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 <linux/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 */
47	const struct ecc_curve *ecc_get_curve25519(void)
48	{
49	return &ecc_25519;
50	}
51	EXPORT_SYMBOL(ecc_get_curve25519);
52
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	case ECC_CURVE_NIST_P521:
64	return &nist_p521;
65	default:
66	return NULL;
67	}
68	}
69	EXPORT_SYMBOL(ecc_get_curve);
70
71	void ecc_digits_from_bytes(const u8 *in, unsigned int nbytes,
72	u64 *out, unsigned int ndigits)
73	{
74	int diff = ndigits - DIV_ROUND_UP_POW2(nbytes, sizeof(u64));
75	unsigned int o = nbytes & 7;
76	__be64 msd = 0;
77
78	/* diff > 0: not enough input bytes: set most significant digits to 0 */
79	if (diff > 0) {
80	ndigits -= diff;
81	memset(&out[ndigits], 0, diff * sizeof(u64));
82	}
83
84	if (o) {
85	memcpy((u8 *)&msd + sizeof(msd) - o, in, o);
86	out[--ndigits] = be64_to_cpu(msd);
87	in += o;
88	}
89	ecc_swap_digits(in, out, ndigits);
90	}
91	EXPORT_SYMBOL(ecc_digits_from_bytes);
92
93	static u64 *ecc_alloc_digits_space(unsigned int ndigits)
94	{
95	size_t len = ndigits * sizeof(u64);
96
97	if (!len)
98	return NULL;
99
100	return kmalloc(len, GFP_KERNEL);
101	}
102
103	static void ecc_free_digits_space(u64 *space)
104	{
105	kfree_sensitive(objp: space);
106	}
107
108	struct ecc_point *ecc_alloc_point(unsigned int ndigits)
109	{
110	struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
111
112	if (!p)
113	return NULL;
114
115	p->x = ecc_alloc_digits_space(ndigits);
116	if (!p->x)
117	goto err_alloc_x;
118
119	p->y = ecc_alloc_digits_space(ndigits);
120	if (!p->y)
121	goto err_alloc_y;
122
123	p->ndigits = ndigits;
124
125	return p;
126
127	err_alloc_y:
128	ecc_free_digits_space(space: p->x);
129	err_alloc_x:
130	kfree(objp: p);
131	return NULL;
132	}
133	EXPORT_SYMBOL(ecc_alloc_point);
134
135	void ecc_free_point(struct ecc_point *p)
136	{
137	if (!p)
138	return;
139
140	kfree_sensitive(objp: p->x);
141	kfree_sensitive(objp: p->y);
142	kfree_sensitive(objp: p);
143	}
144	EXPORT_SYMBOL(ecc_free_point);
145
146	static void vli_clear(u64 *vli, unsigned int ndigits)
147	{
148	int i;
149
150	for (i = 0; i < ndigits; i++)
151	vli[i] = 0;
152	}
153
154	/* Returns true if vli == 0, false otherwise. */
155	bool vli_is_zero(const u64 *vli, unsigned int ndigits)
156	{
157	int i;
158
159	for (i = 0; i < ndigits; i++) {
160	if (vli[i])
161	return false;
162	}
163
164	return true;
165	}
166	EXPORT_SYMBOL(vli_is_zero);
167
168	/* Returns nonzero if bit of vli is set. */
169	static u64 vli_test_bit(const u64 *vli, unsigned int bit)
170	{
171	return (vli[bit / 64] & ((u64)1 << (bit % 64)));
172	}
173
174	static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
175	{
176	return vli_test_bit(vli, bit: ndigits * 64 - 1);
177	}
178
179	/* Counts the number of 64-bit "digits" in vli. */
180	static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
181	{
182	int i;
183
184	/* Search from the end until we find a non-zero digit.
185	* We do it in reverse because we expect that most digits will
186	* be nonzero.
187	*/
188	for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
189
190	return (i + 1);
191	}
192
193	/* Counts the number of bits required for vli. */
194	unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
195	{
196	unsigned int i, num_digits;
197	u64 digit;
198
199	num_digits = vli_num_digits(vli, ndigits);
200	if (num_digits == 0)
201	return 0;
202
203	digit = vli[num_digits - 1];
204	for (i = 0; digit; i++)
205	digit >>= 1;
206
207	return ((num_digits - 1) * 64 + i);
208	}
209	EXPORT_SYMBOL(vli_num_bits);
210
211	/* Set dest from unaligned bit string src. */
212	void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
213	{
214	int i;
215	const u64 *from = src;
216
217	for (i = 0; i < ndigits; i++)
218	dest[i] = get_unaligned_be64(p: &from[ndigits - 1 - i]);
219	}
220	EXPORT_SYMBOL(vli_from_be64);
221
222	void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
223	{
224	int i;
225	const u64 *from = src;
226
227	for (i = 0; i < ndigits; i++)
228	dest[i] = get_unaligned_le64(p: &from[i]);
229	}
230	EXPORT_SYMBOL(vli_from_le64);
231
232	/* Sets dest = src. */
233	static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
234	{
235	int i;
236
237	for (i = 0; i < ndigits; i++)
238	dest[i] = src[i];
239	}
240
241	/* Returns sign of left - right. */
242	int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
243	{
244	int i;
245
246	for (i = ndigits - 1; i >= 0; i--) {
247	if (left[i] > right[i])
248	return 1;
249	else if (left[i] < right[i])
250	return -1;
251	}
252
253	return 0;
254	}
255	EXPORT_SYMBOL(vli_cmp);
256
257	/* Computes result = in << c, returning carry. Can modify in place
258	* (if result == in). 0 < shift < 64.
259	*/
260	static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
261	unsigned int ndigits)
262	{
263	u64 carry = 0;
264	int i;
265
266	for (i = 0; i < ndigits; i++) {
267	u64 temp = in[i];
268
269	result[i] = (temp << shift) | carry;
270	carry = temp >> (64 - shift);
271	}
272
273	return carry;
274	}
275
276	/* Computes vli = vli >> 1. */
277	static void vli_rshift1(u64 *vli, unsigned int ndigits)
278	{
279	u64 *end = vli;
280	u64 carry = 0;
281
282	vli += ndigits;
283
284	while (vli-- > end) {
285	u64 temp = *vli;
286	*vli = (temp >> 1) | carry;
287	carry = temp << 63;
288	}
289	}
290
291	/* Computes result = left + right, returning carry. Can modify in place. */
292	static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
293	unsigned int ndigits)
294	{
295	u64 carry = 0;
296	int i;
297
298	for (i = 0; i < ndigits; i++) {
299	u64 sum;
300
301	sum = left[i] + right[i] + carry;
302	if (sum != left[i])
303	carry = (sum < left[i]);
304
305	result[i] = sum;
306	}
307
308	return carry;
309	}
310
311	/* Computes result = left + right, returning carry. Can modify in place. */
312	static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
313	unsigned int ndigits)
314	{
315	u64 carry = right;
316	int i;
317
318	for (i = 0; i < ndigits; i++) {
319	u64 sum;
320
321	sum = left[i] + carry;
322	if (sum != left[i])
323	carry = (sum < left[i]);
324	else
325	carry = !!carry;
326
327	result[i] = sum;
328	}
329
330	return carry;
331	}
332
333	/* Computes result = left - right, returning borrow. Can modify in place. */
334	u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
335	unsigned int ndigits)
336	{
337	u64 borrow = 0;
338	int i;
339
340	for (i = 0; i < ndigits; i++) {
341	u64 diff;
342
343	diff = left[i] - right[i] - borrow;
344	if (diff != left[i])
345	borrow = (diff > left[i]);
346
347	result[i] = diff;
348	}
349
350	return borrow;
351	}
352	EXPORT_SYMBOL(vli_sub);
353
354	/* Computes result = left - right, returning borrow. Can modify in place. */
355	static u64 vli_usub(u64 *result, const u64 *left, u64 right,
356	unsigned int ndigits)
357	{
358	u64 borrow = right;
359	int i;
360
361	for (i = 0; i < ndigits; i++) {
362	u64 diff;
363
364	diff = left[i] - borrow;
365	if (diff != left[i])
366	borrow = (diff > left[i]);
367
368	result[i] = diff;
369	}
370
371	return borrow;
372	}
373
374	static uint128_t mul_64_64(u64 left, u64 right)
375	{
376	uint128_t result;
377	#if defined(CONFIG_ARCH_SUPPORTS_INT128)
378	unsigned __int128 m = (unsigned __int128)left * right;
379
380	result.m_low = m;
381	result.m_high = m >> 64;
382	#else
383	u64 a0 = left & 0xffffffffull;
384	u64 a1 = left >> 32;
385	u64 b0 = right & 0xffffffffull;
386	u64 b1 = right >> 32;
387	u64 m0 = a0 * b0;
388	u64 m1 = a0 * b1;
389	u64 m2 = a1 * b0;
390	u64 m3 = a1 * b1;
391
392	m2 += (m0 >> 32);
393	m2 += m1;
394
395	/* Overflow */
396	if (m2 < m1)
397	m3 += 0x100000000ull;
398
399	result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
400	result.m_high = m3 + (m2 >> 32);
401	#endif
402	return result;
403	}
404
405	static uint128_t add_128_128(uint128_t a, uint128_t b)
406	{
407	uint128_t result;
408
409	result.m_low = a.m_low + b.m_low;
410	result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
411
412	return result;
413	}
414
415	static void vli_mult(u64 *result, const u64 *left, const u64 *right,
416	unsigned int ndigits)
417	{
418	uint128_t r01 = { 0, 0 };
419	u64 r2 = 0;
420	unsigned int i, k;
421
422	/* Compute each digit of result in sequence, maintaining the
423	* carries.
