1/*
2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25#include "inner.h"
26
27#if BR_INT128 || BR_UMUL128
28
29#if BR_INT128
30
31/*
32 * Compute x*y+v1+v2. Operands are 64-bit, and result is 128-bit, with
33 * high word in "hi" and low word in "lo".
34 */
35#define FMA1(hi, lo, x, y, v1, v2)   do { \
36		unsigned __int128 fmaz; \
37		fmaz = (unsigned __int128)(x) * (unsigned __int128)(y) \
38			+ (unsigned __int128)(v1) + (unsigned __int128)(v2); \
39		(hi) = (uint64_t)(fmaz >> 64); \
40		(lo) = (uint64_t)fmaz; \
41	} while (0)
42
43/*
44 * Compute x1*y1+x2*y2+v1+v2. Operands are 64-bit, and result is 128-bit,
45 * with high word in "hi" and low word in "lo".
46 *
47 * Callers should ensure that the two inner products, and the v1 and v2
48 * operands, are multiple of 4 (this is not used by this specific definition
49 * but may help other implementations).
50 */
51#define FMA2(hi, lo, x1, y1, x2, y2, v1, v2)   do { \
52		unsigned __int128 fmaz; \
53		fmaz = (unsigned __int128)(x1) * (unsigned __int128)(y1) \
54			+ (unsigned __int128)(x2) * (unsigned __int128)(y2) \
55			+ (unsigned __int128)(v1) + (unsigned __int128)(v2); \
56		(hi) = (uint64_t)(fmaz >> 64); \
57		(lo) = (uint64_t)fmaz; \
58	} while (0)
59
60#elif BR_UMUL128
61
62#include <intrin.h>
63
64#define FMA1(hi, lo, x, y, v1, v2)   do { \
65		uint64_t fmahi, fmalo; \
66		unsigned char fmacc; \
67		fmalo = _umul128((x), (y), &fmahi); \
68		fmacc = _addcarry_u64(0, fmalo, (v1), &fmalo); \
69		_addcarry_u64(fmacc, fmahi, 0, &fmahi); \
70		fmacc = _addcarry_u64(0, fmalo, (v2), &(lo)); \
71		_addcarry_u64(fmacc, fmahi, 0, &(hi)); \
72	} while (0)
73
74/*
75 * Normally we should use _addcarry_u64() for FMA2 too, but it makes
76 * Visual Studio crash. Instead we use this version, which leverages
77 * the fact that the vx operands, and the products, are multiple of 4.
78 * This is unfortunately slower.
79 */
80#define FMA2(hi, lo, x1, y1, x2, y2, v1, v2)   do { \
81		uint64_t fma1hi, fma1lo; \
82		uint64_t fma2hi, fma2lo; \
83		uint64_t fmatt; \
84		fma1lo = _umul128((x1), (y1), &fma1hi); \
85		fma2lo = _umul128((x2), (y2), &fma2hi); \
86		fmatt = (fma1lo >> 2) + (fma2lo >> 2) \
87			+ ((v1) >> 2) + ((v2) >> 2); \
88		(lo) = fmatt << 2; \
89		(hi) = fma1hi + fma2hi + (fmatt >> 62); \
90	} while (0)
91
92/*
93 * The FMA2 macro definition we would prefer to use, but it triggers
94 * an internal compiler error in Visual Studio 2015.
95 *
96#define FMA2(hi, lo, x1, y1, x2, y2, v1, v2)   do { \
97		uint64_t fma1hi, fma1lo; \
98		uint64_t fma2hi, fma2lo; \
99		unsigned char fmacc; \
100		fma1lo = _umul128((x1), (y1), &fma1hi); \
101		fma2lo = _umul128((x2), (y2), &fma2hi); \
102		fmacc = _addcarry_u64(0, fma1lo, (v1), &fma1lo); \
103		_addcarry_u64(fmacc, fma1hi, 0, &fma1hi); \
104		fmacc = _addcarry_u64(0, fma2lo, (v2), &fma2lo); \
105		_addcarry_u64(fmacc, fma2hi, 0, &fma2hi); \
106		fmacc = _addcarry_u64(0, fma1lo, fma2lo, &(lo)); \
107		_addcarry_u64(fmacc, fma1hi, fma2hi, &(hi)); \
108	} while (0)
109 */
110
111#endif
112
113#define MASK62           ((uint64_t)0x3FFFFFFFFFFFFFFF)
114#define MUL62_lo(x, y)   (((uint64_t)(x) * (uint64_t)(y)) & MASK62)
115
116/*
117 * Subtract b from a, and return the final carry. If 'ctl32' is 0, then
118 * a[] is kept unmodified, but the final carry is still computed and
119 * returned.
