GFP_KERNEL);
77 }
78 
ecc_free_digits_space(u64 * space)79 static void ecc_free_digits_space(u64 *space)
80 {
81 	kfree_sensitive(space);
82 }
83 
ecc_alloc_point(unsigned int ndigits)84 struct ecc_point *ecc_alloc_point(unsigned int ndigits)
85 {
86 	struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
87 
88 	if (!p)
89 		return NULL;
90 
91 	p->x = ecc_alloc_digits_space(ndigits);
92 	if (!p->x)
93 		goto err_alloc_x;
94 
95 	p->y = ecc_alloc_digits_space(ndigits);
96 	if (!p->y)
97 		goto err_alloc_y;
98 
99 	p->ndigits = ndigits;
100 
101 	return p;
102 
103 err_alloc_y:
104 	ecc_free_digits_space(p->x);
105 err_alloc_x:
106 	kfree(p);
107 	return NULL;
108 }
109 EXPORT_SYMBOL(ecc_alloc_point);
110 
ecc_free_point(struct ecc_point * p)111 void ecc_free_point(struct ecc_point *p)
112 {
113 	if (!p)
114 		return;
115 
116 	kfree_sensitive(p->x);
117 	kfree_sensitive(p->y);
118 	kfree_sensitive(p);
119 }
120 EXPORT_SYMBOL(ecc_free_point);
121 
vli_clear(u64 * vli,unsigned int ndigits)122 static void vli_clear(u64 *vli, unsigned int ndigits)
123 {
124 	int i;
125 
126 	for (i = 0; i < ndigits; i++)
127 		vli[i] = 0;
128 }
129 
130 /* Returns true if vli == 0, false otherwise. */
vli_is_zero(const u64 * vli,unsigned int ndigits)131 bool vli_is_zero(const u64 *vli, unsigned int ndigits)
132 {
133 	int i;
134 
135 	for (i = 0; i < ndigits; i++) {
136 		if (vli[i])
137 			return false;
138 	}
139 
140 	return true;
141 }
142 EXPORT_SYMBOL(vli_is_zero);
143 
144 /* Returns nonzero if bit of vli is set. */
vli_test_bit(const u64 * vli,unsigned int bit)145 static u64 vli_test_bit(const u64 *vli, unsigned int bit)
146 {
147 	return (vli[bit / 64] & ((u64)1 << (bit % 64)));
148 }
149 
vli_is_negative(const u64 * vli,unsigned int ndigits)150 static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
151 {
152 	return vli_test_bit(vli, ndigits * 64 - 1);
153 }
154 
155 /* Counts the number of 64-bit "digits" in vli. */
vli_num_digits(const u64 * vli,unsigned int ndigits)156 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
157 {
158 	int i;
159 
160 	/* Search from the end until we find a non-zero digit.
161 	 * We do it in reverse because we expect that most digits will
162 	 * be nonzero.
163 	 */
164 	for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
165 
166 	return (i + 1);
167 }
168 
169 /* Counts the number of bits required for vli. */
vli_num_bits(const u64 * vli,unsigned int ndigits)170 unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
171 {
172 	unsigned int i, num_digits;
173 	u64 digit;
174 
175 	num_digits = vli_num_digits(vli, ndigits);
176 	if (num_digits == 0)
177 		return 0;
178 
179 	digit = vli[num_digits - 1];
180 	for (i = 0; digit; i++)
181 		digit >>= 1;
182 
183 	return ((num_digits - 1) * 64 + i);
184 }
185 EXPORT_SYMBOL(vli_num_bits);
186 
187 /* Set dest from unaligned bit string src. */
vli_from_be64(u64 * dest,const void * src,unsigned int ndigits)188 void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
189 {
190 	int i;
191 	const u64 *from = src;
192 
193 	for (i = 0; i < ndigits; i++)
194 		dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
195 }
196 EXPORT_SYMBOL(vli_from_be64);
197 
vli_from_le64(u64 * dest,const void * src,unsigned int ndigits)198 void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
199 {
200 	int i;
201 	const u64 *from = src;
202 
203 	for (i = 0; i < ndigits; i++)
204 		dest[i] = get_unaligned_le64(&from[i]);
205 }
206 EXPORT_SYMBOL(vli_from_le64);
207 
208 /* Sets dest = src. */
vli_set(u64 * dest,const u64 * src,unsigned int ndigits)209 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
210 {
211 	int i;
212 
213 	for (i = 0; i < ndigits; i++)
214 		dest[i] = src[i];
215 }
216 
217 /* Returns sign of left - right. */
vli_cmp(const u64 * left,const u64 * right,unsigned int ndigits)218 int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
219 {
220 	int i;
221 
222 	for (i = ndigits - 1; i >= 0; i--) {
223 		if (left[i] > right[i])
224 			return 1;
225 		else if (left[i] < right[i])
226 			return -1;
227 	}
228 
229 	return 0;
230 }
231 EXPORT_SYMBOL(vli_cmp);
232 
233 /* Computes result = in << c, returning carry. Can modify in place
234  * (if result == in). 0 < shift < 64.
235  */
vli_lshift(u64 * result,const u64 * in,unsigned int shift,unsigned int ndigits)236 static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
237 		      unsigned int ndigits)
238 {
239 	u64 carry = 0;
240 	int i;
241 
242 	for (i = 0; i < ndigits; i++) {
243 		u64 temp = in[i];
244 
245 		result[i] = (temp << shift) | carry;
246 		carry = temp >> (64 - shift);
247 	}
248 
249 	return carry;
250 }
251 
252 /* Computes vli = vli >> 1. */
vli_rshift1(u64 * vli,unsigned int ndigits)253 static void vli_rshift1(u64 *vli, unsigned int ndigits)
254 {
255 	u64 *end = vli;
256 	u64 carry = 0;
257 
258 	vli += ndigits;
259 
260 	while (vli-- > end) {
261 		u64 temp = *vli;
262 		*vli = (temp >> 1) | carry;
263 		carry = temp << 63;
264 	}
265 }
266 
267 /* Computes result = left + right, returning carry. Can modify in place. */
vli_add(u64 * result,const u64 * left,const u64 * right,unsigned int ndigits)268 static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
269 		   unsigned int ndigits)
270 {
271 	u64 carry = 0;
272 	int i;
273 
274 	for (i = 0; i < ndigits; i++) {
275 		u64 sum;
276 
277 		sum = left[i] + right[i] + carry;
278 		if (sum != left[i])
279 			carry = (sum < left[i]);
280 
281 		result[i] = sum;
282 	}
283 
284 	return carry;
285 }
286 
287 /* Computes result = left + right, returning carry. Can modify in place. */
vli_uadd(u64 * result,const u64 * left,u64 right,unsigned int ndigits)288 static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
289 		    unsigned int ndigits)
290 {
291 	u64 carry = right;
292 	int i;
293 
294 	for (i = 0; i < ndigits; i++) {
295 		u64 sum;
296 
297 		sum = left[i] + carry;
298 		if (sum != left[i])
299 			carry = (sum < left[i]);
300 		else
301 			carry = !!carry;
302 
303 		result[i] = sum;
304 	}
305 
306 	return carry;
307 }
308 
309 /* Computes result = left - right, returning borrow. Can modify in place. */
vli_sub(u64 * result,const u64 * left,const u64 * right,unsigned int ndigits)310 u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
311 		   unsigned int ndigits)
312 {
313 	u64 borrow = 0;
314 	int i;
315 
316 	for (i = 0; i < ndigits; i++) {
317 		u64 diff;
318 
319 		diff = left[i] - right[i] - borrow;
320 		if (diff != left[i])
321 			borrow = (diff > left[i]);
322 
323 		result[i] = diff;
324 	}
325 
326 	return borrow;
327 }
