| blob | 9c2e35c2fdfedc5fa79de1baa74a6cd1975a668f |
1 /*\r
2 * Bignum routines for RSA and DH and stuff.\r
3 */\r
4 \r
5 #include <stdio.h>\r
6 #include <assert.h>\r
7 #include <stdlib.h>\r
8 #include <string.h>\r
9 #include <limits.h>\r
10 \r
11 #include "misc.h"\r
12 \r
13 /*\r
14 * Usage notes:\r
15 * * Do not call the DIVMOD_WORD macro with expressions such as array\r
16 * subscripts, as some implementations object to this (see below).\r
17 * * Note that none of the division methods below will cope if the\r
18 * quotient won't fit into BIGNUM_INT_BITS. Callers should be careful\r
19 * to avoid this case.\r
20 * If this condition occurs, in the case of the x86 DIV instruction,\r
21 * an overflow exception will occur, which (according to a correspondent)\r
22 * will manifest on Windows as something like\r
23 * 0xC0000095: Integer overflow\r
24 * The C variant won't give the right answer, either.\r
25 */\r
26 \r
27 #if defined __GNUC__ && defined __i386__\r
28 typedef unsigned long BignumInt;\r
29 typedef unsigned long long BignumDblInt;\r
30 #define BIGNUM_INT_MASK 0xFFFFFFFFUL\r
31 #define BIGNUM_TOP_BIT 0x80000000UL\r
32 #define BIGNUM_INT_BITS 32\r
33 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
34 #define DIVMOD_WORD(q, r, hi, lo, w) \\r
35 __asm__("div %2" : \\r
36 "=d" (r), "=a" (q) : \\r
37 "r" (w), "d" (hi), "a" (lo))\r
38 #elif defined _MSC_VER && defined _M_IX86\r
39 typedef unsigned __int32 BignumInt;\r
40 typedef unsigned __int64 BignumDblInt;\r
41 #define BIGNUM_INT_MASK 0xFFFFFFFFUL\r
42 #define BIGNUM_TOP_BIT 0x80000000UL\r
43 #define BIGNUM_INT_BITS 32\r
44 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
45 /* Note: MASM interprets array subscripts in the macro arguments as\r
46 * assembler syntax, which gives the wrong answer. Don't supply them.\r
47 * <http://msdn2.microsoft.com/en-us/library/bf1dw62z.aspx> */\r
48 #define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
49 __asm mov edx, hi \\r
50 __asm mov eax, lo \\r
51 __asm div w \\r
52 __asm mov r, edx \\r
53 __asm mov q, eax \\r
54 } while(0)\r
55 #elif defined _LP64\r
56 /* 64-bit architectures can do 32x32->64 chunks at a time */\r
57 typedef unsigned int BignumInt;\r
58 typedef unsigned long BignumDblInt;\r
59 #define BIGNUM_INT_MASK 0xFFFFFFFFU\r
60 #define BIGNUM_TOP_BIT 0x80000000U\r
61 #define BIGNUM_INT_BITS 32\r
62 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
63 #define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
64 BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \\r
65 q = n / w; \\r
66 r = n % w; \\r
67 } while (0)\r
68 #elif defined _LLP64\r
69 /* 64-bit architectures in which unsigned long is 32 bits, not 64 */\r
70 typedef unsigned long BignumInt;\r
71 typedef unsigned long long BignumDblInt;\r
72 #define BIGNUM_INT_MASK 0xFFFFFFFFUL\r
73 #define BIGNUM_TOP_BIT 0x80000000UL\r
74 #define BIGNUM_INT_BITS 32\r
75 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
76 #define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
77 BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \\r
78 q = n / w; \\r
79 r = n % w; \\r
80 } while (0)\r
81 #else\r
82 /* Fallback for all other cases */\r
83 typedef unsigned short BignumInt;\r
84 typedef unsigned long BignumDblInt;\r
85 #define BIGNUM_INT_MASK 0xFFFFU\r
86 #define BIGNUM_TOP_BIT 0x8000U\r
87 #define BIGNUM_INT_BITS 16\r
88 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
89 #define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
90 BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \\r
91 q = n / w; \\r
92 r = n % w; \\r
93 } while (0)\r
94 #endif\r
95 \r
96 #define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8)\r
97 \r
98 #define BIGNUM_INTERNAL\r
99 typedef BignumInt *Bignum;\r
100 \r
101 #include "ssh.h"\r
102 \r
103 BignumInt bnZero[1] = { 0 };\r
104 BignumInt bnOne[2] = { 1, 1 };\r
105 \r
106 /*\r
107 * The Bignum format is an array of `BignumInt'. The first\r
108 * element of the array counts the remaining elements. The\r
109 * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_\r
110 * significant digit first. (So it's trivial to extract the bit\r
111 * with value 2^n for any n.)\r
112 *\r
113 * All Bignums in this module are positive. Negative numbers must\r
114 * be dealt with outside it.\r
115 *\r
116 * INVARIANT: the most significant word of any Bignum must be\r
117 * nonzero.\r
118 */\r
119 \r
120 Bignum Zero = bnZero, One = bnOne;\r
121 \r
122 static Bignum newbn(int length)\r
123 {\r
124 Bignum b;\r
125 \r
126 assert(length >= 0 && length < INT_MAX / BIGNUM_INT_BITS);\r
127 \r
128 b = snewn(length + 1, BignumInt);\r
129 if (!b)\r
130 abort(); /* FIXME */\r
131 memset(b, 0, (length + 1) * sizeof(*b));\r
132 b[0] = length;\r
133 return b;\r
134 }\r
135 \r
136 void bn_restore_invariant(Bignum b)\r
137 {\r
138 while (b[0] > 1 && b[b[0]] == 0)\r
139 b[0]--;\r
140 }\r
141 \r
142 Bignum copybn(Bignum orig)\r
143 {\r
144 Bignum b = snewn(orig[0] + 1, BignumInt);\r
145 if (!b)\r
146 abort(); /* FIXME */\r
147 memcpy(b, orig, (orig[0] + 1) * sizeof(*b));\r
148 return b;\r
149 }\r
150 \r
151 void freebn(Bignum b)\r
152 {\r
153 /*\r
154 * Burn the evidence, just in case.\r
155 */\r
156 smemclr(b, sizeof(b[0]) * (b[0] + 1));\r
157 sfree(b);\r
158 }\r
159 \r
160 Bignum bn_power_2(int n)\r
161 {\r
162 Bignum ret;\r
163 \r
164 assert(n >= 0);\r
165 \r
166 ret = newbn(n / BIGNUM_INT_BITS + 1);\r
167 bignum_set_bit(ret, n, 1);\r
168 return ret;\r
169 }\r
170 \r
171 /*\r
172 * Internal addition. Sets c = a - b, where 'a', 'b' and 'c' are all\r
173 * big-endian arrays of 'len' BignumInts. Returns a BignumInt carried\r
174 * off the top.\r
175 */\r
176 static BignumInt internal_add(const BignumInt *a, const BignumInt *b,\r
177 BignumInt *c, int len)\r
178 {\r
179 int i;\r
180 BignumDblInt carry = 0;\r
181 \r
182 for (i = len-1; i >= 0; i--) {\r
183 carry += (BignumDblInt)a[i] + b[i];\r
184 c[i] = (BignumInt)carry;\r
185 carry >>= BIGNUM_INT_BITS;\r
186 }\r
187 \r
188 return (BignumInt)carry;\r