120 */
121static uint32_t
122i62_sub(uint64_t *a, const uint64_t *b, size_t num, uint32_t ctl32)
123{
124	uint64_t cc, mask;
125	size_t u;
126
127	cc = 0;
128	ctl32 = -ctl32;
129	mask = (uint64_t)ctl32 | ((uint64_t)ctl32 << 32);
130	for (u = 0; u < num; u ++) {
131		uint64_t aw, bw, dw;
132
133		aw = a[u];
134		bw = b[u];
135		dw = aw - bw - cc;
136		cc = dw >> 63;
137		dw &= MASK62;
138		a[u] = aw ^ (mask & (dw ^ aw));
139	}
140	return (uint32_t)cc;
141}
142
143/*
144 * Montgomery multiplication, over arrays of 62-bit values. The
145 * destination array (d) must be distinct from the other operands
146 * (x, y and m). All arrays are in little-endian format (least
147 * significant word comes first) over 'num' words.
148 */
149static void
150montymul(uint64_t *d, const uint64_t *x, const uint64_t *y,
151	const uint64_t *m, size_t num, uint64_t m0i)
152{
153	uint64_t dh;
154	size_t u, num4;
155
156	num4 = 1 + ((num - 1) & ~(size_t)3);
157	memset(d, 0, num * sizeof *d);
158	dh = 0;
159	for (u = 0; u < num; u ++) {
160		size_t v;
161		uint64_t f, xu;
162		uint64_t r, zh;
163		uint64_t hi, lo;
164
165		xu = x[u] << 2;
166		f = MUL62_lo(d[0] + MUL62_lo(x[u], y[0]), m0i) << 2;
167
168		FMA2(hi, lo, xu, y[0], f, m[0], d[0] << 2, 0);
169		r = hi;
170
171		for (v = 1; v < num4; v += 4) {
172			FMA2(hi, lo, xu, y[v + 0],
173				f, m[v + 0], d[v + 0] << 2, r << 2);
174			r = hi + (r >> 62);
175			d[v - 1] = lo >> 2;
176			FMA2(hi, lo, xu, y[v + 1],
177				f, m[v + 1], d[v + 1] << 2, r << 2);
178			r = hi + (r >> 62);
179			d[v + 0] = lo >> 2;
180			FMA2(hi, lo, xu, y[v + 2],
181				f, m[v + 2], d[v + 2] << 2, r << 2);
182			r = hi + (r >> 62);
183			d[v + 1] = lo >> 2;
184			FMA2(hi, lo, xu, y[v + 3],
185				f, m[v + 3], d[v + 3] << 2, r << 2);
186			r = hi + (r >> 62);
187			d[v + 2] = lo >> 2;
188		}
189		for (; v < num; v ++) {
190			FMA2(hi, lo, xu, y[v], f, m[v], d[v] << 2, r << 2);
191			r = hi + (r >> 62);
192			d[v - 1] = lo >> 2;
193		}
194
195		zh = dh + r;
196		d[num - 1] = zh & MASK62;
197		dh = zh >> 62;
198	}
199	i62_sub(d, m, num, (uint32_t)dh | NOT(i62_sub(d, m, num, 0)));
200}
201
202/*
203 * Conversion back from Montgomery representation.
204 */
205static void
206frommonty(uint64_t *x, const uint64_t *m, size_t num, uint64_t m0i)
207{
208	size_t u, v;
209
210	for (u = 0; u < num; u ++) {
211		uint64_t f, cc;
212
213		f = MUL62_lo(x[0], m0i) << 2;
214		cc = 0;
215		for (v = 0; v < num; v ++) {
216			uint64_t hi, lo;
217
218			FMA1(hi, lo, f, m[v], x[v] << 2, cc);
219			cc = hi << 2;
220			if (v != 0) {
221				x[v - 1] = lo >> 2;
222			}
223		}
224		x[num - 1] = cc >> 2;
225	}
226	i62_sub(x, m, num, NOT(i62_sub(x, m, num, 0)));
227}
228
229/* see inner.h */
230uint32_t
231br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
232	const uint32_t *m31, uint32_t m0i31, uint64_t *tmp, size_t twlen)
233{
234	size_t u, mw31num, mw62num;
235	uint64_t *x, *m, *t1, *t2;
236	uint64_t m0i;
237	uint32_t acc;
238	int win_len, acc_len;
239
240	/*
241	 * Get modulus size, in words.