328 EXPORT_SYMBOL(vli_sub);
329 
330 /* Computes result = left - right, returning borrow. Can modify in place. */
vli_usub(u64 * result,const u64 * left,u64 right,unsigned int ndigits)331 static u64 vli_usub(u64 *result, const u64 *left, u64 right,
332 	     unsigned int ndigits)
333 {
334 	u64 borrow = right;
335 	int i;
336 
337 	for (i = 0; i < ndigits; i++) {
338 		u64 diff;
339 
340 		diff = left[i] - borrow;
341 		if (diff != left[i])
342 			borrow = (diff > left[i]);
343 
344 		result[i] = diff;
345 	}
346 
347 	return borrow;
348 }
349 
mul_64_64(u64 left,u64 right)350 static uint128_t mul_64_64(u64 left, u64 right)
351 {
352 	uint128_t result;
353 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
354 	unsigned __int128 m = (unsigned __int128)left * right;
355 
356 	result.m_low  = m;
357 	result.m_high = m >> 64;
358 #else
359 	u64 a0 = left & 0xffffffffull;
360 	u64 a1 = left >> 32;
361 	u64 b0 = right & 0xffffffffull;
362 	u64 b1 = right >> 32;
363 	u64 m0 = a0 * b0;
364 	u64 m1 = a0 * b1;
365 	u64 m2 = a1 * b0;
366 	u64 m3 = a1 * b1;
367 
368 	m2 += (m0 >> 32);
369 	m2 += m1;
370 
371 	/* Overflow */
372 	if (m2 < m1)
373 		m3 += 0x100000000ull;
374 
375 	result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
376 	result.m_high = m3 + (m2 >> 32);
377 #endif
378 	return result;
379 }
380 
add_128_128(uint128_t a,uint128_t b)381 static uint128_t add_128_128(uint128_t a, uint128_t b)
382 {
383 	uint128_t result;
384 
385 	result.m_low = a.m_low + b.m_low;
386 	result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
387 
388 	return result;
389 }
390 
vli_mult(u64 * result,const u64 * left,const u64 * right,unsigned int ndigits)391 static void vli_mult(u64 *result, const u64 *left, const u64 *right,
392 		     unsigned int ndigits)
393 {
394 	uint128_t r01 = { 0, 0 };
395 	u64 r2 = 0;
396 	unsigned int i, k;
397 
398 	/* Compute each digit of result in sequence, maintaining the
399 	 * carries.
400 	 */
401 	for (k = 0; k < ndigits * 2 - 1; k++) {
402 		unsigned int min;
403 
404 		if (k < ndigits)
405 			min = 0;
406 		else
407 			min = (k + 1) - ndigits;
408 
409 		for (i = min; i <= k && i < ndigits; i++) {
410 			uint128_t product;
411 
412 			product = mul_64_64(left[i], right[k - i]);
413 
414 			r01 = add_128_128(r01, product);
415 			r2 += (r01.m_high < product.m_high);
416 		}
417 
418 		result[k] = r01.m_low;
419 		r01.m_low = r01.m_high;
420 		r01.m_high = r2;
421 		r2 = 0;
422 	}
423 
424 	result[ndigits * 2 - 1] = r01.m_low;
425 }
426 
427 /* Compute product = left * right, for a small right value. */
vli_umult(u64 * result,const u64 * left,u32 right,unsigned int ndigits)428 static void vli_umult(u64 *result, const u64 *left, u32 right,
429 		      unsigned int ndigits)
430 {
431 	uint128_t r01 = { 0 };
432 	unsigned int k;
433 
434 	for (k = 0; k < ndigits; k++) {
435 		uint128_t product;
436 
437 		product = mul_64_64(left[k], right);
438 		r01 = add_128_128(r01, product);
439 		/* no carry */
440 		result[k] = r01.m_low;
441 		r01.m_low = r01.m_high;
442 		r01.m_high = 0;
443 	}
444 	result[k] = r01.m_low;
445 	for (++k; k < ndigits * 2; k++)
446 		result[k] = 0;
447 }
448 
vli_square(u64 * result,const u64 * left,unsigned int ndigits)449 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
450 {
451 	uint128_t r01 = { 0, 0 };
452 	u64 r2 = 0;
453 	int i, k;
454 
455 	for (k = 0; k < ndigits * 2 - 1; k++) {
456 		unsigned int min;
457 
458 		if (k < ndigits)
459 			min = 0;
460 		else
461 			min = (k + 1) - ndigits;
462 
463 		for (i = min; i <= k && i <= k - i; i++) {
464 			uint128_t product;
465 
466 			product = mul_64_64(left[i], left[k - i]);
467 
468 			if (i < k - i) {
469 				r2 += product.m_high >> 63;
470 				product.m_high = (product.m_high << 1) |
471 						 (product.m_low >> 63);
472 				product.m_low <<= 1;
473 			}
474 
475 			r01 = add_128_128(r01, product);
476 			r2 += (r01.m_high < product.m_high);
477 		}
478 
479 		result[k] = r01.m_low;
480 		r01.m_low = r01.m_high;
481 		r01.m_high = r2;
482 		r2 = 0;
483 	}
484 
485 	result[ndigits * 2 - 1] = r01.m_low;
486 }
487 
488 /* Computes result = (left + right) % mod.
489  * Assumes that left < mod and right < mod, result != mod.
490  */
vli_mod_add(u64 * result,const u64 * left,const u64 * right,const u64 * mod,unsigned int ndigits)491 static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
492 			const u64 *mod, unsigned int ndigits)
493 {
494 	u64 carry;
495 
496 	carry = vli_add(result, left, right, ndigits);
497 
498 	/* result > mod (result = mod + remainder), so subtract mod to
499 	 * get remainder.
500 	 */
501 	if (carry || vli_cmp(result, mod, ndigits) >= 0)
502 		vli_sub(result, result, mod, ndigits);
503 }
504 
505 /* Computes result = (left - right) % mod.
506  * Assumes that left < mod and right < mod, result != mod.
507  */
vli_mod_sub(u64 * result,const u64 * left,const u64 * right,const u64 * mod,unsigned int ndigits)508 static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
509 			const u64 *mod, unsigned int ndigits)
510 {
511 	u64 borrow = vli_sub(result, left, right, ndigits);
512 
513 	/* In this case, p_result == -diff == (max int) - diff.
514 	 * Since -x % d == d - x, we can get the correct result from
515 	 * result + mod (with overflow).
516 	 */
517 	if (borrow)
518 		vli_add(result, result, mod, ndigits);
519 }
520 
521 /*
522  * Computes result = product % mod
523  * for special form moduli: p = 2^k-c, for small c (note the minus sign)
524  *
525  * References:
526  * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
527  * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
528  * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
529  */
vli_mmod_special(u64 * result,const u64 * product,const u64 * mod,unsigned int ndigits)530 static void vli_mmod_special(u64 *result, const u64 *product,
531 			      const u64 *mod, unsigned int ndigits)
532 {
533 	u64 c = -mod[0];
534 	u64 t[ECC_MAX_DIGITS * 2];
535 	u64 r[ECC_MAX_DIGITS * 2];
536 
537 	vli_set(r, product, ndigits * 2);
538 	while (!vli_is_zero(r + ndigits, ndigits)) {
539 		vli_umult(t, r + ndigits, c, ndigits);
540 		vli_clear(r + ndigits, ndigits);
541 		vli_add(r, r, t, ndigits * 2);
542 	}
543 	vli_set(t, mod, ndigits);
544 	vli_clear(t + ndigits, ndigits);
545 	while (vli_cmp(r, t, ndigits * 2) >= 0)
546 		vli_sub(r, r, t, ndigits * 2);
547 	vli_set(result, r, ndigits);
548 }
549 
550 /*
551  * Computes result = product % mod
552  * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
553  * where k-1 does not fit into qword boundary by -1 bit (such as 255).