189 }\r
190 \r
191 /*\r
192 * Internal subtraction. Sets c = a - b, where 'a', 'b' and 'c' are\r
193 * all big-endian arrays of 'len' BignumInts. Any borrow from the top\r
194 * is ignored.\r
195 */\r
196 static void internal_sub(const BignumInt *a, const BignumInt *b,\r
197 BignumInt *c, int len)\r
198 {\r
199 int i;\r
200 BignumDblInt carry = 1;\r
201 \r
202 for (i = len-1; i >= 0; i--) {\r
203 carry += (BignumDblInt)a[i] + (b[i] ^ BIGNUM_INT_MASK);\r
204 c[i] = (BignumInt)carry;\r
205 carry >>= BIGNUM_INT_BITS;\r
206 }\r
207 }\r
208 \r
209 /*\r
210 * Compute c = a * b.\r
211 * Input is in the first len words of a and b.\r
212 * Result is returned in the first 2*len words of c.\r
213 *\r
214 * 'scratch' must point to an array of BignumInt of size at least\r
215 * mul_compute_scratch(len). (This covers the needs of internal_mul\r
216 * and all its recursive calls to itself.)\r
217 */\r
218 #define KARATSUBA_THRESHOLD 50\r
219 static int mul_compute_scratch(int len)\r
220 {\r
221 int ret = 0;\r
222 while (len > KARATSUBA_THRESHOLD) {\r
223 int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */\r
224 int midlen = botlen + 1;\r
225 ret += 4*midlen;\r
226 len = midlen;\r
227 }\r
228 return ret;\r
229 }\r
230 static void internal_mul(const BignumInt *a, const BignumInt *b,\r
231 BignumInt *c, int len, BignumInt *scratch)\r
232 {\r
233 if (len > KARATSUBA_THRESHOLD) {\r
234 int i;\r
235 \r
236 /*\r
237 * Karatsuba divide-and-conquer algorithm. Cut each input in\r
238 * half, so that it's expressed as two big 'digits' in a giant\r
239 * base D:\r
240 *\r
241 * a = a_1 D + a_0\r
242 * b = b_1 D + b_0\r
243 *\r
244 * Then the product is of course\r
245 *\r
246 * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0\r
247 *\r
248 * and we compute the three coefficients by recursively\r
249 * calling ourself to do half-length multiplications.\r
250 *\r
251 * The clever bit that makes this worth doing is that we only\r
252 * need _one_ half-length multiplication for the central\r
253 * coefficient rather than the two that it obviouly looks\r
254 * like, because we can use a single multiplication to compute\r
255 *\r
256 * (a_1 + a_0) (b_1 + b_0) = a_1 b_1 + a_1 b_0 + a_0 b_1 + a_0 b_0\r
257 *\r
258 * and then we subtract the other two coefficients (a_1 b_1\r
259 * and a_0 b_0) which we were computing anyway.\r
260 *\r
261 * Hence we get to multiply two numbers of length N in about\r
262 * three times as much work as it takes to multiply numbers of\r
263 * length N/2, which is obviously better than the four times\r
264 * as much work it would take if we just did a long\r
265 * conventional multiply.\r
266 */\r
267 \r
268 int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */\r
269 int midlen = botlen + 1;\r
270 BignumDblInt carry;\r
271 #ifdef KARA_DEBUG\r
272 int i;\r
273 #endif\r
274 \r
275 /*\r
276 * The coefficients a_1 b_1 and a_0 b_0 just avoid overlapping\r
277 * in the output array, so we can compute them immediately in\r
278 * place.\r
279 */\r
280 \r
281 #ifdef KARA_DEBUG\r
282 printf("a1,a0 = 0x");\r
283 for (i = 0; i < len; i++) {\r
284 if (i == toplen) printf(", 0x");\r
285 printf("%0*x", BIGNUM_INT_BITS/4, a[i]);\r
286 }\r
287 printf("\n");\r
288 printf("b1,b0 = 0x");\r
289 for (i = 0; i < len; i++) {\r
290 if (i == toplen) printf(", 0x");\r
291 printf("%0*x", BIGNUM_INT_BITS/4, b[i]);\r
292 }\r
293 printf("\n");\r
294 #endif\r
295 \r
296 /* a_1 b_1 */\r
297 internal_mul(a, b, c, toplen, scratch);\r
298 #ifdef KARA_DEBUG\r
299 printf("a1b1 = 0x");\r
300 for (i = 0; i < 2*toplen; i++) {\r
301 printf("%0*x", BIGNUM_INT_BITS/4, c[i]);\r
302 }\r
303 printf("\n");\r
304 #endif\r
305 \r
306 /* a_0 b_0 */\r
307 internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen, scratch);\r
308 #ifdef KARA_DEBUG\r
309 printf("a0b0 = 0x");\r
310 for (i = 0; i < 2*botlen; i++) {\r
311 printf("%0*x", BIGNUM_INT_BITS/4, c[2*toplen+i]);\r
312 }\r
313 printf("\n");\r
314 #endif\r
315 \r
316 /* Zero padding. midlen exceeds toplen by at most 2, so just\r
317 * zero the first two words of each input and the rest will be\r
318 * copied over. */\r
319 scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0;\r
320 \r
321 for (i = 0; i < toplen; i++) {\r
322 scratch[midlen - toplen + i] = a[i]; /* a_1 */\r
323 scratch[2*midlen - toplen + i] = b[i]; /* b_1 */\r
324 }\r
325 \r
326 /* compute a_1 + a_0 */\r
327 scratch[0] = internal_add(scratch+1, a+toplen, scratch+1, botlen);\r
328 #ifdef KARA_DEBUG\r
329 printf("a1plusa0 = 0x");\r
330 for (i = 0; i < midlen; i++) {\r
331 printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);\r
332 }\r
333 printf("\n");\r
334 #endif\r
335 /* compute b_1 + b_0 */\r
336 scratch[midlen] = internal_add(scratch+midlen+1, b+toplen,\r
337 scratch+midlen+1, botlen);\r
338 #ifdef KARA_DEBUG\r
339 printf("b1plusb0 = 0x");\r
340 for (i = 0; i < midlen; i++) {\r
341 printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen+i]);\r
342 }\r
343 printf("\n");\r
344 #endif\r
345 \r
346 /*\r
347 * Now we can do the third multiplication.\r
348 */\r
349 internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen,\r
350 scratch + 4*midlen);\r
351 #ifdef KARA_DEBUG\r
352 printf("a1plusa0timesb1plusb0 = 0x");\r
353 for (i = 0; i < 2*midlen; i++) {\r
354 printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);\r
355 }\r
356 printf("\n");\r
357 #endif\r
358 \r
359 /*\r
360 * Now we can reuse the first half of 'scratch' to compute the\r
361 * sum of the outer two coefficients, to subtract from that\r
362 * product to obtain the middle one.\r
363 */\r
364 scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0;\r
365 for (i = 0; i < 2*toplen; i++)\r
366 scratch[2*midlen - 2*toplen + i] = c[i];\r
367 scratch[1] = internal_add(scratch+2, c + 2*toplen,\r
368 scratch+2, 2*botlen);\r
369 #ifdef KARA_DEBUG\r
370 printf("a1b1plusa0b0 = 0x");\r
371 for (i = 0; i < 2*midlen; i++) {\r
372 printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);\r
373 }\r
374 printf("\n");\r
375 #endif\r