242	 */
243	mw31num = (m31[0] + 31) >> 5;
244	mw62num = (mw31num + 1) >> 1;
245
246	/*
247	 * In order to apply this function, we must have enough room to
248	 * copy the operand and modulus into the temporary array, along
249	 * with at least two temporaries. If there is not enough room,
250	 * switch to br_i31_modpow(). We also use br_i31_modpow() if the
251	 * modulus length is not at least four words (94 bits or more).
252	 */
253	if (mw31num < 4 || (mw62num << 2) > twlen) {
254		/*
255		 * We assume here that we can split an aligned uint64_t
256		 * into two properly aligned uint32_t. Since both types
257		 * are supposed to have an exact width with no padding,
258		 * then this property must hold.
259		 */
260		size_t txlen;
261
262		txlen = mw31num + 1;
263		if (twlen < txlen) {
264			return 0;
265		}
266		br_i31_modpow(x31, e, elen, m31, m0i31,
267			(uint32_t *)tmp, (uint32_t *)tmp + txlen);
268		return 1;
269	}
270
271	/*
272	 * Convert x to Montgomery representation: this means that
273	 * we replace x with x*2^z mod m, where z is the smallest multiple
274	 * of the word size such that 2^z >= m. We want to reuse the 31-bit
275	 * functions here (for constant-time operation), but we need z
276	 * for a 62-bit word size.
277	 */
278	for (u = 0; u < mw62num; u ++) {
279		br_i31_muladd_small(x31, 0, m31);
280		br_i31_muladd_small(x31, 0, m31);
281	}
282
283	/*
284	 * Assemble operands into arrays of 62-bit words. Note that
285	 * all the arrays of 62-bit words that we will handle here
286	 * are without any leading size word.
287	 *
288	 * We also adjust tmp and twlen to account for the words used
289	 * for these extra arrays.
290	 */
291	m = tmp;
292	x = tmp + mw62num;
293	tmp += (mw62num << 1);
294	twlen -= (mw62num << 1);
295	for (u = 0; u < mw31num; u += 2) {
296		size_t v;
297
298		v = u >> 1;
299		if ((u + 1) == mw31num) {
300			m[v] = (uint64_t)m31[u + 1];
301			x[v] = (uint64_t)x31[u + 1];
302		} else {
303			m[v] = (uint64_t)m31[u + 1]
304				+ ((uint64_t)m31[u + 2] << 31);
305			x[v] = (uint64_t)x31[u + 1]
306				+ ((uint64_t)x31[u + 2] << 31);
307		}
308	}
309
310	/*
311	 * Compute window size. We support windows up to 5 bits; for a
312	 * window of size k bits, we need 2^k+1 temporaries (for k = 1,
313	 * we use special code that uses only 2 temporaries).
314	 */
315	for (win_len = 5; win_len > 1; win_len --) {
316		if ((((uint32_t)1 << win_len) + 1) * mw62num <= twlen) {
317			break;
318		}
319	}
320
321	t1 = tmp;
322	t2 = tmp + mw62num;
323
324	/*
325	 * Compute m0i, which is equal to -(1/m0) mod 2^62. We were
326	 * provided with m0i31, which already fulfills this property
327	 * modulo 2^31; the single expression below is then sufficient.
328	 */
329	m0i = (uint64_t)m0i31;
330	m0i = MUL62_lo(m0i, (uint64_t)2 + MUL62_lo(m0i, m[0]));
331
332	/*
333	 * Compute window contents. If the window has size one bit only,
334	 * then t2 is set to x; otherwise, t2[0] is left untouched, and
335	 * t2[k] is set to x^k (for k >= 1).
336	 */
337	if (win_len == 1) {
338		memcpy(t2, x, mw62num * sizeof *x);
339	} else {
340		uint64_t *base;
341
342		memcpy(t2 + mw62num, x, mw62num * sizeof *x);
343		base = t2 + mw62num;
344		for (u = 2; u < ((unsigned)1 << win_len); u ++) {
345			montymul(base + mw62num, base, x, m, mw62num, m0i);
346			base += mw62num;
347		}
348	}
349
350	/*
351	 * Set x to 1, in Montgomery representation. We again use the
352	 * 31-bit code.