424	*/
425	for (k = 0; k < ndigits * 2 - 1; k++) {
426	unsigned int min;
427
428	if (k < ndigits)
429	min = 0;
430	else
431	min = (k + 1) - ndigits;
432
433	for (i = min; i <= k && i < ndigits; i++) {
434	uint128_t product;
435
436	product = mul_64_64(left: left[i], right: right[k - i]);
437
438	r01 = add_128_128(a: r01, b: product);
439	r2 += (r01.m_high < product.m_high);
440	}
441
442	result[k] = r01.m_low;
443	r01.m_low = r01.m_high;
444	r01.m_high = r2;
445	r2 = 0;
446	}
447
448	result[ndigits * 2 - 1] = r01.m_low;
449	}
450
451	/* Compute product = left * right, for a small right value. */
452	static void vli_umult(u64 *result, const u64 *left, u32 right,
453	unsigned int ndigits)
454	{
455	uint128_t r01 = { 0 };
456	unsigned int k;
457
458	for (k = 0; k < ndigits; k++) {
459	uint128_t product;
460
461	product = mul_64_64(left: left[k], right);
462	r01 = add_128_128(a: r01, b: product);
463	/* no carry */
464	result[k] = r01.m_low;
465	r01.m_low = r01.m_high;
466	r01.m_high = 0;
467	}
468	result[k] = r01.m_low;
469	for (++k; k < ndigits * 2; k++)
470	result[k] = 0;
471	}
472
473	static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
474	{
475	uint128_t r01 = { 0, 0 };
476	u64 r2 = 0;
477	int i, k;
478
479	for (k = 0; k < ndigits * 2 - 1; k++) {
480	unsigned int min;
481
482	if (k < ndigits)
483	min = 0;
484	else
485	min = (k + 1) - ndigits;
486
487	for (i = min; i <= k && i <= k - i; i++) {
488	uint128_t product;
489
490	product = mul_64_64(left: left[i], right: left[k - i]);
491
492	if (i < k - i) {
493	r2 += product.m_high >> 63;
494	product.m_high = (product.m_high << 1) |
495	(product.m_low >> 63);
496	product.m_low <<= 1;
497	}
498
499	r01 = add_128_128(a: r01, b: product);
500	r2 += (r01.m_high < product.m_high);
501	}
502
503	result[k] = r01.m_low;
504	r01.m_low = r01.m_high;
505	r01.m_high = r2;
506	r2 = 0;
507	}
508
509	result[ndigits * 2 - 1] = r01.m_low;
510	}
511
512	/* Computes result = (left + right) % mod.
513	* Assumes that left < mod and right < mod, result != mod.
514	*/
515	static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
516	const u64 *mod, unsigned int ndigits)
517	{
518	u64 carry;
519
520	carry = vli_add(result, left, right, ndigits);
521
522	/* result > mod (result = mod + remainder), so subtract mod to
523	* get remainder.
524	*/
525	if (carry || vli_cmp(result, mod, ndigits) >= 0)
526	vli_sub(result, result, mod, ndigits);
527	}
528
529	/* Computes result = (left - right) % mod.
530	* Assumes that left < mod and right < mod, result != mod.
531	*/
532	static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
533	const u64 *mod, unsigned int ndigits)
534	{
535	u64 borrow = vli_sub(result, left, right, ndigits);
536
537	/* In this case, p_result == -diff == (max int) - diff.
538	* Since -x % d == d - x, we can get the correct result from
539	* result + mod (with overflow).
540	*/
541	if (borrow)
542	vli_add(result, left: result, right: mod, ndigits);
543	}
544
545	/*
546	* Computes result = product % mod
547	* for special form moduli: p = 2^k-c, for small c (note the minus sign)
548	*
549	* References:
550	* R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
551	* 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
552	* Algorithm 9.2.13 (Fast mod operation for special-form moduli).
553	*/
554	static void vli_mmod_special(u64 *result, const u64 *product,
555	const u64 *mod, unsigned int ndigits)
556	{
557	u64 c = -mod[0];
558	u64 t[ECC_MAX_DIGITS * 2];
559	u64 r[ECC_MAX_DIGITS * 2];
560
561	vli_set(dest: r, src: product, ndigits: ndigits * 2);
562	while (!vli_is_zero(r + ndigits, ndigits)) {
563	vli_umult(result: t, left: r + ndigits, right: c, ndigits);
564	vli_clear(vli: r + ndigits, ndigits);
565	vli_add(result: r, left: r, right: t, ndigits: ndigits * 2);
566	}
567	vli_set(dest: t, src: mod, ndigits);
568	vli_clear(vli: t + ndigits, ndigits);
569	while (vli_cmp(r, t, ndigits * 2) >= 0)
570	vli_sub(r, r, t, ndigits * 2);
571	vli_set(dest: result, src: r, ndigits);
572	}
573
574	/*
575	* Computes result = product % mod
576	* for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
577	* where k-1 does not fit into qword boundary by -1 bit (such as 255).
578
579	* References (loosely based on):
580	* A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
581	* 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
582	* URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
583	*
584	* H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
585	* Handbook of Elliptic and Hyperelliptic Curve Cryptography.