554 
555  * References (loosely based on):
556  * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
557  * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
558  * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
559  *
560  * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
561  * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
562  * Algorithm 10.25 Fast reduction for special form moduli
563  */
vli_mmod_special2(u64 * result,const u64 * product,const u64 * mod,unsigned int ndigits)564 static void vli_mmod_special2(u64 *result, const u64 *product,
565 			       const u64 *mod, unsigned int ndigits)
566 {
567 	u64 c2 = mod[0] * 2;
568 	u64 q[ECC_MAX_DIGITS];
569 	u64 r[ECC_MAX_DIGITS * 2];
570 	u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
571 	int carry; /* last bit that doesn't fit into q */
572 	int i;
573 
574 	vli_set(m, mod, ndigits);
575 	vli_clear(m + ndigits, ndigits);
576 
577 	vli_set(r, product, ndigits);
578 	/* q and carry are top bits */
579 	vli_set(q, product + ndigits, ndigits);
580 	vli_clear(r + ndigits, ndigits);
581 	carry = vli_is_negative(r, ndigits);
582 	if (carry)
583 		r[ndigits - 1] &= (1ull << 63) - 1;
584 	for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
585 		u64 qc[ECC_MAX_DIGITS * 2];
586 
587 		vli_umult(qc, q, c2, ndigits);
588 		if (carry)
589 			vli_uadd(qc, qc, mod[0], ndigits * 2);
590 		vli_set(q, qc + ndigits, ndigits);
591 		vli_clear(qc + ndigits, ndigits);
592 		carry = vli_is_negative(qc, ndigits);
593 		if (carry)
594 			qc[ndigits - 1] &= (1ull << 63) - 1;
595 		if (i & 1)
596 			vli_sub(r, r, qc, ndigits * 2);
597 		else
598 			vli_add(r, r, qc, ndigits * 2);
599 	}
600 	while (vli_is_negative(r, ndigits * 2))
601 		vli_add(r, r, m, ndigits * 2);
602 	while (vli_cmp(r, m, ndigits * 2) >= 0)
603 		vli_sub(r, r, m, ndigits * 2);
604 
605 	vli_set(result, r, ndigits);
606 }
607 
608 /*
609  * Computes result = product % mod, where product is 2N words long.
610  * Reference: Ken MacKay's micro-ecc.
611  * Currently only designed to work for curve_p or curve_n.
612  */
vli_mmod_slow(u64 * result,u64 * product,const u64 * mod,unsigned int ndigits)613 static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
614 			  unsigned int ndigits)
615 {
616 	u64 mod_m[2 * ECC_MAX_DIGITS];
617 	u64 tmp[2 * ECC_MAX_DIGITS];
618 	u64 *v[2] = { tmp, product };
619 	u64 carry = 0;
620 	unsigned int i;
621 	/* Shift mod so its highest set bit is at the maximum position. */
622 	int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
623 	int word_shift = shift / 64;
624 	int bit_shift = shift % 64;
625 
626 	vli_clear(mod_m, word_shift);
627 	if (bit_shift > 0) {
628 		for (i = 0; i < ndigits; ++i) {
629 			mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
630 			carry = mod[i] >> (64 - bit_shift);
631 		}
632 	} else
633 		vli_set(mod_m + word_shift, mod, ndigits);
634 
635 	for (i = 1; shift >= 0; --shift) {
636 		u64 borrow = 0;
637 		unsigned int j;
638 
639 		for (j = 0; j < ndigits * 2; ++j) {
640 			u64 diff = v[i][j] - mod_m[j] - borrow;
641 
642 			if (diff != v[i][j])
643 				borrow = (diff > v[i][j]);
644 			v[1 - i][j] = diff;
645 		}
646 		i = !(i ^ borrow); /* Swap the index if there was no borrow */
647 		vli_rshift1(mod_m, ndigits);
648 		mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
649 		vli_rshift1(mod_m + ndigits, ndigits);
650 	}
651 	vli_set(result, v[i], ndigits);
652 }
653 
654 /* Computes result = product % mod using Barrett's reduction with precomputed
655  * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
656  * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
657  * boundary.
658  *
659  * Reference:
660  * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
661  * 2.4.1 Barrett's algorithm. Algorithm 2.5.
662  */
vli_mmod_barrett(u64 * result,u64 * product,const u64 * mod,unsigned int ndigits)663 static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
664 			     unsigned int ndigits)
665 {
666 	u64 q[ECC_MAX_DIGITS * 2];
667 	u64 r[ECC_MAX_DIGITS * 2];
668 	const u64 *mu = mod + ndigits;
669 
670 	vli_mult(q, product + ndigits, mu, ndigits);
671 	if (mu[ndigits])
672 		vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
673 	vli_mult(r, mod, q + ndigits, ndigits);
674 	vli_sub(r, product, r, ndigits * 2);
675 	while (!vli_is_zero(r + ndigits, ndigits) ||
676 	       vli_cmp(r, mod, ndigits) != -1) {
677 		u64 carry;
678 
679 		carry = vli_sub(r, r, mod, ndigits);
680 		vli_usub(r + ndigits, r + ndigits, carry, ndigits);
681 	}
682 	vli_set(result, r, ndigits);
683 }
684 
685 /* Computes p_result = p_product % curve_p.