353	 */
354	br_i31_zero(x31, m31[0]);
355	x31[(m31[0] + 31) >> 5] = 1;
356	br_i31_muladd_small(x31, 0, m31);
357	if (mw31num & 1) {
358		br_i31_muladd_small(x31, 0, m31);
359	}
360	for (u = 0; u < mw31num; u += 2) {
361		size_t v;
362
363		v = u >> 1;
364		if ((u + 1) == mw31num) {
365			x[v] = (uint64_t)x31[u + 1];
366		} else {
367			x[v] = (uint64_t)x31[u + 1]
368				+ ((uint64_t)x31[u + 2] << 31);
369		}
370	}
371
372	/*
373	 * We process bits from most to least significant. At each
374	 * loop iteration, we have acc_len bits in acc.
375	 */
376	acc = 0;
377	acc_len = 0;
378	while (acc_len > 0 || elen > 0) {
379		int i, k;
380		uint32_t bits;
381		uint64_t mask1, mask2;
382
383		/*
384		 * Get the next bits.
385		 */
386		k = win_len;
387		if (acc_len < win_len) {
388			if (elen > 0) {
389				acc = (acc << 8) | *e ++;
390				elen --;
391				acc_len += 8;
392			} else {
393				k = acc_len;
394			}
395		}
396		bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
397		acc_len -= k;
398
399		/*
400		 * We could get exactly k bits. Compute k squarings.
401		 */
402		for (i = 0; i < k; i ++) {
403			montymul(t1, x, x, m, mw62num, m0i);
404			memcpy(x, t1, mw62num * sizeof *x);
405		}
406
407		/*
408		 * Window lookup: we want to set t2 to the window
409		 * lookup value, assuming the bits are non-zero. If
410		 * the window length is 1 bit only, then t2 is
411		 * already set; otherwise, we do a constant-time lookup.
412		 */
413		if (win_len > 1) {
414			uint64_t *base;
415
416			memset(t2, 0, mw62num * sizeof *t2);
417			base = t2 + mw62num;
418			for (u = 1; u < ((uint32_t)1 << k); u ++) {
419				uint64_t mask;
420				size_t v;
421
422				mask = -(uint64_t)EQ(u, bits);
423				for (v = 0; v < mw62num; v ++) {
424					t2[v] |= mask & base[v];
425				}
426				base += mw62num;
427			}
428		}
429
430		/*
431		 * Multiply with the looked-up value. We keep the product
432		 * only if the exponent bits are not all-zero.
433		 */
434		montymul(t1, x, t2, m, mw62num, m0i);
435		mask1 = -(uint64_t)EQ(bits, 0);
436		mask2 = ~mask1;
437		for (u = 0; u < mw62num; u ++) {
438			x[u] = (mask1 & x[u]) | (mask2 & t1[u]);
439		}
440	}
441
442	/*
443	 * Convert back from Montgomery representation.
444	 */
445	frommonty(x, m, mw62num, m0i);
446
447	/*
448	 * Convert result into 31-bit words.
449	 */
450	for (u = 0; u < mw31num; u += 2) {
451		uint64_t zw;
452
453		zw = x[u >> 1];
454		x31[u + 1] = (uint32_t)zw & 0x7FFFFFFF;
455		if ((u + 1) < mw31num) {
456			x31[u + 2] = (uint32_t)(zw >> 31);
457		}
458	}
459	return 1;
460}
461
462#else
463
464/* see inner.h */
465uint32_t
466br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
467	const uint32_t *m31, uint32_t m0i31, uint64_t *tmp, size_t twlen)
468{
469	size_t mwlen;
470
471	mwlen = (m31[0] + 63) >> 5;
472	if (twlen < mwlen) {
473		return 0;
474	}
475	return br_i31_modpow_opt(x31, e, elen, m31, m0i31,
476		(uint32_t *)tmp, twlen << 1);
477}
478
479#endif
480
481/* see inner.h */
482uint32_t
483br_i62_modpow_opt_as_i31(uint32_t *x31, const unsigned char *e, size_t elen,
484	const uint32_t *m31, uint32_t m0i31, uint32_t *tmp, size_t twlen)
485{
486	/*
487	 * As documented, this function expects the 'tmp' argument to be
488	 * 64-bit aligned. This is OK since this function is internal (it
489	 * is not part of BearSSL's public API).
490	 */
491	return br_i62_modpow_opt(x31, e, elen, m31, m0i31,
492		(uint64_t *)tmp, twlen >> 1);
493}
494