586	* Algorithm 10.25 Fast reduction for special form moduli
587	*/
588	static void vli_mmod_special2(u64 *result, const u64 *product,
589	const u64 *mod, unsigned int ndigits)
590	{
591	u64 c2 = mod[0] * 2;
592	u64 q[ECC_MAX_DIGITS];
593	u64 r[ECC_MAX_DIGITS * 2];
594	u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
595	int carry; /* last bit that doesn't fit into q */
596	int i;
597
598	vli_set(dest: m, src: mod, ndigits);
599	vli_clear(vli: m + ndigits, ndigits);
600
601	vli_set(dest: r, src: product, ndigits);
602	/* q and carry are top bits */
603	vli_set(dest: q, src: product + ndigits, ndigits);
604	vli_clear(vli: r + ndigits, ndigits);
605	carry = vli_is_negative(vli: r, ndigits);
606	if (carry)
607	r[ndigits - 1] &= (1ull << 63) - 1;
608	for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
609	u64 qc[ECC_MAX_DIGITS * 2];
610
611	vli_umult(result: qc, left: q, right: c2, ndigits);
612	if (carry)
613	vli_uadd(result: qc, left: qc, right: mod[0], ndigits: ndigits * 2);
614	vli_set(dest: q, src: qc + ndigits, ndigits);
615	vli_clear(vli: qc + ndigits, ndigits);
616	carry = vli_is_negative(vli: qc, ndigits);
617	if (carry)
618	qc[ndigits - 1] &= (1ull << 63) - 1;
619	if (i & 1)
620	vli_sub(r, r, qc, ndigits * 2);
621	else
622	vli_add(result: r, left: r, right: qc, ndigits: ndigits * 2);
623	}
624	while (vli_is_negative(vli: r, ndigits: ndigits * 2))
625	vli_add(result: r, left: r, right: m, ndigits: ndigits * 2);
626	while (vli_cmp(r, m, ndigits * 2) >= 0)
627	vli_sub(r, r, m, ndigits * 2);
628
629	vli_set(dest: result, src: r, ndigits);
630	}
631
632	/*
633	* Computes result = product % mod, where product is 2N words long.
634	* Reference: Ken MacKay's micro-ecc.
635	* Currently only designed to work for curve_p or curve_n.
636	*/
637	static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
638	unsigned int ndigits)
639	{
640	u64 mod_m[2 * ECC_MAX_DIGITS];
641	u64 tmp[2 * ECC_MAX_DIGITS];
642	u64 *v[2] = { tmp, product };
643	u64 carry = 0;
644	unsigned int i;
645	/* Shift mod so its highest set bit is at the maximum position. */
646	int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
647	int word_shift = shift / 64;
648	int bit_shift = shift % 64;
649
650	vli_clear(vli: mod_m, ndigits: word_shift);
651	if (bit_shift > 0) {
652	for (i = 0; i < ndigits; ++i) {
653	mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
654	carry = mod[i] >> (64 - bit_shift);
655	}
656	} else
657	vli_set(dest: mod_m + word_shift, src: mod, ndigits);
658
659	for (i = 1; shift >= 0; --shift) {
660	u64 borrow = 0;
661	unsigned int j;
662
663	for (j = 0; j < ndigits * 2; ++j) {
664	u64 diff = v[i][j] - mod_m[j] - borrow;
665
666	if (diff != v[i][j])
667	borrow = (diff > v[i][j]);
668	v[1 - i][j] = diff;
669	}
670	i = !(i ^ borrow); /* Swap the index if there was no borrow */
671	vli_rshift1(vli: mod_m, ndigits);
672	mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
673	vli_rshift1(vli: mod_m + ndigits, ndigits);
674	}
675	vli_set(dest: result, src: v[i], ndigits);
676	}
677
678	/* Computes result = product % mod using Barrett's reduction with precomputed
679	* value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
680	* length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
681	* boundary.
682	*
683	* Reference:
684	* R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
685	* 2.4.1 Barrett's algorithm. Algorithm 2.5.
686	*/
687	static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
688	unsigned int ndigits)
689	{
690	u64 q[ECC_MAX_DIGITS * 2];
691	u64 r[ECC_MAX_DIGITS * 2];
692	const u64 *mu = mod + ndigits;
693
694	vli_mult(result: q, left: product + ndigits, right: mu, ndigits);
695	if (mu[ndigits])
696	vli_add(result: q + ndigits, left: q + ndigits, right: product + ndigits, ndigits);
697	vli_mult(result: r, left: mod, right: q + ndigits, ndigits);
698	vli_sub(r, product, r, ndigits * 2);
699	while (!vli_is_zero(r + ndigits, ndigits) ||
700	vli_cmp(r, mod, ndigits) != -1) {
701	u64 carry;
702
703	carry = vli_sub(r, r, mod, ndigits);
704	vli_usub(result: r + ndigits, left: r + ndigits, right: carry, ndigits);
705	}
706	vli_set(dest: result, src: r, ndigits);
707	}
708
709	/* Computes p_result = p_product % curve_p.
710	* See algorithm 5 and 6 from
711	* http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
712	*/
713	static void vli_mmod_fast_192(u64 *result, const u64 *product,
714	const u64 *curve_prime, u64 *tmp)
715	{
716	const unsigned int ndigits = ECC_CURVE_NIST_P192_DIGITS;
717	int carry;
718
719	vli_set(dest: result, src: product, ndigits);
720
721	vli_set(dest: tmp, src: &product[3], ndigits);
722	carry = vli_add(result, left: result, right: tmp, ndigits);
723
724	tmp[0] = 0;
725	tmp[1] = product[3];
726	tmp[2] = product[4];
727	carry += vli_add(result, left: result, right: tmp, ndigits);
728
729	tmp[0] = tmp[1] = product[5];
730	tmp[2] = 0;
731	carry += vli_add(result, left: result, right: tmp, ndigits);
732
733	while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
734	carry -= vli_sub(result, result, curve_prime, ndigits);
735	}
736
737	/* Computes result = product % curve_prime
738	* from http://www.nsa.gov/ia/_files/nist-routines.pdf
739	*/
740	static void vli_mmod_fast_256(u64 *result, const u64 *product,
741	const u64 *curve_prime, u64 *tmp)
742	{
743	int carry;
744	const unsigned int ndigits = ECC_CURVE_NIST_P256_DIGITS;
745
746	/* t */
747	vli_set(dest: result, src: product, ndigits);
748
749	/* s1 */
750	tmp[0] = 0;
751	tmp[1] = product[5] & 0xffffffff00000000ull;
752	tmp[2] = product[6];
753	tmp[3] = product[7];
754	carry = vli_lshift(result: tmp, in: tmp, shift: 1, ndigits);
755	carry += vli_add(result, left: result, right: tmp, ndigits);
756
757	/* s2 */
758	tmp[1] = product[6] << 32;
759	tmp[2] = (product[6] >> 32) | (product[7] << 32);
760	tmp[3] = product[7] >> 32;
761	carry += vli_lshift(result: tmp, in: tmp, shift: 1, ndigits);
762	carry += vli_add(result, left: result, right: tmp, ndigits);
763
764	/* s3 */
765	tmp[0] = product[4];
766	tmp[1] = product[5] & 0xffffffff;
767	tmp[2] = 0;
768	tmp[3] = product[7];
769	carry += vli_add(result, left: result, right: tmp, ndigits);
770
771	/* s4 */
772	tmp[0] = (product[4] >> 32) | (product[5] << 32);
773	tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
774	tmp[2] = product[7];
775	tmp[3] = (product[6] >> 32) | (product[4] << 32);
776	carry += vli_add(result, left: result, right: tmp, ndigits);
777
778	/* d1 */
779	tmp[0] = (product[5] >> 32) | (product[6] << 32);
780	tmp[1] = (product[6] >> 32);
781	tmp[2] = 0;
782	tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
783	carry -= vli_sub(result, result, tmp, ndigits);
784
785	/* d2 */
786	tmp[0] = product[6];
787	tmp[1] = product[7];
788	tmp[2] = 0;
789	tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
790	carry -= vli_sub(result, result, tmp, ndigits);
791
792	/* d3 */
793	tmp[0] = (product[6] >> 32) | (product[7] << 32);