686  * See algorithm 5 and 6 from
687  * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
688  */
vli_mmod_fast_192(u64 * result,const u64 * product,const u64 * curve_prime,u64 * tmp)689 static void vli_mmod_fast_192(u64 *result, const u64 *product,
690 			      const u64 *curve_prime, u64 *tmp)
691 {
692 	const unsigned int ndigits = 3;
693 	int carry;
694 
695 	vli_set(result, product, ndigits);
696 
697 	vli_set(tmp, &product[3], ndigits);
698 	carry = vli_add(result, result, tmp, ndigits);
699 
700 	tmp[0] = 0;
701 	tmp[1] = product[3];
702 	tmp[2] = product[4];
703 	carry += vli_add(result, result, tmp, ndigits);
704 
705 	tmp[0] = tmp[1] = product[5];
706 	tmp[2] = 0;
707 	carry += vli_add(result, result, tmp, ndigits);
708 
709 	while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
710 		carry -= vli_sub(result, result, curve_prime, ndigits);
711 }
712 
713 /* Computes result = product % curve_prime
714  * from http://www.nsa.gov/ia/_files/nist-routines.pdf
715  */
vli_mmod_fast_256(u64 * result,const u64 * product,const u64 * curve_prime,u64 * tmp)716 static void vli_mmod_fast_256(u64 *result, const u64 *product,
717 			      const u64 *curve_prime, u64 *tmp)
718 {
719 	int carry;
720 	const unsigned int ndigits = 4;
721 
722 	/* t */
723 	vli_set(result, product, ndigits);
724 
725 	/* s1 */
726 	tmp[0] = 0;
727 	tmp[1] = product[5] & 0xffffffff00000000ull;
728 	tmp[2] = product[6];
729 	tmp[3] = product[7];
730 	carry = vli_lshift(tmp, tmp, 1, ndigits);
731 	carry += vli_add(result, result, tmp, ndigits);
732 
733 	/* s2 */
734 	tmp[1] = product[6] << 32;
735 	tmp[2] = (product[6] >> 32) | (product[7] << 32);
736 	tmp[3] = product[7] >> 32;
737 	carry += vli_lshift(tmp, tmp, 1, ndigits);
738 	carry += vli_add(result, result, tmp, ndigits);
739 
740 	/* s3 */
741 	tmp[0] = product[4];
742 	tmp[1] = product[5] & 0xffffffff;
743 	tmp[2] = 0;
744 	tmp[3] = product[7];
745 	carry += vli_add(result, result, tmp, ndigits);
746 
747 	/* s4 */
748 	tmp[0] = (product[4] >> 32) | (product[5] << 32);
749 	tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
750 	tmp[2] = product[7];
751 	tmp[3] = (product[6] >> 32) | (product[4] << 32);
752 	carry += vli_add(result, result, tmp, ndigits);
753 
754 	/* d1 */
755 	tmp[0] = (product[5] >> 32) | (product[6] << 32);
756 	tmp[1] = (product[6] >> 32);
757 	tmp[2] = 0;
758 	tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
759 	carry -= vli_sub(result, result, tmp, ndigits);
760 
761 	/* d2 */
762 	tmp[0] = product[6];
763 	tmp[1] = product[7];
764 	tmp[2] = 0;
765 	tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
766 	carry -= vli_sub(result, result, tmp, ndigits);
767 
768 	/* d3 */
769 	tmp[0] = (product[6] >> 32) | (product[7] << 32);
770 	tmp[1] = (product[7] >> 32) | (product[4] << 32);
771 	tmp[2] = (product[4] >> 32) | (product[5] << 32);
772 	tmp[3] = (product[6] << 32);
773 	carry -= vli_sub(result, result, tmp, ndigits);
774 
775 	/* d4 */
776 	tmp[0] = product[7];
777 	tmp[1] = product[4] & 0xffffffff00000000ull;
778 	tmp[2] = product[5];
779 	tmp[3] = product[6] & 0xffffffff00000000ull;
780 	carry -= vli_sub(result, result, tmp, ndigits);
781 
782 	if (carry < 0) {
783 		do {
784 			carry += vli_add(result, result, curve_prime, ndigits);
785 		} while (carry < 0);
786 	} else {
787 		while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
788 			carry -= vli_sub(result, result, curve_prime, ndigits);
789 	}
790 }
791 
792 #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
793 #define AND64H(x64)  (x64 & 0xffFFffFF00000000ull)
794 #define AND64L(x64)  (x64 & 0x00000000ffFFffFFull)
795 
796 /* Computes result = product % curve_prime
797  * from "Mathematical routines for the NIST prime elliptic curves"
798  */
vli_mmod_fast_384(u64 * result,const u64 * product,const u64 * curve_prime,u64 * tmp)799 static void vli_mmod_fast_384(u64 *result, const u64 *product,
800 				const u64 *curve_prime, u64 *tmp)
801 {
802 	int carry;
803 	const unsigned int ndigits = 6;
804 
805 	/* t */
806 	vli_set(result, product, ndigits);
807 
808 	/* s1 */
809 	tmp[0] = 0;		// 0 || 0
810 	tmp[1] = 0;		// 0 || 0
811 	tmp[2] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
812 	tmp[3] = product[11]>>32;	// 0 ||a23
813 	tmp[4] = 0;		// 0 || 0
814 	tmp[5] = 0;		// 0 || 0
815 	carry = vli_lshift(tmp, tmp, 1, ndigits);
816 	carry += vli_add(result, result, tmp, ndigits);
817 
818 	/* s2 */
819 	tmp[0] = product[6];	//a13||a12
820 	tmp[1] = product[7];	//a15||a14
821 	tmp[2] = product[8];	//a17||a16
822 	tmp[3] = product[9];	//a19||a18
823 	tmp[4] = product[10];	//a21||a20
824 	tmp[5] = product[11];	//a23||a22
825 	carry += vli_add(result, result, tmp, ndigits);
826 
827 	/* s3 */
828 	tmp[0] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
829 	tmp[1] = SL32OR32(product[6], (product[11]>>32));	//a12||a23
830 	tmp[2] = SL32OR32(product[7], (product[6])>>32);	//a14||a13
831 	tmp[3] = SL32OR32(product[8], (product[7]>>32));	//a16||a15
832 	tmp[4] = SL32OR32(product[9], (product[8]>>32));	//a18||a17
833 	tmp[5] = SL32OR32(product[10], (product[9]>>32));	//a20||a19
834 	carry += vli_add(result, result, tmp, ndigits);
835 
836 	/* s4 */
837 	tmp[0] = AND64H(product[11]);	//a23|| 0
838 	tmp[1] = (product[10]<<32);	//a20|| 0
839 	tmp[2] = product[6];	//a13||a12
840 	tmp[3] = product[7];	//a15||a14
841 	tmp[4] = product[8];	//a17||a16
842 	tmp[5] = product[9];	//a19||a18
843 	carry += vli_add(result, result, tmp, ndigits);
844 
845 	/* s5 */
846 	tmp[0] = 0;		//  0|| 0
847 	tmp[1] = 0;		//  0|| 0
848 	tmp[2] = product[10];	//a21||a20
849 	tmp[3] = product[11];	//a23||a22
850 	tmp[4] = 0;		//  0|| 0
851 	tmp[5] = 0;		//  0|| 0
852 	carry += vli_add(result, result, tmp, ndigits);
853 
854 	/* s6 */
855 	tmp[0] = AND64L(product[10]);	// 0 ||a20
856 	tmp[1] = AND64H(product[10]);	//a21|| 0
857 	tmp[2] = product[11];	//a23||a22
858 	tmp[3] = 0;		// 0 || 0
859 	tmp[4] = 0;		// 0 || 0
860 	tmp[5] = 0;		// 0 || 0
861 	carry += vli_add(result, result, tmp, ndigits);
862 
863 	/* d1 */
864 	tmp[0] = SL32OR32(product[6], (product[11]>>32));	//a12||a23
865 	tmp[1] = SL32OR32(product[7], (product[6]>>32));	//a14||a13
866 	tmp[2] = SL32OR32(product[8], (product[7]>>32));	//a16||a15
867 	tmp[3] = SL32OR32(product[9], (product[8]>>32));	//a18||a17
868 	tmp[4] = SL32OR32(product[10], (product[9]>>32));	//a20||a19
869 	tmp[5] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
870 	carry -= vli_sub(result, result, tmp, ndigits);
871 
872 	/* d2 */
873 	tmp[0] = (product[10]<<32);	//a20|| 0
874 	tmp[1] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
875 	tmp[2] = (product[11]>>32);	// 0 ||a23
876 	tmp[3] = 0;		// 0 || 0
877 	tmp[4] = 0;		// 0 || 0
878 	tmp[5] = 0;		// 0 || 0
879 	carry -= vli_sub(result, result, tmp, ndigits);
880 
881 	/* d3 */
882 	tmp[0] = 0;		// 0 || 0
883 	tmp[1] = AND64H(product[11]);	//a23|| 0
884 	tmp[2] = product[11]>>32;	// 0 ||a23
885 	tmp[3] = 0;		// 0 || 0
886 	tmp[4] = 0;		// 0 || 0
887 	tmp[5] = 0;		// 0 || 0
888 	carry -= vli_sub(result, result, tmp, ndigits);
889 
890 	if (carry < 0) {
891 		do {
892 			carry += vli_add(result, result, curve_prime, ndigits);
893 		} while (carry < 0);
894 	} else {
895 		while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
896 			carry -= vli_sub(result, result, curve_prime, ndigits);
897 	}
898 
899 }
900 
901 #undef SL32OR32
902 #undef AND64H
903 #undef AND64L
904 
905 /* Computes result = product % curve_prime for different curve_primes.