376 \r
377 internal_sub(scratch + 2*midlen, scratch,\r
378 scratch + 2*midlen, 2*midlen);\r
379 #ifdef KARA_DEBUG\r
380 printf("a1b0plusa0b1 = 0x");\r
381 for (i = 0; i < 2*midlen; i++) {\r
382 printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);\r
383 }\r
384 printf("\n");\r
385 #endif\r
386 \r
387 /*\r
388 * And now all we need to do is to add that middle coefficient\r
389 * back into the output. We may have to propagate a carry\r
390 * further up the output, but we can be sure it won't\r
391 * propagate right the way off the top.\r
392 */\r
393 carry = internal_add(c + 2*len - botlen - 2*midlen,\r
394 scratch + 2*midlen,\r
395 c + 2*len - botlen - 2*midlen, 2*midlen);\r
396 i = 2*len - botlen - 2*midlen - 1;\r
397 while (carry) {\r
398 assert(i >= 0);\r
399 carry += c[i];\r
400 c[i] = (BignumInt)carry;\r
401 carry >>= BIGNUM_INT_BITS;\r
402 i--;\r
403 }\r
404 #ifdef KARA_DEBUG\r
405 printf("ab = 0x");\r
406 for (i = 0; i < 2*len; i++) {\r
407 printf("%0*x", BIGNUM_INT_BITS/4, c[i]);\r
408 }\r
409 printf("\n");\r
410 #endif\r
411 \r
412 } else {\r
413 int i;\r
414 BignumInt carry;\r
415 BignumDblInt t;\r
416 const BignumInt *ap, *bp;\r
417 BignumInt *cp, *cps;\r
418 \r
419 /*\r
420 * Multiply in the ordinary O(N^2) way.\r
421 */\r
422 \r
423 for (i = 0; i < 2 * len; i++)\r
424 c[i] = 0;\r
425 \r
426 for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) {\r
427 carry = 0;\r
428 for (cp = cps, bp = b + len; cp--, bp-- > b ;) {\r
429 t = (MUL_WORD(*ap, *bp) + carry) + *cp;\r
430 *cp = (BignumInt) t;\r
431 carry = (BignumInt)(t >> BIGNUM_INT_BITS);\r
432 }\r
433 *cp = carry;\r
434 }\r
435 }\r
436 }\r
437 \r
438 /*\r
439 * Variant form of internal_mul used for the initial step of\r
440 * Montgomery reduction. Only bothers outputting 'len' words\r
441 * (everything above that is thrown away).\r
442 */\r
443 static void internal_mul_low(const BignumInt *a, const BignumInt *b,\r
444 BignumInt *c, int len, BignumInt *scratch)\r
445 {\r
446 if (len > KARATSUBA_THRESHOLD) {\r
447 int i;\r
448 \r
449 /*\r
450 * Karatsuba-aware version of internal_mul_low. As before, we\r
451 * express each input value as a shifted combination of two\r
452 * halves:\r
453 *\r
454 * a = a_1 D + a_0\r
455 * b = b_1 D + b_0\r
456 *\r
457 * Then the full product is, as before,\r
458 *\r
459 * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0\r
460 *\r
461 * Provided we choose D on the large side (so that a_0 and b_0\r
462 * are _at least_ as long as a_1 and b_1), we don't need the\r
463 * topmost term at all, and we only need half of the middle\r
464 * term. So there's no point in doing the proper Karatsuba\r
465 * optimisation which computes the middle term using the top\r
466 * one, because we'd take as long computing the top one as\r
467 * just computing the middle one directly.\r
468 *\r
469 * So instead, we do a much more obvious thing: we call the\r
470 * fully optimised internal_mul to compute a_0 b_0, and we\r
471 * recursively call ourself to compute the _bottom halves_ of\r
472 * a_1 b_0 and a_0 b_1, each of which we add into the result\r
473 * in the obvious way.\r
474 *\r
475 * In other words, there's no actual Karatsuba _optimisation_\r
476 * in this function; the only benefit in doing it this way is\r
477 * that we call internal_mul proper for a large part of the\r
478 * work, and _that_ can optimise its operation.\r
479 */\r
480 \r
481 int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */\r
482 \r
483 /*\r
484 * Scratch space for the various bits and pieces we're going\r
485 * to be adding together: we need botlen*2 words for a_0 b_0\r
486 * (though we may end up throwing away its topmost word), and\r
487 * toplen words for each of a_1 b_0 and a_0 b_1. That adds up\r
488 * to exactly 2*len.\r
489 */\r
490 \r
491 /* a_0 b_0 */\r
492 internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen,\r
493 scratch + 2*len);\r
494 \r
495 /* a_1 b_0 */\r
496 internal_mul_low(a, b + len - toplen, scratch + toplen, toplen,\r
497 scratch + 2*len);\r
498 \r
499 /* a_0 b_1 */\r
500 internal_mul_low(a + len - toplen, b, scratch, toplen,\r
501 scratch + 2*len);\r
502 \r
503 /* Copy the bottom half of the big coefficient into place */\r
504 for (i = 0; i < botlen; i++)\r
505 c[toplen + i] = scratch[2*toplen + botlen + i];\r
506 \r
507 /* Add the two small coefficients, throwing away the returned carry */\r
508 internal_add(scratch, scratch + toplen, scratch, toplen);\r
509 \r
510 /* And add that to the large coefficient, leaving the result in c. */\r
511 internal_add(scratch, scratch + 2*toplen + botlen - toplen,\r
512 c, toplen);\r
513 \r
514 } else {\r
515 int i;\r
516 BignumInt carry;\r
517 BignumDblInt t;\r
518 const BignumInt *ap, *bp;\r
519 BignumInt *cp, *cps;\r
520 \r
521 /*\r
522 * Multiply in the ordinary O(N^2) way.\r
523 */\r
524 \r
525 for (i = 0; i < len; i++)\r
526 c[i] = 0;\r
527 \r
528 for (cps = c + len, ap = a + len; ap-- > a; cps--) {\r
529 carry = 0;\r
530 for (cp = cps, bp = b + len; bp--, cp-- > c ;) {\r
531 t = (MUL_WORD(*ap, *bp) + carry) + *cp;\r
532 *cp = (BignumInt) t;\r
533 carry = (BignumInt)(t >> BIGNUM_INT_BITS);\r
534 }\r
535 }\r
536 }\r
537 }\r
538 \r
539 /*\r
540 * Montgomery reduction. Expects x to be a big-endian array of 2*len\r
541 * BignumInts whose value satisfies 0 <= x < rn (where r = 2^(len *\r
542 * BIGNUM_INT_BITS) is the Montgomery base). Returns in the same array\r
543 * a value x' which is congruent to xr^{-1} mod n, and satisfies 0 <=\r
544 * x' < n.\r
545 *\r
546 * 'n' and 'mninv' should be big-endian arrays of 'len' BignumInts\r
547 * each, containing respectively n and the multiplicative inverse of\r
548 * -n mod r.\r
549 *\r
550 * 'tmp' is an array of BignumInt used as scratch space, of length at\r
551 * least 3*len + mul_compute_scratch(len).\r
552 */\r
553 static void monty_reduce(BignumInt *x, const BignumInt *n,\r
554 const BignumInt *mninv, BignumInt *tmp, int len)\r
555 {\r
556 int i;\r
557 BignumInt carry;\r
558 \r
559 /*\r