794	tmp[1] = (product[7] >> 32) | (product[4] << 32);
795	tmp[2] = (product[4] >> 32) | (product[5] << 32);
796	tmp[3] = (product[6] << 32);
797	carry -= vli_sub(result, result, tmp, ndigits);
798
799	/* d4 */
800	tmp[0] = product[7];
801	tmp[1] = product[4] & 0xffffffff00000000ull;
802	tmp[2] = product[5];
803	tmp[3] = product[6] & 0xffffffff00000000ull;
804	carry -= vli_sub(result, result, tmp, ndigits);
805
806	if (carry < 0) {
807	do {
808	carry += vli_add(result, left: result, right: curve_prime, ndigits);
809	} while (carry < 0);
810	} else {
811	while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
812	carry -= vli_sub(result, result, curve_prime, ndigits);
813	}
814	}
815
816	#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
817	#define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
818	#define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
819
820	/* Computes result = product % curve_prime
821	* from "Mathematical routines for the NIST prime elliptic curves"
822	*/
823	static void vli_mmod_fast_384(u64 *result, const u64 *product,
824	const u64 *curve_prime, u64 *tmp)
825	{
826	int carry;
827	const unsigned int ndigits = ECC_CURVE_NIST_P384_DIGITS;
828
829	/* t */
830	vli_set(dest: result, src: product, ndigits);
831
832	/* s1 */
833	tmp[0] = 0; // 0 || 0
834	tmp[1] = 0; // 0 || 0
835	tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
836	tmp[3] = product[11]>>32; // 0 ||a23
837	tmp[4] = 0; // 0 || 0
838	tmp[5] = 0; // 0 || 0
839	carry = vli_lshift(result: tmp, in: tmp, shift: 1, ndigits);
840	carry += vli_add(result, left: result, right: tmp, ndigits);
841
842	/* s2 */
843	tmp[0] = product[6]; //a13||a12
844	tmp[1] = product[7]; //a15||a14
845	tmp[2] = product[8]; //a17||a16
846	tmp[3] = product[9]; //a19||a18
847	tmp[4] = product[10]; //a21||a20
848	tmp[5] = product[11]; //a23||a22
849	carry += vli_add(result, left: result, right: tmp, ndigits);
850
851	/* s3 */
852	tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
853	tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
854	tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13
855	tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
856	tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
857	tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
858	carry += vli_add(result, left: result, right: tmp, ndigits);
859
860	/* s4 */
861	tmp[0] = AND64H(product[11]); //a23|| 0
862	tmp[1] = (product[10]<<32); //a20|| 0
863	tmp[2] = product[6]; //a13||a12
864	tmp[3] = product[7]; //a15||a14
865	tmp[4] = product[8]; //a17||a16
866	tmp[5] = product[9]; //a19||a18
867	carry += vli_add(result, left: result, right: tmp, ndigits);
868
869	/* s5 */
870	tmp[0] = 0; // 0|| 0
871	tmp[1] = 0; // 0|| 0
872	tmp[2] = product[10]; //a21||a20
873	tmp[3] = product[11]; //a23||a22
874	tmp[4] = 0; // 0|| 0
875	tmp[5] = 0; // 0|| 0
876	carry += vli_add(result, left: result, right: tmp, ndigits);
877
878	/* s6 */
879	tmp[0] = AND64L(product[10]); // 0 ||a20
880	tmp[1] = AND64H(product[10]); //a21|| 0
881	tmp[2] = product[11]; //a23||a22
882	tmp[3] = 0; // 0 || 0
883	tmp[4] = 0; // 0 || 0
884	tmp[5] = 0; // 0 || 0
885	carry += vli_add(result, left: result, right: tmp, ndigits);
886
887	/* d1 */
888	tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
889	tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13
890	tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
891	tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
892	tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
893	tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
894	carry -= vli_sub(result, result, tmp, ndigits);
895
896	/* d2 */
897	tmp[0] = (product[10]<<32); //a20|| 0
898	tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
899	tmp[2] = (product[11]>>32); // 0 ||a23
900	tmp[3] = 0; // 0 || 0
901	tmp[4] = 0; // 0 || 0
902	tmp[5] = 0; // 0 || 0
903	carry -= vli_sub(result, result, tmp, ndigits);
904
905	/* d3 */
906	tmp[0] = 0; // 0 || 0
907	tmp[1] = AND64H(product[11]); //a23|| 0
908	tmp[2] = product[11]>>32; // 0 ||a23
909	tmp[3] = 0; // 0 || 0
910	tmp[4] = 0; // 0 || 0
911	tmp[5] = 0; // 0 || 0
912	carry -= vli_sub(result, result, tmp, ndigits);
913
914	if (carry < 0) {
915	do {
916	carry += vli_add(result, left: result, right: curve_prime, ndigits);
917	} while (carry < 0);
918	} else {
919	while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
920	carry -= vli_sub(result, result, curve_prime, ndigits);
921	}
922
923	}
924
925	#undef SL32OR32
926	#undef AND64H
927	#undef AND64L
928
929	/*
930	* Computes result = product % curve_prime
931	* from "Recommendations for Discrete Logarithm-Based Cryptography:
932	* Elliptic Curve Domain Parameters" section G.1.4
933	*/
934	static void vli_mmod_fast_521(u64 *result, const u64 *product,
935	const u64 *curve_prime, u64 *tmp)
936	{
937	const unsigned int ndigits = ECC_CURVE_NIST_P521_DIGITS;
938	size_t i;
939
940	/* Initialize result with lowest 521 bits from product */
941	vli_set(dest: result, src: product, ndigits);
942	result[8] &= 0x1ff;
943
944	for (i = 0; i < ndigits; i++)
945	tmp[i] = (product[8 + i] >> 9) | (product[9 + i] << 55);
946	tmp[8] &= 0x1ff;
947
948	vli_mod_add(result, left: result, right: tmp, mod: curve_prime, ndigits);
949	}
950
951	/* Computes result = product % curve_prime for different curve_primes.
952	*
953	* Note that curve_primes are distinguished just by heuristic check and
954	* not by complete conformance check.
955	*/
956	static bool vli_mmod_fast(u64 *result, u64 *product,
957	const struct ecc_curve *curve)
958	{
959	u64 tmp[2 * ECC_MAX_DIGITS];
960	const u64 *curve_prime = curve->p;
961	const unsigned int ndigits = curve->g.ndigits;
962
963	/* All NIST curves have name prefix 'nist_' */
964	if (strncmp(curve->name, "nist_", 5) != 0) {
965	/* Try to handle Pseudo-Marsenne primes. */
966	if (curve_prime[ndigits - 1] == -1ull) {
967	vli_mmod_special(result, product, mod: curve_prime,
968	ndigits);
969	return true;
970	} else if (curve_prime[ndigits - 1] == 1ull << 63 &&
971	curve_prime[ndigits - 2] == 0) {
972	vli_mmod_special2(result, product, mod: curve_prime,
973	ndigits);
974	return true;
975	}
976	vli_mmod_barrett(result, product, mod: curve_prime, ndigits);
977	return true;
978	}
979
980	switch (ndigits) {
981	case ECC_CURVE_NIST_P192_DIGITS:
982	vli_mmod_fast_192(result, product, curve_prime, tmp);
983	break;
984	case ECC_CURVE_NIST_P256_DIGITS:
985	vli_mmod_fast_256(result, product, curve_prime, tmp);
986	break;
987	case ECC_CURVE_NIST_P384_DIGITS:
988	vli_mmod_fast_384(result, product, curve_prime, tmp);
989	break;
990	case ECC_CURVE_NIST_P521_DIGITS:
991	vli_mmod_fast_521(result, product, curve_prime, tmp);
992	break;
993	default:
994	pr_err_ratelimited("ecc: unsupported digits size!\n");
995	return false;
996	}
997
998	return true;
999	}
1000
1001	/* Computes result = (left * right) % mod.