906  *
907  * Note that curve_primes are distinguished just by heuristic check and
908  * not by complete conformance check.
909  */
vli_mmod_fast(u64 * result,u64 * product,const struct ecc_curve * curve)910 static bool vli_mmod_fast(u64 *result, u64 *product,
911 			  const struct ecc_curve *curve)
912 {
913 	u64 tmp[2 * ECC_MAX_DIGITS];
914 	const u64 *curve_prime = curve->p;
915 	const unsigned int ndigits = curve->g.ndigits;
916 
917 	/* All NIST curves have name prefix 'nist_' */
918 	if (strncmp(curve->name, "nist_", 5) != 0) {
919 		/* Try to handle Pseudo-Marsenne primes. */
920 		if (curve_prime[ndigits - 1] == -1ull) {
921 			vli_mmod_special(result, product, curve_prime,
922 					 ndigits);
923 			return true;
924 		} else if (curve_prime[ndigits - 1] == 1ull << 63 &&
925 			   curve_prime[ndigits - 2] == 0) {
926 			vli_mmod_special2(result, product, curve_prime,
927 					  ndigits);
928 			return true;
929 		}
930 		vli_mmod_barrett(result, product, curve_prime, ndigits);
931 		return true;
932 	}
933 
934 	switch (ndigits) {
935 	case 3:
936 		vli_mmod_fast_192(result, product, curve_prime, tmp);
937 		break;
938 	case 4:
939 		vli_mmod_fast_256(result, product, curve_prime, tmp);
940 		break;
941 	case 6:
942 		vli_mmod_fast_384(result, product, curve_prime, tmp);
943 		break;
944 	default:
945 		pr_err_ratelimited("ecc: unsupported digits size!\n");
946 		return false;
947 	}
948 
949 	return true;
950 }
951 
952 /* Computes result = (left * right) % mod.
953  * Assumes that mod is big enough curve order.
954  */
vli_mod_mult_slow(u64 * result,const u64 * left,const u64 * right,const u64 * mod,unsigned int ndigits)955 void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
956 		       const u64 *mod, unsigned int ndigits)
957 {
958 	u64 product[ECC_MAX_DIGITS * 2];
959 
960 	vli_mult(product, left, right, ndigits);
961 	vli_mmod_slow(result, product, mod, ndigits);
962 }
963 EXPORT_SYMBOL(vli_mod_mult_slow);
964 
965 /* Computes result = (left * right) % curve_prime. */
vli_mod_mult_fast(u64 * result,const u64 * left,const u64 * right,const struct ecc_curve * curve)966 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
967 			      const struct ecc_curve *curve)
968 {
969 	u64 product[2 * ECC_MAX_DIGITS];
970 
971 	vli_mult(product, left, right, curve->g.ndigits);
972 	vli_mmod_fast(result, product, curve);
973 }
974 
975 /* Computes result = left^2 % curve_prime. */
vli_mod_square_fast(u64 * result,const u64 * left,const struct ecc_curve * curve)976 static void vli_mod_square_fast(u64 *result, const u64 *left,
977 				const struct ecc_curve *curve)
978 {
979 	u64 product[2 * ECC_MAX_DIGITS];
980 
981 	vli_square(product, left, curve->g.ndigits);
982 	vli_mmod_fast(result, product, curve);
983 }
984 
985 #define EVEN(vli) (!(vli[0] & 1))
986 /* Computes result = (1 / p_input) % mod. All VLIs are the same size.
987  * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
988  * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
989  */
vli_mod_inv(u64 * result,const u64 * input,const u64 * mod,unsigned int ndigits)990 void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
991 			unsigned int ndigits)
992 {
993 	u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
994 	u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
995 	u64 carry;
996 	int cmp_result;
997 
998 	if (vli_is_zero(input, ndigits)) {
999 		vli_clear(result, ndigits);
1000 		return;
1001 	}
1002 
1003 	vli_set(a, input, ndigits);
1004 	vli_set(b, mod, ndigits);
1005 	vli_clear(u, ndigits);
1006 	u[0] = 1;
1007 	vli_clear(v, ndigits);
1008 
1009 	while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
1010 		carry = 0;
1011 
1012 		if (EVEN(a)) {
1013 			vli_rshift1(a, ndigits);
1014 
1015 			if (!EVEN(u))
1016 				carry = vli_add(u, u, mod, ndigits);
1017 
1018 			vli_rshift1(u, ndigits);
1019 			if (carry)
1020 				u[ndigits - 1] |= 0x8000000000000000ull;
1021 		} else if (EVEN(b)) {
1022 			vli_rshift1(b, ndigits);
1023 
1024 			if (!EVEN(v))
1025 				carry = vli_add(v, v, mod, ndigits);
1026 
1027 			vli_rshift1(v, ndigits);
1028 			if (carry)
1029 				v[ndigits - 1] |= 0x8000000000000000ull;
1030 		} else if (cmp_result > 0) {
1031 			vli_sub(a, a, b, ndigits);
1032 			vli_rshift1(a, ndigits);
1033 
1034 			if (vli_cmp(u, v, ndigits) < 0)
1035 				vli_add(u, u, mod, ndigits);
1036 
1037 			vli_sub(u, u, v, ndigits);
1038 			if (!EVEN(u))
1039 				carry = vli_add(u, u, mod, ndigits);
1040 
1041 			vli_rshift1(u, ndigits);
1042 			if (carry)
1043 				u[ndigits - 1] |= 0x8000000000000000ull;
1044 		} else {
1045 			vli_sub(b, b, a, ndigits);
1046 			vli_rshift1(b, ndigits);
1047 
1048 			if (vli_cmp(v, u, ndigits) < 0)
1049 				vli_add(v, v, mod, ndigits);
1050 
1051 			vli_sub(v, v, u, ndigits);
1052 			if (!EVEN(v))
1053 				carry = vli_add(v, v, mod, ndigits);
1054 
1055 			vli_rshift1(v, ndigits);
1056 			if (carry)
1057 				v[ndigits - 1] |= 0x8000000000000000ull;
1058 		}
1059 	}
1060 
1061 	vli_set(result, u, ndigits);
1062 }
1063 EXPORT_SYMBOL(vli_mod_inv);
1064 
1065 /* ------ Point operations ------ */
1066 
1067 /* Returns true if p_point is the point at infinity, false otherwise. */
ecc_point_is_zero(const struct ecc_point * point)1068 bool ecc_point_is_zero(const struct ecc_point *point)
1069 {
1070 	return (vli_is_zero(point->x, point->ndigits) &&
1071 		vli_is_zero(point->y, point->ndigits));
1072 }
1073 EXPORT_SYMBOL(ecc_point_is_zero);
1074 
1075 /* Point multiplication algorithm using Montgomery's ladder with co-Z
1076  * coordinates. From https://eprint.iacr.org/2011/338.pdf
1077  */
1078 
1079 /* Double in place */
ecc_point_double_jacobian(u64 * x1,u64 * y1,u64 * z1,const struct ecc_curve * curve)1080 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1081 					const struct ecc_curve *curve)
1082 {
1083 	/* t1 = x, t2 = y, t3 = z */
1084 	u64 t4[ECC_MAX_DIGITS];
1085 	u64 t5[ECC_MAX_DIGITS];
1086 	const u64 *curve_prime = curve->p;
1087 	const unsigned int ndigits = curve->g.ndigits;
1088 
1089 	if (vli_is_zero(z1, ndigits))
1090 		return;
1091 
1092 	/* t4 = y1^2 */
1093 	vli_mod_square_fast(t4, y1, curve);
1094 	/* t5 = x1*y1^2 = A */
1095 	vli_mod_mult_fast(t5, x1, t4, curve);
1096 	/* t4 = y1^4 */
1097 	vli_mod_square_fast(t4, t4, curve);
1098 	/* t2 = y1*z1 = z3 */
1099 	vli_mod_mult_fast(y1, y1, z1, curve);
1100 	/* t3 = z1^2 */
1101 	vli_mod_square_fast(z1, z1, curve);
1102 