560 * Multiply x by (-n)^{-1} mod r. This gives us a value m such\r
561 * that mn is congruent to -x mod r. Hence, mn+x is an exact\r
562 * multiple of r, and is also (obviously) congruent to x mod n.\r
563 */\r
564 internal_mul_low(x + len, mninv, tmp, len, tmp + 3*len);\r
565 \r
566 /*\r
567 * Compute t = (mn+x)/r in ordinary, non-modular, integer\r
568 * arithmetic. By construction this is exact, and is congruent mod\r
569 * n to x * r^{-1}, i.e. the answer we want.\r
570 *\r
571 * The following multiply leaves that answer in the _most_\r
572 * significant half of the 'x' array, so then we must shift it\r
573 * down.\r
574 */\r
575 internal_mul(tmp, n, tmp+len, len, tmp + 3*len);\r
576 carry = internal_add(x, tmp+len, x, 2*len);\r
577 for (i = 0; i < len; i++)\r
578 x[len + i] = x[i], x[i] = 0;\r
579 \r
580 /*\r
581 * Reduce t mod n. This doesn't require a full-on division by n,\r
582 * but merely a test and single optional subtraction, since we can\r
583 * show that 0 <= t < 2n.\r
584 *\r
585 * Proof:\r
586 * + we computed m mod r, so 0 <= m < r.\r
587 * + so 0 <= mn < rn, obviously\r
588 * + hence we only need 0 <= x < rn to guarantee that 0 <= mn+x < 2rn\r
589 * + yielding 0 <= (mn+x)/r < 2n as required.\r
590 */\r
591 if (!carry) {\r
592 for (i = 0; i < len; i++)\r
593 if (x[len + i] != n[i])\r
594 break;\r
595 }\r
596 if (carry || i >= len || x[len + i] > n[i])\r
597 internal_sub(x+len, n, x+len, len);\r
598 }\r
599 \r
600 static void internal_add_shifted(BignumInt *number,\r
601 unsigned n, int shift)\r
602 {\r
603 int word = 1 + (shift / BIGNUM_INT_BITS);\r
604 int bshift = shift % BIGNUM_INT_BITS;\r
605 BignumDblInt addend;\r
606 \r
607 addend = (BignumDblInt)n << bshift;\r
608 \r
609 while (addend) {\r
610 assert(word <= number[0]);\r
611 addend += number[word];\r
612 number[word] = (BignumInt) addend & BIGNUM_INT_MASK;\r
613 addend >>= BIGNUM_INT_BITS;\r
614 word++;\r
615 }\r
616 }\r
617 \r
618 /*\r
619 * Compute a = a % m.\r
620 * Input in first alen words of a and first mlen words of m.\r
621 * Output in first alen words of a\r
622 * (of which first alen-mlen words will be zero).\r
623 * The MSW of m MUST have its high bit set.\r
624 * Quotient is accumulated in the `quotient' array, which is a Bignum\r
625 * rather than the internal bigendian format. Quotient parts are shifted\r
626 * left by `qshift' before adding into quot.\r
627 */\r
628 static void internal_mod(BignumInt *a, int alen,\r
629 BignumInt *m, int mlen,\r
630 BignumInt *quot, int qshift)\r
631 {\r
632 BignumInt m0, m1;\r
633 unsigned int h;\r
634 int i, k;\r
635 \r
636 m0 = m[0];\r
637 assert(m0 >> (BIGNUM_INT_BITS-1) == 1);\r
638 if (mlen > 1)\r
639 m1 = m[1];\r
640 else\r
641 m1 = 0;\r
642 \r
643 for (i = 0; i <= alen - mlen; i++) {\r
644 BignumDblInt t;\r
645 unsigned int q, r, c, ai1;\r
646 \r
647 if (i == 0) {\r
648 h = 0;\r
649 } else {\r
650 h = a[i - 1];\r
651 a[i - 1] = 0;\r
652 }\r
653 \r
654 if (i == alen - 1)\r
655 ai1 = 0;\r
656 else\r
657 ai1 = a[i + 1];\r
658 \r
659 /* Find q = h:a[i] / m0 */\r
660 if (h >= m0) {\r
661 /*\r
662 * Special case.\r
663 * \r
664 * To illustrate it, suppose a BignumInt is 8 bits, and\r
665 * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then\r
666 * our initial division will be 0xA123 / 0xA1, which\r
667 * will give a quotient of 0x100 and a divide overflow.\r
668 * However, the invariants in this division algorithm\r
669 * are not violated, since the full number A1:23:... is\r
670 * _less_ than the quotient prefix A1:B2:... and so the\r
671 * following correction loop would have sorted it out.\r
672 * \r
673 * In this situation we set q to be the largest\r
674 * quotient we _can_ stomach (0xFF, of course).\r
675 */\r
676 q = BIGNUM_INT_MASK;\r
677 } else {\r
678 /* Macro doesn't want an array subscript expression passed\r
679 * into it (see definition), so use a temporary. */\r
680 BignumInt tmplo = a[i];\r
681 DIVMOD_WORD(q, r, h, tmplo, m0);\r
682 \r
683 /* Refine our estimate of q by looking at\r
684 h:a[i]:a[i+1] / m0:m1 */\r
685 t = MUL_WORD(m1, q);\r
686 if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {\r
687 q--;\r
688 t -= m1;\r
689 r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */\r
690 if (r >= (BignumDblInt) m0 &&\r
691 t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;\r
692 }\r
693 }\r
694 \r
695 /* Subtract q * m from a[i...] */\r
696 c = 0;\r
697 for (k = mlen - 1; k >= 0; k--) {\r
698 t = MUL_WORD(q, m[k]);\r
699 t += c;\r
700 c = (unsigned)(t >> BIGNUM_INT_BITS);\r
701 if ((BignumInt) t > a[i + k])\r
702 c++;\r
703 a[i + k] -= (BignumInt) t;\r
704 }\r
705 \r
706 /* Add back m in case of borrow */\r
707 if (c != h) {\r
708 t = 0;\r
709 for (k = mlen - 1; k >= 0; k--) {\r
710 t += m[k];\r
711 t += a[i + k];\r
712 a[i + k] = (BignumInt) t;\r
713 t = t >> BIGNUM_INT_BITS;\r
714 }\r
715 q--;\r
716 }\r
717 if (quot)\r
718 internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));\r
719 }\r
720 }\r
721 \r
722 /*\r
723 * Compute (base ^ exp) % mod, the pedestrian way.\r
724 */\r
725 Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod)\r
726 {\r
727 BignumInt *a, *b, *n, *m, *scratch;\r
728 int mshift;\r
729 int mlen, scratchlen, i, j;\r
730 Bignum base, result;\r
731 \r
732 /*\r
733 * The most significant word of mod needs to be non-zero. It\r
734 * should already be, but let's make sure.\r
735 */\r
736 assert(mod[mod[0]] != 0);\r
737 \r
738 /*\r
739 * Make sure the base is smaller than the modulus, by reducing\r
740 * it modulo the modulus if not.\r
741 */\r
742 base = bigmod(base_in, mod);\r
743 \r
744 /* Allocate m of size mlen, copy mod to m */\r
745 /* We use big endian internally */\r
746 mlen = mod[0];\r
747 m = snewn(mlen, BignumInt);\r
748 for (j = 0; j < mlen; j++)\r
749 m[j] = mod[mod[0] - j];\r
750 \r
751 /* Shift m left to make msb bit set */\r
752 for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)\r
753 if ((m[0] << mshift) & BIGNUM_TOP_BIT)\r
754 break;\r
755 if (mshift) {\r
756 for (i = 0; i < mlen - 1; i++)\r