1002	* Assumes that mod is big enough curve order.
1003	*/
1004	void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
1005	const u64 *mod, unsigned int ndigits)
1006	{
1007	u64 product[ECC_MAX_DIGITS * 2];
1008
1009	vli_mult(result: product, left, right, ndigits);
1010	vli_mmod_slow(result, product, mod, ndigits);
1011	}
1012	EXPORT_SYMBOL(vli_mod_mult_slow);
1013
1014	/* Computes result = (left * right) % curve_prime. */
1015	static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
1016	const struct ecc_curve *curve)
1017	{
1018	u64 product[2 * ECC_MAX_DIGITS];
1019
1020	vli_mult(result: product, left, right, ndigits: curve->g.ndigits);
1021	vli_mmod_fast(result, product, curve);
1022	}
1023
1024	/* Computes result = left^2 % curve_prime. */
1025	static void vli_mod_square_fast(u64 *result, const u64 *left,
1026	const struct ecc_curve *curve)
1027	{
1028	u64 product[2 * ECC_MAX_DIGITS];
1029
1030	vli_square(result: product, left, ndigits: curve->g.ndigits);
1031	vli_mmod_fast(result, product, curve);
1032	}
1033
1034	#define EVEN(vli) (!(vli[0] & 1))
1035	/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
1036	* See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
1037	* https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
1038	*/
1039	void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
1040	unsigned int ndigits)
1041	{
1042	u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
1043	u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
1044	u64 carry;
1045	int cmp_result;
1046
1047	if (vli_is_zero(input, ndigits)) {
1048	vli_clear(vli: result, ndigits);
1049	return;
1050	}
1051
1052	vli_set(dest: a, src: input, ndigits);
1053	vli_set(dest: b, src: mod, ndigits);
1054	vli_clear(vli: u, ndigits);
1055	u[0] = 1;
1056	vli_clear(vli: v, ndigits);
1057
1058	while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
1059	carry = 0;
1060
1061	if (EVEN(a)) {
1062	vli_rshift1(vli: a, ndigits);
1063
1064	if (!EVEN(u))
1065	carry = vli_add(result: u, left: u, right: mod, ndigits);
1066
1067	vli_rshift1(vli: u, ndigits);
1068	if (carry)
1069	u[ndigits - 1] |= 0x8000000000000000ull;
1070	} else if (EVEN(b)) {
1071	vli_rshift1(vli: b, ndigits);
1072
1073	if (!EVEN(v))
1074	carry = vli_add(result: v, left: v, right: mod, ndigits);
1075
1076	vli_rshift1(vli: v, ndigits);
1077	if (carry)
1078	v[ndigits - 1] |= 0x8000000000000000ull;
1079	} else if (cmp_result > 0) {
1080	vli_sub(a, a, b, ndigits);
1081	vli_rshift1(vli: a, ndigits);
1082
1083	if (vli_cmp(u, v, ndigits) < 0)
1084	vli_add(result: u, left: u, right: mod, ndigits);
1085
1086	vli_sub(u, u, v, ndigits);
1087	if (!EVEN(u))
1088	carry = vli_add(result: u, left: u, right: mod, ndigits);
1089
1090	vli_rshift1(vli: u, ndigits);
1091	if (carry)
1092	u[ndigits - 1] |= 0x8000000000000000ull;
1093	} else {
1094	vli_sub(b, b, a, ndigits);
1095	vli_rshift1(vli: b, ndigits);
1096
1097	if (vli_cmp(v, u, ndigits) < 0)
1098	vli_add(result: v, left: v, right: mod, ndigits);
1099
1100	vli_sub(v, v, u, ndigits);
1101	if (!EVEN(v))
1102	carry = vli_add(result: v, left: v, right: mod, ndigits);
1103
1104	vli_rshift1(vli: v, ndigits);
1105	if (carry)
1106	v[ndigits - 1] |= 0x8000000000000000ull;
1107	}
1108	}
1109
1110	vli_set(dest: result, src: u, ndigits);
1111	}
1112	EXPORT_SYMBOL(vli_mod_inv);
1113
1114	/* ------ Point operations ------ */
1115
1116	/* Returns true if p_point is the point at infinity, false otherwise. */
1117	bool ecc_point_is_zero(const struct ecc_point *point)
1118	{
1119	return (vli_is_zero(point->x, point->ndigits) &&
1120	vli_is_zero(point->y, point->ndigits));
1121	}
1122	EXPORT_SYMBOL(ecc_point_is_zero);
1123
1124	/* Point multiplication algorithm using Montgomery's ladder with co-Z
1125	* coordinates. From https://eprint.iacr.org/2011/338.pdf
1126	*/
1127
1128	/* Double in place */
1129	static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1130	const struct ecc_curve *curve)
1131	{
1132	/* t1 = x, t2 = y, t3 = z */
1133	u64 t4[ECC_MAX_DIGITS];
1134	u64 t5[ECC_MAX_DIGITS];
1135	const u64 *curve_prime = curve->p;
1136	const unsigned int ndigits = curve->g.ndigits;
1137
1138	if (vli_is_zero(z1, ndigits))
1139	return;
1140
1141	/* t4 = y1^2 */
1142	vli_mod_square_fast(result: t4, left: y1, curve);
1143	/* t5 = x1*y1^2 = A */
1144	vli_mod_mult_fast(result: t5, left: x1, right: t4, curve);
1145	/* t4 = y1^4 */
1146	vli_mod_square_fast(result: t4, left: t4, curve);
1147	/* t2 = y1*z1 = z3 */
1148	vli_mod_mult_fast(result: y1, left: y1, right: z1, curve);
1149	/* t3 = z1^2 */
1150	vli_mod_square_fast(result: z1, left: z1, curve);
1151
1152	/* t1 = x1 + z1^2 */
1153	vli_mod_add(result: x1, left: x1, right: z1, mod: curve_prime, ndigits);
1154	/* t3 = 2*z1^2 */
1155	vli_mod_add(result: z1, left: z1, right: z1, mod: curve_prime, ndigits);
1156	/* t3 = x1 - z1^2 */
1157	vli_mod_sub(result: z1, left: x1, right: z1, mod: curve_prime, ndigits);
1158	/* t1 = x1^2 - z1^4 */
1159	vli_mod_mult_fast(result: x1, left: x1, right: z1, curve);
1160
1161	/* t3 = 2*(x1^2 - z1^4) */
1162	vli_mod_add(result: z1, left: x1, right: x1, mod: curve_prime, ndigits);
1163	/* t1 = 3*(x1^2 - z1^4) */
1164	vli_mod_add(result: x1, left: x1, right: z1, mod: curve_prime, ndigits);
1165	if (vli_test_bit(vli: x1, bit: 0)) {
1166	u64 carry = vli_add(result: x1, left: x1, right: curve_prime, ndigits);
1167
1168	vli_rshift1(vli: x1, ndigits);
1169	x1[ndigits - 1] |= carry << 63;
1170	} else {
1171	vli_rshift1(vli: x1, ndigits);
1172	}
1173	/* t1 = 3/2*(x1^2 - z1^4) = B */
1174
1175	/* t3 = B^2 */
1176	vli_mod_square_fast(result: z1, left: x1, curve);
1177	/* t3 = B^2 - A */