1103 	/* t1 = x1 + z1^2 */
1104 	vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1105 	/* t3 = 2*z1^2 */
1106 	vli_mod_add(z1, z1, z1, curve_prime, ndigits);
1107 	/* t3 = x1 - z1^2 */
1108 	vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
1109 	/* t1 = x1^2 - z1^4 */
1110 	vli_mod_mult_fast(x1, x1, z1, curve);
1111 
1112 	/* t3 = 2*(x1^2 - z1^4) */
1113 	vli_mod_add(z1, x1, x1, curve_prime, ndigits);
1114 	/* t1 = 3*(x1^2 - z1^4) */
1115 	vli_mod_add(x1, x1, z1, curve_prime, ndigits);
1116 	if (vli_test_bit(x1, 0)) {
1117 		u64 carry = vli_add(x1, x1, curve_prime, ndigits);
1118 
1119 		vli_rshift1(x1, ndigits);
1120 		x1[ndigits - 1] |= carry << 63;
1121 	} else {
1122 		vli_rshift1(x1, ndigits);
1123 	}
1124 	/* t1 = 3/2*(x1^2 - z1^4) = B */
1125 
1126 	/* t3 = B^2 */
1127 	vli_mod_square_fast(z1, x1, curve);
1128 	/* t3 = B^2 - A */
1129 	vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1130 	/* t3 = B^2 - 2A = x3 */
1131 	vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
1132 	/* t5 = A - x3 */
1133 	vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
1134 	/* t1 = B * (A - x3) */
1135 	vli_mod_mult_fast(x1, x1, t5, curve);
1136 	/* t4 = B * (A - x3) - y1^4 = y3 */
1137 	vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1138 
1139 	vli_set(x1, z1, ndigits);
1140 	vli_set(z1, y1, ndigits);
1141 	vli_set(y1, t4, ndigits);
1142 }
1143 
1144 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
apply_z(u64 * x1,u64 * y1,u64 * z,const struct ecc_curve * curve)1145 static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1146 {
1147 	u64 t1[ECC_MAX_DIGITS];
1148 
1149 	vli_mod_square_fast(t1, z, curve);		/* z^2 */
1150 	vli_mod_mult_fast(x1, x1, t1, curve);	/* x1 * z^2 */
1151 	vli_mod_mult_fast(t1, t1, z, curve);	/* z^3 */
1152 	vli_mod_mult_fast(y1, y1, t1, curve);	/* y1 * z^3 */
1153 }
1154 
1155 /* P = (x1, y1) => 2P, (x2, y2) => P' */
xycz_initial_double(u64 * x1,u64 * y1,u64 * x2,u64 * y2,u64 * p_initial_z,const struct ecc_curve * curve)1156 static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1157 				u64 *p_initial_z, const struct ecc_curve *curve)
1158 {
1159 	u64 z[ECC_MAX_DIGITS];
1160 	const unsigned int ndigits = curve->g.ndigits;
1161 
1162 	vli_set(x2, x1, ndigits);
1163 	vli_set(y2, y1, ndigits);
1164 
1165 	vli_clear(z, ndigits);
1166 	z[0] = 1;
1167 
1168 	if (p_initial_z)
1169 		vli_set(z, p_initial_z, ndigits);
1170 
1171 	apply_z(x1, y1, z, curve);
1172 
1173 	ecc_point_double_jacobian(x1, y1, z, curve);
1174 
1175 	apply_z(x2, y2, z, curve);
1176 }
1177 
1178 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1179  * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1180  * or P => P', Q => P + Q
1181  */
xycz_add(u64 * x1,u64 * y1,u64 * x2,u64 * y2,const struct ecc_curve * curve)1182 static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1183 			const struct ecc_curve *curve)
1184 {
1185 	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1186 	u64 t5[ECC_MAX_DIGITS];
1187 	const u64 *curve_prime = curve->p;
1188 	const unsigned int ndigits = curve->g.ndigits;
1189 
1190 	/* t5 = x2 - x1 */
1191 	vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1192 	/* t5 = (x2 - x1)^2 = A */
1193 	vli_mod_square_fast(t5, t5, curve);
1194 	/* t1 = x1*A = B */
1195 	vli_mod_mult_fast(x1, x1, t5, curve);
1196 	/* t3 = x2*A = C */
1197 	vli_mod_mult_fast(x2, x2, t5, curve);
1198 	/* t4 = y2 - y1 */
1199 	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1200 	/* t5 = (y2 - y1)^2 = D */
1201 	vli_mod_square_fast(t5, y2, curve);
1202 
1203 	/* t5 = D - B */
1204 	vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1205 	/* t5 = D - B - C = x3 */
1206 	vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1207 	/* t3 = C - B */
1208 	vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1209 	/* t2 = y1*(C - B) */
1210 	vli_mod_mult_fast(y1, y1, x2, curve);
1211 	/* t3 = B - x3 */
1212 	vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1213 	/* t4 = (y2 - y1)*(B - x3) */
1214 	vli_mod_mult_fast(y2, y2, x2, curve);
1215 	/* t4 = y3 */
1216 	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1217 
1218 	vli_set(x2, t5, ndigits);
1219 }
1220 
1221 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1222  * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1223  * or P => P - Q, Q => P + Q
1224  */
xycz_add_c(u64 * x1,u64 * y1,u64 * x2,u64 * y2,const struct ecc_curve * curve)1225 static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1226 			const struct ecc_curve *curve)
1227 {
1228 	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1229 	u64 t5[ECC_MAX_DIGITS];
1230 	u64 t6[ECC_MAX_DIGITS];
1231 	u64 t7[ECC_MAX_DIGITS];
1232 	const u64 *curve_prime = curve->p;
1233 	const unsigned int ndigits = curve->g.ndigits;
1234 
1235 	/* t5 = x2 - x1 */
1236 	vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1237 	/* t5 = (x2 - x1)^2 = A */
1238 	vli_mod_square_fast(t5, t5, curve);
1239 	/* t1 = x1*A = B */
1240 	vli_mod_mult_fast(x1, x1, t5, curve);
1241 	/* t3 = x2*A = C */
1242 	vli_mod_mult_fast(x2, x2, t5, curve);
1243 	/* t4 = y2 + y1 */
1244 	vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1245 	/* t4 = y2 - y1 */
1246 	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1247 
1248 	/* t6 = C - B */
1249 	vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1250 	/* t2 = y1 * (C - B) */
1251 	vli_mod_mult_fast(y1, y1, t6, curve);
1252 	/* t6 = B + C */
1253 	vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1254 	/* t3 = (y2 - y1)^2 */
1255 	vli_mod_square_fast(x2, y2, curve);
1256 	/* t3 = x3 */
1257 	vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1258 
1259 	/* t7 = B - x3 */
1260 	vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1261 	/* t4 = (y2 - y1)*(B - x3) */
1262 	vli_mod_mult_fast(y2, y2, t7, curve);
1263 	/* t4 = y3 */
1264 	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1265 
1266 	/* t7 = (y2 + y1)^2 = F */
1267 	vli_mod_square_fast(t7, t5, curve);
1268 	/* t7 = x3' */
1269 	vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1270 	/* t6 = x3' - B */
1271 	vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1272 	/* t6 = (y2 + y1)*(x3' - B) */
1273 	vli_mod_mult_fast(t6, t6, t5, curve);
1274 	/* t2 = y3' */
1275 	vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1276 
1277 	vli_set(x1, t7, ndigits);
1278 }
1279 