757 m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
758 m[mlen - 1] = m[mlen - 1] << mshift;\r
759 }\r
760 \r
761 /* Allocate n of size mlen, copy base to n */\r
762 n = snewn(mlen, BignumInt);\r
763 i = mlen - base[0];\r
764 for (j = 0; j < i; j++)\r
765 n[j] = 0;\r
766 for (j = 0; j < (int)base[0]; j++)\r
767 n[i + j] = base[base[0] - j];\r
768 \r
769 /* Allocate a and b of size 2*mlen. Set a = 1 */\r
770 a = snewn(2 * mlen, BignumInt);\r
771 b = snewn(2 * mlen, BignumInt);\r
772 for (i = 0; i < 2 * mlen; i++)\r
773 a[i] = 0;\r
774 a[2 * mlen - 1] = 1;\r
775 \r
776 /* Scratch space for multiplies */\r
777 scratchlen = mul_compute_scratch(mlen);\r
778 scratch = snewn(scratchlen, BignumInt);\r
779 \r
780 /* Skip leading zero bits of exp. */\r
781 i = 0;\r
782 j = BIGNUM_INT_BITS-1;\r
783 while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {\r
784 j--;\r
785 if (j < 0) {\r
786 i++;\r
787 j = BIGNUM_INT_BITS-1;\r
788 }\r
789 }\r
790 \r
791 /* Main computation */\r
792 while (i < (int)exp[0]) {\r
793 while (j >= 0) {\r
794 internal_mul(a + mlen, a + mlen, b, mlen, scratch);\r
795 internal_mod(b, mlen * 2, m, mlen, NULL, 0);\r
796 if ((exp[exp[0] - i] & (1 << j)) != 0) {\r
797 internal_mul(b + mlen, n, a, mlen, scratch);\r
798 internal_mod(a, mlen * 2, m, mlen, NULL, 0);\r
799 } else {\r
800 BignumInt *t;\r
801 t = a;\r
802 a = b;\r
803 b = t;\r
804 }\r
805 j--;\r
806 }\r
807 i++;\r
808 j = BIGNUM_INT_BITS-1;\r
809 }\r
810 \r
811 /* Fixup result in case the modulus was shifted */\r
812 if (mshift) {\r
813 for (i = mlen - 1; i < 2 * mlen - 1; i++)\r
814 a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
815 a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;\r
816 internal_mod(a, mlen * 2, m, mlen, NULL, 0);\r
817 for (i = 2 * mlen - 1; i >= mlen; i--)\r
818 a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));\r
819 }\r
820 \r
821 /* Copy result to buffer */\r
822 result = newbn(mod[0]);\r
823 for (i = 0; i < mlen; i++)\r
824 result[result[0] - i] = a[i + mlen];\r
825 while (result[0] > 1 && result[result[0]] == 0)\r
826 result[0]--;\r
827 \r
828 /* Free temporary arrays */\r
829 smemclr(a, 2 * mlen * sizeof(*a));\r
830 sfree(a);\r
831 smemclr(scratch, scratchlen * sizeof(*scratch));\r
832 sfree(scratch);\r
833 smemclr(b, 2 * mlen * sizeof(*b));\r
834 sfree(b);\r
835 smemclr(m, mlen * sizeof(*m));\r
836 sfree(m);\r
837 smemclr(n, mlen * sizeof(*n));\r
838 sfree(n);\r
839 \r
840 freebn(base);\r
841 \r
842 return result;\r
843 }\r
844 \r
845 /*\r
846 * Compute (base ^ exp) % mod. Uses the Montgomery multiplication\r
847 * technique where possible, falling back to modpow_simple otherwise.\r
848 */\r
849 Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)\r
850 {\r
851 BignumInt *a, *b, *x, *n, *mninv, *scratch;\r
852 int len, scratchlen, i, j;\r
853 Bignum base, base2, r, rn, inv, result;\r
854 \r
855 /*\r
856 * The most significant word of mod needs to be non-zero. It\r
857 * should already be, but let's make sure.\r
858 */\r
859 assert(mod[mod[0]] != 0);\r
860 \r
861 /*\r
862 * mod had better be odd, or we can't do Montgomery multiplication\r
863 * using a power of two at all.\r
864 */\r
865 if (!(mod[1] & 1))\r
866 return modpow_simple(base_in, exp, mod);\r
867 \r
868 /*\r
869 * Make sure the base is smaller than the modulus, by reducing\r
870 * it modulo the modulus if not.\r
871 */\r
872 base = bigmod(base_in, mod);\r
873 \r
874 /*\r
875 * Compute the inverse of n mod r, for monty_reduce. (In fact we\r
876 * want the inverse of _minus_ n mod r, but we'll sort that out\r
877 * below.)\r
878 */\r
879 len = mod[0];\r
880 r = bn_power_2(BIGNUM_INT_BITS * len);\r
881 inv = modinv(mod, r);\r
882 assert(inv); /* cannot fail, since mod is odd and r is a power of 2 */\r
883 \r
884 /*\r
885 * Multiply the base by r mod n, to get it into Montgomery\r
886 * representation.\r
887 */\r
888 base2 = modmul(base, r, mod);\r
889 freebn(base);\r
890 base = base2;\r
891 \r
892 rn = bigmod(r, mod); /* r mod n, i.e. Montgomerified 1 */\r
893 \r
894 freebn(r); /* won't need this any more */\r
895 \r
896 /*\r
897 * Set up internal arrays of the right lengths, in big-endian\r
898 * format, containing the base, the modulus, and the modulus's\r
899 * inverse.\r
900 */\r
901 n = snewn(len, BignumInt);\r
902 for (j = 0; j < len; j++)\r
903 n[len - 1 - j] = mod[j + 1];\r
904 \r
905 mninv = snewn(len, BignumInt);\r
906 for (j = 0; j < len; j++)\r
907 mninv[len - 1 - j] = (j < (int)inv[0] ? inv[j + 1] : 0);\r
908 freebn(inv); /* we don't need this copy of it any more */\r
909 /* Now negate mninv mod r, so it's the inverse of -n rather than +n. */\r
910 x = snewn(len, BignumInt);\r
911 for (j = 0; j < len; j++)\r
912 x[j] = 0;\r
913 internal_sub(x, mninv, mninv, len);\r
914 \r
915 /* x = snewn(len, BignumInt); */ /* already done above */\r
916 for (j = 0; j < len; j++)\r
917 x[len - 1 - j] = (j < (int)base[0] ? base[j + 1] : 0);\r
918 freebn(base); /* we don't need this copy of it any more */\r
919 \r
920 a = snewn(2*len, BignumInt);\r
921 b = snewn(2*len, BignumInt);\r
922 for (j = 0; j < len; j++)\r
923 a[2*len - 1 - j] = (j < (int)rn[0] ? rn[j + 1] : 0);\r
924 freebn(rn);\r
925 \r
926 /* Scratch space for multiplies */\r
927 scratchlen = 3*len + mul_compute_scratch(len);\r
928 scratch = snewn(scratchlen, BignumInt);\r
929 \r
930 /* Skip leading zero bits of exp. */\r
931 i = 0;\r
932 j = BIGNUM_INT_BITS-1;\r
933 while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {\r
934 j--;\r
935 if (j < 0) {\r
936 i++;\r
937 j = BIGNUM_INT_BITS-1;\r
938 }\r
939 }\r
940 \r
941 /* Main computation */\r
942 while (i < (int)exp[0]) {\r
943 while (j >= 0) {\r
944 internal_mul(a + len, a + len, b, len, scratch);\r
945 monty_reduce(b, n, mninv, scratch, len);\r
946 if ((exp[exp[0] - i] & (1 << j)) != 0) {\r
947 internal_mul(b + len, x, a, len, scratch);\r
948 monty_reduce(a, n, mninv, scratch, len);\r
949 } else {\r
950 BignumInt *t;\r
951 t = a;\r
952 a = b;\r
953 b = t;\r
954 }\r
955 j--;\r
956 }\r
957 i++;\r