1178	vli_mod_sub(result: z1, left: z1, right: t5, mod: curve_prime, ndigits);
1179	/* t3 = B^2 - 2A = x3 */
1180	vli_mod_sub(result: z1, left: z1, right: t5, mod: curve_prime, ndigits);
1181	/* t5 = A - x3 */
1182	vli_mod_sub(result: t5, left: t5, right: z1, mod: curve_prime, ndigits);
1183	/* t1 = B * (A - x3) */
1184	vli_mod_mult_fast(result: x1, left: x1, right: t5, curve);
1185	/* t4 = B * (A - x3) - y1^4 = y3 */
1186	vli_mod_sub(result: t4, left: x1, right: t4, mod: curve_prime, ndigits);
1187
1188	vli_set(dest: x1, src: z1, ndigits);
1189	vli_set(dest: z1, src: y1, ndigits);
1190	vli_set(dest: y1, src: t4, ndigits);
1191	}
1192
1193	/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1194	static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1195	{
1196	u64 t1[ECC_MAX_DIGITS];
1197
1198	vli_mod_square_fast(result: t1, left: z, curve); /* z^2 */
1199	vli_mod_mult_fast(result: x1, left: x1, right: t1, curve); /* x1 * z^2 */
1200	vli_mod_mult_fast(result: t1, left: t1, right: z, curve); /* z^3 */
1201	vli_mod_mult_fast(result: y1, left: y1, right: t1, curve); /* y1 * z^3 */
1202	}
1203
1204	/* P = (x1, y1) => 2P, (x2, y2) => P' */
1205	static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1206	u64 *p_initial_z, const struct ecc_curve *curve)
1207	{
1208	u64 z[ECC_MAX_DIGITS];
1209	const unsigned int ndigits = curve->g.ndigits;
1210
1211	vli_set(dest: x2, src: x1, ndigits);
1212	vli_set(dest: y2, src: y1, ndigits);
1213
1214	vli_clear(vli: z, ndigits);
1215	z[0] = 1;
1216
1217	if (p_initial_z)
1218	vli_set(dest: z, src: p_initial_z, ndigits);
1219
1220	apply_z(x1, y1, z, curve);
1221
1222	ecc_point_double_jacobian(x1, y1, z1: z, curve);
1223
1224	apply_z(x1: x2, y1: y2, z, curve);
1225	}
1226
1227	/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1228	* Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1229	* or P => P', Q => P + Q
1230	*/
1231	static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1232	const struct ecc_curve *curve)
1233	{
1234	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1235	u64 t5[ECC_MAX_DIGITS];
1236	const u64 *curve_prime = curve->p;
1237	const unsigned int ndigits = curve->g.ndigits;
1238
1239	/* t5 = x2 - x1 */
1240	vli_mod_sub(result: t5, left: x2, right: x1, mod: curve_prime, ndigits);
1241	/* t5 = (x2 - x1)^2 = A */
1242	vli_mod_square_fast(result: t5, left: t5, curve);
1243	/* t1 = x1*A = B */
1244	vli_mod_mult_fast(result: x1, left: x1, right: t5, curve);
1245	/* t3 = x2*A = C */
1246	vli_mod_mult_fast(result: x2, left: x2, right: t5, curve);
1247	/* t4 = y2 - y1 */
1248	vli_mod_sub(result: y2, left: y2, right: y1, mod: curve_prime, ndigits);
1249	/* t5 = (y2 - y1)^2 = D */
1250	vli_mod_square_fast(result: t5, left: y2, curve);
1251
1252	/* t5 = D - B */
1253	vli_mod_sub(result: t5, left: t5, right: x1, mod: curve_prime, ndigits);
1254	/* t5 = D - B - C = x3 */
1255	vli_mod_sub(result: t5, left: t5, right: x2, mod: curve_prime, ndigits);
1256	/* t3 = C - B */
1257	vli_mod_sub(result: x2, left: x2, right: x1, mod: curve_prime, ndigits);
1258	/* t2 = y1*(C - B) */
1259	vli_mod_mult_fast(result: y1, left: y1, right: x2, curve);
1260	/* t3 = B - x3 */
1261	vli_mod_sub(result: x2, left: x1, right: t5, mod: curve_prime, ndigits);
1262	/* t4 = (y2 - y1)*(B - x3) */
1263	vli_mod_mult_fast(result: y2, left: y2, right: x2, curve);
1264	/* t4 = y3 */
1265	vli_mod_sub(result: y2, left: y2, right: y1, mod: curve_prime, ndigits);
1266
1267	vli_set(dest: x2, src: t5, ndigits);
1268	}
1269
1270	/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1271	* Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1272	* or P => P - Q, Q => P + Q
1273	*/
1274	static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1275	const struct ecc_curve *curve)
1276	{
1277	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1278	u64 t5[ECC_MAX_DIGITS];
1279	u64 t6[ECC_MAX_DIGITS];
1280	u64 t7[ECC_MAX_DIGITS];
1281	const u64 *curve_prime = curve->p;
1282	const unsigned int ndigits = curve->g.ndigits;
1283
1284	/* t5 = x2 - x1 */
1285	vli_mod_sub(result: t5, left: x2, right: x1, mod: curve_prime, ndigits);
1286	/* t5 = (x2 - x1)^2 = A */
1287	vli_mod_square_fast(result: t5, left: t5, curve);
1288	/* t1 = x1*A = B */
1289	vli_mod_mult_fast(result: x1, left: x1, right: t5, curve);
1290	/* t3 = x2*A = C */
1291	vli_mod_mult_fast(result: x2, left: x2, right: t5, curve);
1292	/* t4 = y2 + y1 */
1293	vli_mod_add(result: t5, left: y2, right: y1, mod: curve_prime, ndigits);
1294	/* t4 = y2 - y1 */
1295	vli_mod_sub(result: y2, left: y2, right: y1, mod: curve_prime, ndigits);
1296
1297	/* t6 = C - B */
1298	vli_mod_sub(result: t6, left: x2, right: x1, mod: curve_prime, ndigits);
1299	/* t2 = y1 * (C - B) */
1300	vli_mod_mult_fast(result: y1, left: y1, right: t6, curve);
1301	/* t6 = B + C */
1302	vli_mod_add(result: t6, left: x1, right: x2, mod: curve_prime, ndigits);
1303	/* t3 = (y2 - y1)^2 */
1304	vli_mod_square_fast(result: x2, left: y2, curve);
1305	/* t3 = x3 */
1306	vli_mod_sub(result: x2, left: x2, right: t6, mod: curve_prime, ndigits);
1307
1308	/* t7 = B - x3 */
1309	vli_mod_sub(result: t7, left: x1, right: x2, mod: curve_prime, ndigits);
1310	/* t4 = (y2 - y1)*(B - x3) */
1311	vli_mod_mult_fast(result: y2, left: y2, right: t7, curve);
1312	/* t4 = y3 */
1313	vli_mod_sub(result: y2, left: y2, right: y1, mod: curve_prime, ndigits);
1314
1315	/* t7 = (y2 + y1)^2 = F */
1316	vli_mod_square_fast(result: t7, left: t5, curve);
1317	/* t7 = x3' */
1318	vli_mod_sub(result: t7, left: t7, right: t6, mod: curve_prime, ndigits);
1319	/* t6 = x3' - B */
1320	vli_mod_sub(result: t6, left: t7, right: x1, mod: curve_prime, ndigits);