ecc_point_mult(struct ecc_point * result,const struct ecc_point * point,const u64 * scalar,u64 * initial_z,const struct ecc_curve * curve,unsigned int ndigits)1280 static void ecc_point_mult(struct ecc_point *result,
1281 			   const struct ecc_point *point, const u64 *scalar,
1282 			   u64 *initial_z, const struct ecc_curve *curve,
1283 			   unsigned int ndigits)
1284 {
1285 	/* R0 and R1 */
1286 	u64 rx[2][ECC_MAX_DIGITS];
1287 	u64 ry[2][ECC_MAX_DIGITS];
1288 	u64 z[ECC_MAX_DIGITS];
1289 	u64 sk[2][ECC_MAX_DIGITS];
1290 	u64 *curve_prime = curve->p;
1291 	int i, nb;
1292 	int num_bits;
1293 	int carry;
1294 
1295 	carry = vli_add(sk[0], scalar, curve->n, ndigits);
1296 	vli_add(sk[1], sk[0], curve->n, ndigits);
1297 	scalar = sk[!carry];
1298 	num_bits = sizeof(u64) * ndigits * 8 + 1;
1299 
1300 	vli_set(rx[1], point->x, ndigits);
1301 	vli_set(ry[1], point->y, ndigits);
1302 
1303 	xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
1304 
1305 	for (i = num_bits - 2; i > 0; i--) {
1306 		nb = !vli_test_bit(scalar, i);
1307 		xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1308 		xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1309 	}
1310 
1311 	nb = !vli_test_bit(scalar, 0);
1312 	xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1313 
1314 	/* Find final 1/Z value. */
1315 	/* X1 - X0 */
1316 	vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1317 	/* Yb * (X1 - X0) */
1318 	vli_mod_mult_fast(z, z, ry[1 - nb], curve);
1319 	/* xP * Yb * (X1 - X0) */
1320 	vli_mod_mult_fast(z, z, point->x, curve);
1321 
1322 	/* 1 / (xP * Yb * (X1 - X0)) */
1323 	vli_mod_inv(z, z, curve_prime, point->ndigits);
1324 
1325 	/* yP / (xP * Yb * (X1 - X0)) */
1326 	vli_mod_mult_fast(z, z, point->y, curve);
1327 	/* Xb * yP / (xP * Yb * (X1 - X0)) */
1328 	vli_mod_mult_fast(z, z, rx[1 - nb], curve);
1329 	/* End 1/Z calculation */
1330 
1331 	xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1332 
1333 	apply_z(rx[0], ry[0], z, curve);
1334 
1335 	vli_set(result->x, rx[0], ndigits);
1336 	vli_set(result->y, ry[0], ndigits);
1337 }
1338 
1339 /* Computes R = P + Q mod p */
ecc_point_add(const struct ecc_point * result,const struct ecc_point * p,const struct ecc_point * q,const struct ecc_curve * curve)1340 static void ecc_point_add(const struct ecc_point *result,
1341 		   const struct ecc_point *p, const struct ecc_point *q,
1342 		   const struct ecc_curve *curve)
1343 {
1344 	u64 z[ECC_MAX_DIGITS];
1345 	u64 px[ECC_MAX_DIGITS];
1346 	u64 py[ECC_MAX_DIGITS];
1347 	unsigned int ndigits = curve->g.ndigits;
1348 
1349 	vli_set(result->x, q->x, ndigits);
1350 	vli_set(result->y, q->y, ndigits);
1351 	vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1352 	vli_set(px, p->x, ndigits);
1353 	vli_set(py, p->y, ndigits);
1354 	xycz_add(px, py, result->x, result->y, curve);
1355 	vli_mod_inv(z, z, curve->p, ndigits);
1356 	apply_z(result->x, result->y, z, curve);
1357 }
1358 
1359 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1360  * Based on: Kenneth MacKay's micro-ecc (2014).
1361  */
ecc_point_mult_shamir(const struct ecc_point * result,const u64 * u1,const struct ecc_point * p,const u64 * u2,const struct ecc_point * q,const struct ecc_curve * curve)1362 void ecc_point_mult_shamir(const struct ecc_point *result,
1363 			   const u64 *u1, const struct ecc_point *p,
1364 			   const u64 *u2, const struct ecc_point *q,
1365 			   const struct ecc_curve *curve)
1366 {
1367 	u64 z[ECC_MAX_DIGITS];
1368 	u64 sump[2][ECC_MAX_DIGITS];
1369 	u64 *rx = result->x;
1370 	u64 *ry = result->y;
1371 	unsigned int ndigits = curve->g.ndigits;
1372 	unsigned int num_bits;
1373 	struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1374 	const struct ecc_point *points[4];
1375 	const struct ecc_point *point;
1376 	unsigned int idx;
1377 	int i;
1378 
1379 	ecc_point_add(&sum, p, q, curve);
1380 	points[0] = NULL;
1381 	points[1] = p;
1382 	points[2] = q;
1383 	points[3] = &sum;
1384 
1385 	num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1386 	i = num_bits - 1;
1387 	idx = !!vli_test_bit(u1, i);
1388 	idx |= (!!vli_test_bit(u2, i)) << 1;
1389 	point = points[idx];
1390 
1391 	vli_set(rx, point->x, ndigits);
1392 	vli_set(ry, point->y, ndigits);
1393 	vli_clear(z + 1, ndigits - 1);
1394 	z[0] = 1;
1395 
1396 	for (--i; i >= 0; i--) {
1397 		ecc_point_double_jacobian(rx, ry, z, curve);
1398 		idx = !!vli_test_bit(u1, i);
1399 		idx |= (!!vli_test_bit(u2, i)) << 1;
1400 		point = points[idx];
1401 		if (point) {
1402 			u64 tx[ECC_MAX_DIGITS];
1403 			u64 ty[ECC_MAX_DIGITS];
1404 			u64 tz[ECC_MAX_DIGITS];
1405 
1406 			vli_set(tx, point->x, ndigits);
1407 			vli_set(ty, point->y, ndigits);
1408 			apply_z(tx, ty, z, curve);
1409 			vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1410 			xycz_add(tx, ty, rx, ry, curve);
1411 			vli_mod_mult_fast(z, z, tz, curve);
1412 		}
1413 	}
1414 	vli_mod_inv(z, z, curve->p, ndigits);
1415 	apply_z(rx, ry, z, curve);
1416 }
1417 EXPORT_SYMBOL(ecc_point_mult_shamir);
1418 
__ecc_is_key_valid(const struct ecc_curve * curve,const u64 * private_key,unsigned int ndigits)1419 static int __ecc_is_key_valid(const struct ecc_curve *curve,
1420 			      const u64 *private_key, unsigned int ndigits)
1421 {
1422 	u64 one[ECC_MAX_DIGITS] = { 1, };
1423 	u64 res[ECC_MAX_DIGITS];
1424 
1425 	if (!private_key)
1426 		return -EINVAL;
1427 
1428 	if (curve->g.ndigits != ndigits)
1429 		return -EINVAL;
1430 
1431 	/* Make sure the private key is in the range [2, n-3]. */
1432 	if (vli_cmp(one, private_key, ndigits) != -1)
1433 		return -EINVAL;
1434 	vli_sub(res, curve->n, one, ndigits);
1435 	vli_sub(res, res, one, ndigits);
1436 	if (vli_cmp(res, private_key, ndigits) != 1)
1437 		return -EINVAL;
1438 
1439 	return 0;
1440 }
1441 
ecc_is_key_valid(unsigned int curve_id,unsigned int ndigits,const u64 * private_key,unsigned int private_key_len)1442 int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1443 		     const u64 *private_key, unsigned int private_key_len)
1444 {
1445 	int nbytes;
1446 	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1447 
1448 	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1449 
1450 	if (private_key_len != nbytes)
1451 		return -EINVAL;
1452 
1453 	return __ecc_is_key_valid(curve, private_key, ndigits);
1454 }
1455 EXPORT_SYMBOL(ecc_is_key_valid);
1456 
1457 /*
1458  * ECC private keys are generated using the method of extra random bits,
1459  * equivalent to that described in FIPS 186-4, Appendix B.4.1.