958 j = BIGNUM_INT_BITS-1;\r
959 }\r
960 \r
961 /*\r
962 * Final monty_reduce to get back from the adjusted Montgomery\r
963 * representation.\r
964 */\r
965 monty_reduce(a, n, mninv, scratch, len);\r
966 \r
967 /* Copy result to buffer */\r
968 result = newbn(mod[0]);\r
969 for (i = 0; i < len; i++)\r
970 result[result[0] - i] = a[i + len];\r
971 while (result[0] > 1 && result[result[0]] == 0)\r
972 result[0]--;\r
973 \r
974 /* Free temporary arrays */\r
975 smemclr(scratch, scratchlen * sizeof(*scratch));\r
976 sfree(scratch);\r
977 smemclr(a, 2 * len * sizeof(*a));\r
978 sfree(a);\r
979 smemclr(b, 2 * len * sizeof(*b));\r
980 sfree(b);\r
981 smemclr(mninv, len * sizeof(*mninv));\r
982 sfree(mninv);\r
983 smemclr(n, len * sizeof(*n));\r
984 sfree(n);\r
985 smemclr(x, len * sizeof(*x));\r
986 sfree(x);\r
987 \r
988 return result;\r
989 }\r
990 \r
991 /*\r
992 * Compute (p * q) % mod.\r
993 * The most significant word of mod MUST be non-zero.\r
994 * We assume that the result array is the same size as the mod array.\r
995 */\r
996 Bignum modmul(Bignum p, Bignum q, Bignum mod)\r
997 {\r
998 BignumInt *a, *n, *m, *o, *scratch;\r
999 int mshift, scratchlen;\r
1000 int pqlen, mlen, rlen, i, j;\r
1001 Bignum result;\r
1002 \r
1003 /*\r
1004 * The most significant word of mod needs to be non-zero. It\r
1005 * should already be, but let's make sure.\r
1006 */\r
1007 assert(mod[mod[0]] != 0);\r
1008 \r
1009 /* Allocate m of size mlen, copy mod to m */\r
1010 /* We use big endian internally */\r
1011 mlen = mod[0];\r
1012 m = snewn(mlen, BignumInt);\r
1013 for (j = 0; j < mlen; j++)\r
1014 m[j] = mod[mod[0] - j];\r
1015 \r
1016 /* Shift m left to make msb bit set */\r
1017 for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)\r
1018 if ((m[0] << mshift) & BIGNUM_TOP_BIT)\r
1019 break;\r
1020 if (mshift) {\r
1021 for (i = 0; i < mlen - 1; i++)\r
1022 m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
1023 m[mlen - 1] = m[mlen - 1] << mshift;\r
1024 }\r
1025 \r
1026 pqlen = (p[0] > q[0] ? p[0] : q[0]);\r
1027 \r
1028 /*\r
1029 * Make sure that we're allowing enough space. The shifting below\r
1030 * will underflow the vectors we allocate if pqlen is too small.\r
1031 */\r
1032 if (2*pqlen <= mlen)\r
1033 pqlen = mlen/2 + 1;\r
1034 \r
1035 /* Allocate n of size pqlen, copy p to n */\r
1036 n = snewn(pqlen, BignumInt);\r
1037 i = pqlen - p[0];\r
1038 for (j = 0; j < i; j++)\r
1039 n[j] = 0;\r
1040 for (j = 0; j < (int)p[0]; j++)\r
1041 n[i + j] = p[p[0] - j];\r
1042 \r
1043 /* Allocate o of size pqlen, copy q to o */\r
1044 o = snewn(pqlen, BignumInt);\r
1045 i = pqlen - q[0];\r
1046 for (j = 0; j < i; j++)\r
1047 o[j] = 0;\r
1048 for (j = 0; j < (int)q[0]; j++)\r
1049 o[i + j] = q[q[0] - j];\r
1050 \r
1051 /* Allocate a of size 2*pqlen for result */\r
1052 a = snewn(2 * pqlen, BignumInt);\r
1053 \r
1054 /* Scratch space for multiplies */\r
1055 scratchlen = mul_compute_scratch(pqlen);\r
1056 scratch = snewn(scratchlen, BignumInt);\r
1057 \r
1058 /* Main computation */\r
1059 internal_mul(n, o, a, pqlen, scratch);\r
1060 internal_mod(a, pqlen * 2, m, mlen, NULL, 0);\r
1061 \r
1062 /* Fixup result in case the modulus was shifted */\r
1063 if (mshift) {\r
1064 for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)\r
1065 a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
1066 a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;\r
1067 internal_mod(a, pqlen * 2, m, mlen, NULL, 0);\r
1068 for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)\r
1069 a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));\r
1070 }\r
1071 \r
1072 /* Copy result to buffer */\r
1073 rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);\r
1074 result = newbn(rlen);\r
1075 for (i = 0; i < rlen; i++)\r
1076 result[result[0] - i] = a[i + 2 * pqlen - rlen];\r
1077 while (result[0] > 1 && result[result[0]] == 0)\r
1078 result[0]--;\r
1079 \r
1080 /* Free temporary arrays */\r
1081 smemclr(scratch, scratchlen * sizeof(*scratch));\r
1082 sfree(scratch);\r
1083 smemclr(a, 2 * pqlen * sizeof(*a));\r
1084 sfree(a);\r
1085 smemclr(m, mlen * sizeof(*m));\r
1086 sfree(m);\r
1087 smemclr(n, pqlen * sizeof(*n));\r
1088 sfree(n);\r
1089 smemclr(o, pqlen * sizeof(*o));\r
1090 sfree(o);\r
1091 \r
1092 return result;\r
1093 }\r
1094 \r
1095 /*\r
1096 * Compute p % mod.\r
1097 * The most significant word of mod MUST be non-zero.\r
1098 * We assume that the result array is the same size as the mod array.\r
1099 * We optionally write out a quotient if `quotient' is non-NULL.\r
1100 * We can avoid writing out the result if `result' is NULL.\r
1101 */\r
1102 static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)\r
1103 {\r
1104 BignumInt *n, *m;\r
1105 int mshift;\r
1106 int plen, mlen, i, j;\r
1107 \r
1108 /*\r
1109 * The most significant word of mod needs to be non-zero. It\r
1110 * should already be, but let's make sure.\r
1111 */\r
1112 assert(mod[mod[0]] != 0);\r
1113 \r
1114 /* Allocate m of size mlen, copy mod to m */\r
1115 /* We use big endian internally */\r
1116 mlen = mod[0];\r
1117 m = snewn(mlen, BignumInt);\r
1118 for (j = 0; j < mlen; j++)\r
1119 m[j] = mod[mod[0] - j];\r
1120 \r
1121 /* Shift m left to make msb bit set */\r
1122 for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)\r
1123 if ((m[0] << mshift) & BIGNUM_TOP_BIT)\r
1124 break;\r
1125 if (mshift) {\r
1126 for (i = 0; i < mlen - 1; i++)\r
1127 m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
1128 m[mlen - 1] = m[mlen - 1] << mshift;\r
1129 }\r
1130 \r
1131 plen = p[0];\r
1132 /* Ensure plen > mlen */\r
1133 if (plen <= mlen)\r
1134 plen = mlen + 1;\r
1135 \r
1136 /* Allocate n of size plen, copy p to n */\r
1137 n = snewn(plen, BignumInt);\r
1138 for (j = 0; j < plen; j++)\r
1139 n[j] = 0;\r
1140 for (j = 1; j <= (int)p[0]; j++)\r
1141 n[plen - j] = p[j];\r
1142 \r
1143 /* Main computation */\r
1144 internal_mod(n, plen, m, mlen, quotient, mshift);\r
1145 \r
1146 /* Fixup result in case the modulus was shifted */\r
1147 if (mshift) {\r