1321	/* t6 = (y2 + y1)*(x3' - B) */
1322	vli_mod_mult_fast(result: t6, left: t6, right: t5, curve);
1323	/* t2 = y3' */
1324	vli_mod_sub(result: y1, left: t6, right: y1, mod: curve_prime, ndigits);
1325
1326	vli_set(dest: x1, src: t7, ndigits);
1327	}
1328
1329	static void ecc_point_mult(struct ecc_point *result,
1330	const struct ecc_point *point, const u64 *scalar,
1331	u64 *initial_z, const struct ecc_curve *curve,
1332	unsigned int ndigits)
1333	{
1334	/* R0 and R1 */
1335	u64 rx[2][ECC_MAX_DIGITS];
1336	u64 ry[2][ECC_MAX_DIGITS];
1337	u64 z[ECC_MAX_DIGITS];
1338	u64 sk[2][ECC_MAX_DIGITS];
1339	u64 *curve_prime = curve->p;
1340	int i, nb;
1341	int num_bits;
1342	int carry;
1343
1344	carry = vli_add(result: sk[0], left: scalar, right: curve->n, ndigits);
1345	vli_add(result: sk[1], left: sk[0], right: curve->n, ndigits);
1346	scalar = sk[!carry];
1347	if (curve->nbits == 521) /* NIST P521 */
1348	num_bits = curve->nbits + 2;
1349	else
1350	num_bits = sizeof(u64) * ndigits * 8 + 1;
1351
1352	vli_set(dest: rx[1], src: point->x, ndigits);
1353	vli_set(dest: ry[1], src: point->y, ndigits);
1354
1355	xycz_initial_double(x1: rx[1], y1: ry[1], x2: rx[0], y2: ry[0], p_initial_z: initial_z, curve);
1356
1357	for (i = num_bits - 2; i > 0; i--) {
1358	nb = !vli_test_bit(vli: scalar, bit: i);
1359	xycz_add_c(x1: rx[1 - nb], y1: ry[1 - nb], x2: rx[nb], y2: ry[nb], curve);
1360	xycz_add(x1: rx[nb], y1: ry[nb], x2: rx[1 - nb], y2: ry[1 - nb], curve);
1361	}
1362
1363	nb = !vli_test_bit(vli: scalar, bit: 0);
1364	xycz_add_c(x1: rx[1 - nb], y1: ry[1 - nb], x2: rx[nb], y2: ry[nb], curve);
1365
1366	/* Find final 1/Z value. */
1367	/* X1 - X0 */
1368	vli_mod_sub(result: z, left: rx[1], right: rx[0], mod: curve_prime, ndigits);
1369	/* Yb * (X1 - X0) */
1370	vli_mod_mult_fast(result: z, left: z, right: ry[1 - nb], curve);
1371	/* xP * Yb * (X1 - X0) */
1372	vli_mod_mult_fast(result: z, left: z, right: point->x, curve);
1373
1374	/* 1 / (xP * Yb * (X1 - X0)) */
1375	vli_mod_inv(z, z, curve_prime, point->ndigits);
1376
1377	/* yP / (xP * Yb * (X1 - X0)) */
1378	vli_mod_mult_fast(result: z, left: z, right: point->y, curve);
1379	/* Xb * yP / (xP * Yb * (X1 - X0)) */
1380	vli_mod_mult_fast(result: z, left: z, right: rx[1 - nb], curve);
1381	/* End 1/Z calculation */
1382
1383	xycz_add(x1: rx[nb], y1: ry[nb], x2: rx[1 - nb], y2: ry[1 - nb], curve);
1384
1385	apply_z(x1: rx[0], y1: ry[0], z, curve);
1386
1387	vli_set(dest: result->x, src: rx[0], ndigits);
1388	vli_set(dest: result->y, src: ry[0], ndigits);
1389	}
1390
1391	/* Computes R = P + Q mod p */
1392	static void ecc_point_add(const struct ecc_point *result,
1393	const struct ecc_point *p, const struct ecc_point *q,
1394	const struct ecc_curve *curve)
1395	{
1396	u64 z[ECC_MAX_DIGITS];
1397	u64 px[ECC_MAX_DIGITS];
1398	u64 py[ECC_MAX_DIGITS];
1399	unsigned int ndigits = curve->g.ndigits;
1400
1401	vli_set(dest: result->x, src: q->x, ndigits);
1402	vli_set(dest: result->y, src: q->y, ndigits);
1403	vli_mod_sub(result: z, left: result->x, right: p->x, mod: curve->p, ndigits);
1404	vli_set(dest: px, src: p->x, ndigits);
1405	vli_set(dest: py, src: p->y, ndigits);
1406	xycz_add(x1: px, y1: py, x2: result->x, y2: result->y, curve);
1407	vli_mod_inv(z, z, curve->p, ndigits);
1408	apply_z(x1: result->x, y1: result->y, z, curve);
1409	}
1410
1411	/* Computes R = u1P + u2Q mod p using Shamir's trick.
1412	* Based on: Kenneth MacKay's micro-ecc (2014).
1413	*/
1414	void ecc_point_mult_shamir(const struct ecc_point *result,
1415	const u64 *u1, const struct ecc_point *p,
1416	const u64 *u2, const struct ecc_point *q,
1417	const struct ecc_curve *curve)
1418	{
1419	u64 z[ECC_MAX_DIGITS];
1420	u64 sump[2][ECC_MAX_DIGITS];
1421	u64 *rx = result->x;
1422	u64 *ry = result->y;
1423	unsigned int ndigits = curve->g.ndigits;
1424	unsigned int num_bits;
1425	struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1426	const struct ecc_point *points[4];
1427	const struct ecc_point *point;
1428	unsigned int idx;
1429	int i;
1430
1431	ecc_point_add(result: &sum, p, q, curve);
1432	points[0] = NULL;
1433	points[1] = p;
1434	points[2] = q;
1435	points[3] = &sum;
1436
1437	num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1438	i = num_bits - 1;
1439	idx = !!vli_test_bit(vli: u1, bit: i);
1440	idx |= (!!vli_test_bit(vli: u2, bit: i)) << 1;
1441	point = points[idx];
1442
1443	vli_set(dest: rx, src: point->x, ndigits);
1444	vli_set(dest: ry, src: point->y, ndigits);
1445	vli_clear(vli: z + 1, ndigits: ndigits - 1);
1446	z[0] = 1;
1447
1448	for (--i; i >= 0; i--) {
1449	ecc_point_double_jacobian(x1: rx, y1: ry, z1: z, curve);
1450	idx = !!vli_test_bit(vli: u1, bit: i);
1451	idx |= (!!vli_test_bit(vli: u2, bit: i)) << 1;
1452	point = points[idx];
1453	if (point) {
1454	u64 tx[ECC_MAX_DIGITS];
1455	u64 ty[ECC_MAX_DIGITS];
1456	u64 tz[ECC_MAX_DIGITS];
1457
1458	vli_set(dest: tx, src: point->x, ndigits);
1459	vli_set(dest: ty, src: point->y, ndigits);
1460	apply_z(x1: tx, y1: ty, z, curve);
1461	vli_mod_sub(result: tz, left: rx, right: tx, mod: curve->p, ndigits);
1462	xycz_add(x1: tx, y1: ty, x2: rx, y2: ry, curve);
1463	vli_mod_mult_fast(result: z, left: z, right: tz, curve);
1464	}
1465	}
1466	vli_mod_inv(z, z, curve->p, ndigits);
1467	apply_z(x1: rx, y1: ry, z, curve);
1468	}
1469	EXPORT_SYMBOL(ecc_point_mult_shamir);
1470
1471	/*
1472	* This function performs checks equivalent to Appendix A.4.2 of FIPS 186-5.
1473	* Whereas A.4.2 results in an integer in the interval [1, n-1], this function
1474	* ensures that the integer is in the range of [2, n-3]. We are slightly
1475	* stricter because of the currently used scalar multiplication algorithm.