1460  *
1461  * d = (c mod(n–1)) + 1    where c is a string of random bits, 64 bits longer
1462  *                         than requested
1463  * 0 <= c mod(n-1) <= n-2  and implies that
1464  * 1 <= d <= n-1
1465  *
1466  * This method generates a private key uniformly distributed in the range
1467  * [1, n-1].
1468  */
ecc_gen_privkey(unsigned int curve_id,unsigned int ndigits,u64 * privkey)1469 int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
1470 {
1471 	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1472 	u64 priv[ECC_MAX_DIGITS];
1473 	unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1474 	unsigned int nbits = vli_num_bits(curve->n, ndigits);
1475 	int err;
1476 
1477 	/* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
1478 	if (nbits < 160 || ndigits > ARRAY_SIZE(priv))
1479 		return -EINVAL;
1480 
1481 	/*
1482 	 * FIPS 186-4 recommends that the private key should be obtained from a
1483 	 * RBG with a security strength equal to or greater than the security
1484 	 * strength associated with N.
1485 	 *
1486 	 * The maximum security strength identified by NIST SP800-57pt1r4 for
1487 	 * ECC is 256 (N >= 512).
1488 	 *
1489 	 * This condition is met by the default RNG because it selects a favored
1490 	 * DRBG with a security strength of 256.
1491 	 */
1492 	if (crypto_get_default_rng())
1493 		return -EFAULT;
1494 
1495 	err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
1496 	crypto_put_default_rng();
1497 	if (err)
1498 		return err;
1499 
1500 	/* Make sure the private key is in the valid range. */
1501 	if (__ecc_is_key_valid(curve, priv, ndigits))
1502 		return -EINVAL;
1503 
1504 	ecc_swap_digits(priv, privkey, ndigits);
1505 
1506 	return 0;
1507 }
1508 EXPORT_SYMBOL(ecc_gen_privkey);
1509 
ecc_make_pub_key(unsigned int curve_id,unsigned int ndigits,const u64 * private_key,u64 * public_key)1510 int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1511 		     const u64 *private_key, u64 *public_key)
1512 {
1513 	int ret = 0;
1514 	struct ecc_point *pk;
1515 	u64 priv[ECC_MAX_DIGITS];
1516 	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1517 
1518 	if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {
1519 		ret = -EINVAL;
1520 		goto out;
1521 	}
1522 
1523 	ecc_swap_digits(private_key, priv, ndigits);
1524 
1525 	pk = ecc_alloc_point(ndigits);
1526 	if (!pk) {
1527 		ret = -ENOMEM;
1528 		goto out;
1529 	}
1530 
1531 	ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
1532 
1533 	/* SP800-56A rev 3 5.6.2.1.3 key check */
1534 	if (ecc_is_pubkey_valid_full(curve, pk)) {
1535 		ret = -EAGAIN;
1536 		goto err_free_point;
1537 	}
1538 
1539 	ecc_swap_digits(pk->x, public_key, ndigits);
1540 	ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1541 
1542 err_free_point:
1543 	ecc_free_point(pk);
1544 out:
1545 	return ret;
1546 }
1547 EXPORT_SYMBOL(ecc_make_pub_key);
1548 
1549 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
ecc_is_pubkey_valid_partial(const struct ecc_curve * curve,struct ecc_point * pk)1550 int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1551 				struct ecc_point *pk)
1552 {
1553 	u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1554 
1555 	if (WARN_ON(pk->ndigits != curve->g.ndigits))
1556 		return -EINVAL;
1557 
1558 	/* Check 1: Verify key is not the zero point. */
1559 	if (ecc_point_is_zero(pk))
1560 		return -EINVAL;
1561 
1562 	/* Check 2: Verify key is in the range [1, p-1]. */
1563 	if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1564 		return -EINVAL;
1565 	if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1566 		return -EINVAL;
1567 
1568 	/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1569 	vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
1570 	vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
1571 	vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
1572 	vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
1573 	vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1574 	vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1575 	if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1576 		return -EINVAL;
1577 
1578 	return 0;
1579 }
1580 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1581 
1582 /* SP800-56A section 5.6.2.3.3 full verification */
ecc_is_pubkey_valid_full(const struct ecc_curve * curve,struct ecc_point * pk)1583 int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1584 			     struct ecc_point *pk)
1585 {
1586 	struct ecc_point *nQ;
1587 
1588 	/* Checks 1 through 3 */
1589 	int ret = ecc_is_pubkey_valid_partial(curve, pk);
1590 
1591 	if (ret)
1592 		return ret;
1593 
1594 	/* Check 4: Verify that nQ is the zero point. */
1595 	nQ = ecc_alloc_point(pk->ndigits);
1596 	if (!nQ)
1597 		return -ENOMEM;
1598 
1599 	ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
1600 	if (!ecc_point_is_zero(nQ))
1601 		ret = -EINVAL;
1602 
1603 	ecc_free_point(nQ);
1604 
1605 	return ret;
1606 }
1607 EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1608 
crypto_ecdh_shared_secret(unsigned int curve_id,unsigned int ndigits,const u64 * private_key,const u64 * public_key,u64 * secret)1609 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1610 			      const u64 *private_key, const u64 *public_key,
1611 			      u64 *secret)
1612 {
1613 	int ret = 0;
1614 	struct ecc_point *product, *pk;
1615 	u64 priv[ECC_MAX_DIGITS];
1616 	u64 rand_z[ECC_MAX_DIGITS];
1617 	unsigned int nbytes;
1618 	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1619 
1620 	if (!private_key || !public_key || !curve ||
1621 	    ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
1622 		ret = -EINVAL;
1623 		goto out;
1624 	}
1625 
1626 	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1627 
1628 	get_random_bytes(rand_z, nbytes);
1629 
1630 	pk = ecc_alloc_point(ndigits);
1631 	if (!pk) {
1632 		ret = -ENOMEM;
1633 		goto out;
1634 	}
1635 
1636 	ecc_swap_digits(public_key, pk->x, ndigits);
1637 	ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1638 	ret = ecc_is_pubkey_valid_partial(curve, pk);
1639 	if (ret)
1640 		goto err_alloc_product;
1641 
1642 	ecc_swap_digits(private_key, priv, ndigits);
1643 
1644 	product = ecc_alloc_point(ndigits);
1645 	if (!product) {
1646 		ret = -ENOMEM;
1647 		goto err_alloc_product;
1648 	}
1649 
1650 	ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
1651 
1652 	if (ecc_point_is_zero(product)) {
1653 		ret = -EFAULT;
1654 		goto err_validity;
1655 	}
1656 
1657 	ecc_swap_digits(product->x, secret, ndigits);
1658 
1659 err_validity:
1660 	memzero_explicit(priv, sizeof(priv));
1661 	memzero_explicit(rand_z, sizeof(rand_z));
1662 	ecc_free_point(product);
1663 err_alloc_product:
1664 	ecc_free_point(pk);
1665 out:
1666 	return ret;
1667 }
1668 EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1669 
1670 MODULE_LICENSE("Dual BSD/GPL");
1671