1148 for (i = plen - mlen - 1; i < plen - 1; i++)\r
1149 n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
1150 n[plen - 1] = n[plen - 1] << mshift;\r
1151 internal_mod(n, plen, m, mlen, quotient, 0);\r
1152 for (i = plen - 1; i >= plen - mlen; i--)\r
1153 n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift));\r
1154 }\r
1155 \r
1156 /* Copy result to buffer */\r
1157 if (result) {\r
1158 for (i = 1; i <= (int)result[0]; i++) {\r
1159 int j = plen - i;\r
1160 result[i] = j >= 0 ? n[j] : 0;\r
1161 }\r
1162 }\r
1163 \r
1164 /* Free temporary arrays */\r
1165 smemclr(m, mlen * sizeof(*m));\r
1166 sfree(m);\r
1167 smemclr(n, plen * sizeof(*n));\r
1168 sfree(n);\r
1169 }\r
1170 \r
1171 /*\r
1172 * Decrement a number.\r
1173 */\r
1174 void decbn(Bignum bn)\r
1175 {\r
1176 int i = 1;\r
1177 while (i < (int)bn[0] && bn[i] == 0)\r
1178 bn[i++] = BIGNUM_INT_MASK;\r
1179 bn[i]--;\r
1180 }\r
1181 \r
1182 Bignum bignum_from_bytes(const unsigned char *data, int nbytes)\r
1183 {\r
1184 Bignum result;\r
1185 int w, i;\r
1186 \r
1187 assert(nbytes >= 0 && nbytes < INT_MAX/8);\r
1188 \r
1189 w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */\r
1190 \r
1191 result = newbn(w);\r
1192 for (i = 1; i <= w; i++)\r
1193 result[i] = 0;\r
1194 for (i = nbytes; i--;) {\r
1195 unsigned char byte = *data++;\r
1196 result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS);\r
1197 }\r
1198 \r
1199 while (result[0] > 1 && result[result[0]] == 0)\r
1200 result[0]--;\r
1201 return result;\r
1202 }\r
1203 \r
1204 /*\r
1205 * Read an SSH-1-format bignum from a data buffer. Return the number\r
1206 * of bytes consumed, or -1 if there wasn't enough data.\r
1207 */\r
1208 int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result)\r
1209 {\r
1210 const unsigned char *p = data;\r
1211 int i;\r
1212 int w, b;\r
1213 \r
1214 if (len < 2)\r
1215 return -1;\r
1216 \r
1217 w = 0;\r
1218 for (i = 0; i < 2; i++)\r
1219 w = (w << 8) + *p++;\r
1220 b = (w + 7) / 8; /* bits -> bytes */\r
1221 \r
1222 if (len < b+2)\r
1223 return -1;\r
1224 \r
1225 if (!result) /* just return length */\r
1226 return b + 2;\r
1227 \r
1228 *result = bignum_from_bytes(p, b);\r
1229 \r
1230 return p + b - data;\r
1231 }\r
1232 \r
1233 /*\r
1234 * Return the bit count of a bignum, for SSH-1 encoding.\r
1235 */\r
1236 int bignum_bitcount(Bignum bn)\r
1237 {\r
1238 int bitcount = bn[0] * BIGNUM_INT_BITS - 1;\r
1239 while (bitcount >= 0\r
1240 && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--;\r
1241 return bitcount + 1;\r
1242 }\r
1243 \r
1244 /*\r
1245 * Return the byte length of a bignum when SSH-1 encoded.\r
1246 */\r
1247 int ssh1_bignum_length(Bignum bn)\r
1248 {\r
1249 return 2 + (bignum_bitcount(bn) + 7) / 8;\r
1250 }\r
1251 \r
1252 /*\r
1253 * Return the byte length of a bignum when SSH-2 encoded.\r
1254 */\r
1255 int ssh2_bignum_length(Bignum bn)\r
1256 {\r
1257 return 4 + (bignum_bitcount(bn) + 8) / 8;\r
1258 }\r
1259 \r
1260 /*\r
1261 * Return a byte from a bignum; 0 is least significant, etc.\r
1262 */\r
1263 int bignum_byte(Bignum bn, int i)\r
1264 {\r
1265 if (i < 0 || i >= (int)(BIGNUM_INT_BYTES * bn[0]))\r
1266 return 0; /* beyond the end */\r
1267 else\r
1268 return (bn[i / BIGNUM_INT_BYTES + 1] >>\r
1269 ((i % BIGNUM_INT_BYTES)*8)) & 0xFF;\r
1270 }\r
1271 \r
1272 /*\r
1273 * Return a bit from a bignum; 0 is least significant, etc.\r
1274 */\r
1275 int bignum_bit(Bignum bn, int i)\r
1276 {\r
1277 if (i < 0 || i >= (int)(BIGNUM_INT_BITS * bn[0]))\r
1278 return 0; /* beyond the end */\r
1279 else\r
1280 return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1;\r
1281 }\r
1282 \r
1283 /*\r
1284 * Set a bit in a bignum; 0 is least significant, etc.\r
1285 */\r
1286 void bignum_set_bit(Bignum bn, int bitnum, int value)\r
1287 {\r
1288 if (bitnum < 0 || bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))\r
1289 abort(); /* beyond the end */\r
1290 else {\r
1291 int v = bitnum / BIGNUM_INT_BITS + 1;\r
1292 int mask = 1 << (bitnum % BIGNUM_INT_BITS);\r
1293 if (value)\r
1294 bn[v] |= mask;\r
1295 else\r
1296 bn[v] &= ~mask;\r
1297 }\r
1298 }\r
1299 \r
1300 /*\r
1301 * Write a SSH-1-format bignum into a buffer. It is assumed the\r
1302 * buffer is big enough. Returns the number of bytes used.\r
1303 */\r
1304 int ssh1_write_bignum(void *data, Bignum bn)\r
1305 {\r
1306 unsigned char *p = data;\r
1307 int len = ssh1_bignum_length(bn);\r
1308 int i;\r
1309 int bitc = bignum_bitcount(bn);\r
1310 \r
1311 *p++ = (bitc >> 8) & 0xFF;\r
1312 *p++ = (bitc) & 0xFF;\r
1313 for (i = len - 2; i--;)\r
1314 *p++ = bignum_byte(bn, i);\r
1315 return len;\r
1316 }\r
1317 \r
1318 /*\r
1319 * Compare two bignums. Returns like strcmp.\r
1320 */\r
1321 int bignum_cmp(Bignum a, Bignum b)\r
1322 {\r
1323 int amax = a[0], bmax = b[0];\r
1324 int i;\r
1325 \r
1326 /* Annoyingly we have two representations of zero */\r
1327 if (amax == 1 && a[amax] == 0)\r
1328 amax = 0;\r
1329 if (bmax == 1 && b[bmax] == 0)\r
1330 bmax = 0;\r
1331 \r
1332 assert(amax == 0 || a[amax] != 0);\r
1333 assert(bmax == 0 || b[bmax] != 0);\r
1334 \r
1335 i = (amax > bmax ? amax : bmax);\r
1336 while (i) {\r
1337 BignumInt aval = (i > amax ? 0 : a[i]);\r
1338 BignumInt bval = (i > bmax ? 0 : b[i]);\r
1339 if (aval < bval)\r
1340 return -1;\r
1341 if (aval > bval)\r
1342 return +1;\r
1343 i--;\r
1344 }\r
1345 return 0;\r
1346 }\r
1347 \r
1348 /*\r
1349 * Right-shift one bignum to form another.\r
1350 */\r
1351 Bignum bignum_rshift(Bignum a, int shift)\r
1352 {\r
1353 Bignum ret;\r
1354 int i, shiftw, shiftb, shiftbb, bits;\r
1355 BignumInt ai, ai1;\r
1356 \r
1357 assert(shift >= 0);\r
1358 \r
1359 bits = bignum_bitcount(a) - shift;\r
1360 ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);\r
1361 \r
1362 if (ret) {\r
1363 shiftw = shift / BIGNUM_INT_BITS;\r
1364 shiftb = shift % BIGNUM_INT_BITS;\r
1365 shiftbb = BIGNUM_INT_BITS - shiftb;\r
1366 \r
1367 ai1 = a[shiftw + 1];\r
1368 for (i = 1; i <= (int)ret[0]; i++) {\r
1369 ai = ai1;\r
1370 ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0);\r