1476	*/
1477	static int __ecc_is_key_valid(const struct ecc_curve *curve,
1478	const u64 *private_key, unsigned int ndigits)
1479	{
1480	u64 one[ECC_MAX_DIGITS] = { 1, };
1481	u64 res[ECC_MAX_DIGITS];
1482
1483	if (!private_key)
1484	return -EINVAL;
1485
1486	if (curve->g.ndigits != ndigits)
1487	return -EINVAL;
1488
1489	/* Make sure the private key is in the range [2, n-3]. */
1490	if (vli_cmp(one, private_key, ndigits) != -1)
1491	return -EINVAL;
1492	vli_sub(res, curve->n, one, ndigits);
1493	vli_sub(res, res, one, ndigits);
1494	if (vli_cmp(res, private_key, ndigits) != 1)
1495	return -EINVAL;
1496
1497	return 0;
1498	}
1499
1500	int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1501	const u64 *private_key, unsigned int private_key_len)
1502	{
1503	int nbytes;
1504	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1505
1506	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1507
1508	if (private_key_len != nbytes)
1509	return -EINVAL;
1510
1511	return __ecc_is_key_valid(curve, private_key, ndigits);
1512	}
1513	EXPORT_SYMBOL(ecc_is_key_valid);
1514
1515	/*
1516	* ECC private keys are generated using the method of rejection sampling,
1517	* equivalent to that described in FIPS 186-5, Appendix A.2.2.
1518	*
1519	* This method generates a private key uniformly distributed in the range
1520	* [2, n-3].
1521	*/
1522	int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits,
1523	u64 *private_key)
1524	{
1525	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1526	unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1527	unsigned int nbits = vli_num_bits(curve->n, ndigits);
1528	int err;
1529
1530	/*
1531	* Step 1 & 2: check that N is included in Table 1 of FIPS 186-5,
1532	* section 6.1.1.
1533	*/
1534	if (nbits < 224)
1535	return -EINVAL;
1536
1537	/*
1538	* FIPS 186-5 recommends that the private key should be obtained from a
1539	* RBG with a security strength equal to or greater than the security
1540	* strength associated with N.
1541	*
1542	* The maximum security strength identified by NIST SP800-57pt1r4 for
1543	* ECC is 256 (N >= 512).
1544	*
1545	* This condition is met by the default RNG because it selects a favored
1546	* DRBG with a security strength of 256.
1547	*/
1548	if (crypto_get_default_rng())
1549	return -EFAULT;
1550
1551	/* Step 3: obtain N returned_bits from the DRBG. */
1552	err = crypto_rng_get_bytes(tfm: crypto_default_rng,
1553	rdata: (u8 *)private_key, dlen: nbytes);
1554	crypto_put_default_rng();
1555	if (err)
1556	return err;
1557
1558	/* Step 4: make sure the private key is in the valid range. */
1559	if (__ecc_is_key_valid(curve, private_key, ndigits))
1560	return -EINVAL;
1561
1562	return 0;
1563	}
1564	EXPORT_SYMBOL(ecc_gen_privkey);
1565
1566	int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1567	const u64 *private_key, u64 *public_key)
1568	{
1569	int ret = 0;
1570	struct ecc_point *pk;
1571	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1572
1573	if (!private_key) {
1574	ret = -EINVAL;
1575	goto out;
1576	}
1577
1578	pk = ecc_alloc_point(ndigits);
1579	if (!pk) {
1580	ret = -ENOMEM;
1581	goto out;
1582	}
1583
1584	ecc_point_mult(result: pk, point: &curve->g, scalar: private_key, NULL, curve, ndigits);
1585
1586	/* SP800-56A rev 3 5.6.2.1.3 key check */
1587	if (ecc_is_pubkey_valid_full(curve, pk)) {
1588	ret = -EAGAIN;
1589	goto err_free_point;
1590	}
1591
1592	ecc_swap_digits(in: pk->x, out: public_key, ndigits);
1593	ecc_swap_digits(in: pk->y, out: &public_key[ndigits], ndigits);
1594
1595	err_free_point:
1596	ecc_free_point(pk);
1597	out:
1598	return ret;
1599	}
1600	EXPORT_SYMBOL(ecc_make_pub_key);
1601
1602	/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1603	int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1604	struct ecc_point *pk)
1605	{
1606	u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1607
1608	if (WARN_ON(pk->ndigits != curve->g.ndigits))
1609	return -EINVAL;
1610
1611	/* Check 1: Verify key is not the zero point. */
1612	if (ecc_point_is_zero(pk))
1613	return -EINVAL;
1614
1615	/* Check 2: Verify key is in the range [1, p-1]. */
1616	if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1617	return -EINVAL;
1618	if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1619	return -EINVAL;
1620
1621	/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1622	vli_mod_square_fast(result: yy, left: pk->y, curve); /* y^2 */
1623	vli_mod_square_fast(result: xxx, left: pk->x, curve); /* x^2 */
1624	vli_mod_mult_fast(result: xxx, left: xxx, right: pk->x, curve); /* x^3 */
1625	vli_mod_mult_fast(result: w, left: curve->a, right: pk->x, curve); /* a·x */
1626	vli_mod_add(result: w, left: w, right: curve->b, mod: curve->p, ndigits: pk->ndigits); /* a·x + b */
1627	vli_mod_add(result: w, left: w, right: xxx, mod: curve->p, ndigits: pk->ndigits); /* x^3 + a·x + b */
1628	if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1629	return -EINVAL;
1630
1631	return 0;
1632	}
1633	EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1634
1635	/* SP800-56A section 5.6.2.3.3 full verification */
1636	int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
1637	struct ecc_point *pk)
1638	{
1639	struct ecc_point *nQ;
1640
1641	/* Checks 1 through 3 */
1642	int ret = ecc_is_pubkey_valid_partial(curve, pk);
1643
1644	if (ret)
1645	return ret;
1646
1647	/* Check 4: Verify that nQ is the zero point. */
1648	nQ = ecc_alloc_point(pk->ndigits);
1649	if (!nQ)
1650	return -ENOMEM;
1651
1652	ecc_point_mult(result: nQ, point: pk, scalar: curve->n, NULL, curve, ndigits: pk->ndigits);
1653	if (!ecc_point_is_zero(nQ))
1654	ret = -EINVAL;
1655
1656	ecc_free_point(nQ);
1657
1658	return ret;
1659	}
1660	EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
1661
1662	int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1663	const u64 *private_key, const u64 *public_key,
1664	u64 *secret)
1665	{
1666	int ret = 0;
1667	struct ecc_point *product, *pk;
1668	u64 rand_z[ECC_MAX_DIGITS];
1669	unsigned int nbytes;
1670	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1671
1672	if (!private_key || !public_key || ndigits > ARRAY_SIZE(rand_z)) {
1673	ret = -EINVAL;
1674	goto out;
1675	}
1676
1677	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1678
1679	get_random_bytes(buf: rand_z, len: nbytes);
1680
1681	pk = ecc_alloc_point(ndigits);
1682	if (!pk) {
1683	ret = -ENOMEM;
1684	goto out;
1685	}
1686
1687	ecc_swap_digits(in: public_key, out: pk->x, ndigits);
1688	ecc_swap_digits(in: &public_key[ndigits], out: pk->y, ndigits);
1689	ret = ecc_is_pubkey_valid_partial(curve, pk);
1690	if (ret)
1691	goto err_alloc_product;
1692
1693	product = ecc_alloc_point(ndigits);
1694	if (!product) {
1695	ret = -ENOMEM;
1696	goto err_alloc_product;
1697	}
1698
1699	ecc_point_mult(result: product, point: pk, scalar: private_key, initial_z: rand_z, curve, ndigits);
1700
1701	if (ecc_point_is_zero(product)) {
1702	ret = -EFAULT;
1703	goto err_validity;
1704	}
1705
1706	ecc_swap_digits(in: product->x, out: secret, ndigits);
1707
1708	err_validity:
1709	memzero_explicit(s: rand_z, count: sizeof(rand_z));
1710	ecc_free_point(product);
1711	err_alloc_product:
1712	ecc_free_point(pk);
1713	out:
1714	return ret;
1715	}
1716	EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1717
1718	MODULE_DESCRIPTION("core elliptic curve module");
1719	MODULE_LICENSE("Dual BSD/GPL");
1720