1371 ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK;\r
1372 }\r
1373 }\r
1374 \r
1375 return ret;\r
1376 }\r
1377 \r
1378 /*\r
1379 * Non-modular multiplication and addition.\r
1380 */\r
1381 Bignum bigmuladd(Bignum a, Bignum b, Bignum addend)\r
1382 {\r
1383 int alen = a[0], blen = b[0];\r
1384 int mlen = (alen > blen ? alen : blen);\r
1385 int rlen, i, maxspot;\r
1386 int wslen;\r
1387 BignumInt *workspace;\r
1388 Bignum ret;\r
1389 \r
1390 /* mlen space for a, mlen space for b, 2*mlen for result,\r
1391 * plus scratch space for multiplication */\r
1392 wslen = mlen * 4 + mul_compute_scratch(mlen);\r
1393 workspace = snewn(wslen, BignumInt);\r
1394 for (i = 0; i < mlen; i++) {\r
1395 workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0);\r
1396 workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0);\r
1397 }\r
1398 \r
1399 internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,\r
1400 workspace + 2 * mlen, mlen, workspace + 4 * mlen);\r
1401 \r
1402 /* now just copy the result back */\r
1403 rlen = alen + blen + 1;\r
1404 if (addend && rlen <= (int)addend[0])\r
1405 rlen = addend[0] + 1;\r
1406 ret = newbn(rlen);\r
1407 maxspot = 0;\r
1408 for (i = 1; i <= (int)ret[0]; i++) {\r
1409 ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);\r
1410 if (ret[i] != 0)\r
1411 maxspot = i;\r
1412 }\r
1413 ret[0] = maxspot;\r
1414 \r
1415 /* now add in the addend, if any */\r
1416 if (addend) {\r
1417 BignumDblInt carry = 0;\r
1418 for (i = 1; i <= rlen; i++) {\r
1419 carry += (i <= (int)ret[0] ? ret[i] : 0);\r
1420 carry += (i <= (int)addend[0] ? addend[i] : 0);\r
1421 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
1422 carry >>= BIGNUM_INT_BITS;\r
1423 if (ret[i] != 0 && i > maxspot)\r
1424 maxspot = i;\r
1425 }\r
1426 }\r
1427 ret[0] = maxspot;\r
1428 \r
1429 smemclr(workspace, wslen * sizeof(*workspace));\r
1430 sfree(workspace);\r
1431 return ret;\r
1432 }\r
1433 \r
1434 /*\r
1435 * Non-modular multiplication.\r
1436 */\r
1437 Bignum bigmul(Bignum a, Bignum b)\r
1438 {\r
1439 return bigmuladd(a, b, NULL);\r
1440 }\r
1441 \r
1442 /*\r
1443 * Simple addition.\r
1444 */\r
1445 Bignum bigadd(Bignum a, Bignum b)\r
1446 {\r
1447 int alen = a[0], blen = b[0];\r
1448 int rlen = (alen > blen ? alen : blen) + 1;\r
1449 int i, maxspot;\r
1450 Bignum ret;\r
1451 BignumDblInt carry;\r
1452 \r
1453 ret = newbn(rlen);\r
1454 \r
1455 carry = 0;\r
1456 maxspot = 0;\r
1457 for (i = 1; i <= rlen; i++) {\r
1458 carry += (i <= (int)a[0] ? a[i] : 0);\r
1459 carry += (i <= (int)b[0] ? b[i] : 0);\r
1460 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
1461 carry >>= BIGNUM_INT_BITS;\r
1462 if (ret[i] != 0 && i > maxspot)\r
1463 maxspot = i;\r
1464 }\r
1465 ret[0] = maxspot;\r
1466 \r
1467 return ret;\r
1468 }\r
1469 \r
1470 /*\r
1471 * Subtraction. Returns a-b, or NULL if the result would come out\r
1472 * negative (recall that this entire bignum module only handles\r
1473 * positive numbers).\r
1474 */\r
1475 Bignum bigsub(Bignum a, Bignum b)\r
1476 {\r
1477 int alen = a[0], blen = b[0];\r
1478 int rlen = (alen > blen ? alen : blen);\r
1479 int i, maxspot;\r
1480 Bignum ret;\r
1481 BignumDblInt carry;\r
1482 \r
1483 ret = newbn(rlen);\r
1484 \r
1485 carry = 1;\r
1486 maxspot = 0;\r
1487 for (i = 1; i <= rlen; i++) {\r
1488 carry += (i <= (int)a[0] ? a[i] : 0);\r
1489 carry += (i <= (int)b[0] ? b[i] ^ BIGNUM_INT_MASK : BIGNUM_INT_MASK);\r
1490 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
1491 carry >>= BIGNUM_INT_BITS;\r
1492 if (ret[i] != 0 && i > maxspot)\r
1493 maxspot = i;\r
1494 }\r
1495 ret[0] = maxspot;\r
1496 \r
1497 if (!carry) {\r
1498 freebn(ret);\r
1499 return NULL;\r
1500 }\r
1501 \r
1502 return ret;\r
1503 }\r
1504 \r
1505 /*\r
1506 * Create a bignum which is the bitmask covering another one. That\r
1507 * is, the smallest integer which is >= N and is also one less than\r
1508 * a power of two.\r
1509 */\r
1510 Bignum bignum_bitmask(Bignum n)\r
1511 {\r
1512 Bignum ret = copybn(n);\r
1513 int i;\r
1514 BignumInt j;\r
1515 \r
1516 i = ret[0];\r
1517 while (n[i] == 0 && i > 0)\r
1518 i--;\r
1519 if (i <= 0)\r
1520 return ret; /* input was zero */\r
1521 j = 1;\r
1522 while (j < n[i])\r
1523 j = 2 * j + 1;\r
1524 ret[i] = j;\r
1525 while (--i > 0)\r
1526 ret[i] = BIGNUM_INT_MASK;\r
1527 return ret;\r
1528 }\r
1529 \r
1530 /*\r
1531 * Convert a (max 32-bit) long into a bignum.\r
1532 */\r
1533 Bignum bignum_from_long(unsigned long nn)\r
1534 {\r
1535 Bignum ret;\r
1536 BignumDblInt n = nn;\r
1537 \r
1538 ret = newbn(3);\r
1539 ret[1] = (BignumInt)(n & BIGNUM_INT_MASK);\r
1540 ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK);\r
1541 ret[3] = 0;\r
1542 ret[0] = (ret[2] ? 2 : 1);\r
1543 return ret;\r
1544 }\r
1545 \r
1546 /*\r
1547 * Add a long to a bignum.\r
1548 */\r
1549 Bignum bignum_add_long(Bignum number, unsigned long addendx)\r
1550 {\r
1551 Bignum ret = newbn(number[0] + 1);\r
1552 int i, maxspot = 0;\r
1553 BignumDblInt carry = 0, addend = addendx;\r
1554 \r
1555 for (i = 1; i <= (int)ret[0]; i++) {\r
1556 carry += addend & BIGNUM_INT_MASK;\r
1557 carry += (i <= (int)number[0] ? number[i] : 0);\r
1558 addend >>= BIGNUM_INT_BITS;\r
1559 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
1560 carry >>= BIGNUM_INT_BITS;\r
1561 if (ret[i] != 0)\r
1562 maxspot = i;\r
1563 }\r
1564 ret[0] = maxspot;\r
1565 return ret;\r
1566 }\r
1567 \r
1568 /*\r
1569 * Compute the residue of a bignum, modulo a (max 16-bit) short.\r
1570 */\r
1571 unsigned short bignum_mod_short(Bignum number, unsigned short modulus)\r
1572 {\r
1573 BignumDblInt mod, r;\r
1574 int i;\r
1575 \r
1576 r = 0;\r
1577 mod = modulus;\r
1578 for (i = number[0]; i > 0; i--)\r
1579 r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod;\r
1580 return (unsigned short) r;\r
1581 }\r
1582 \r
1583 #ifdef DEBUG\r
1584 void diagbn(char *prefix, Bignum md)\r
1585 {\r
1586 int i, nibbles, morenibbles;\r
1587 static const char hex[] = "0123456789ABCDEF";\r
1588 \r
1589 debug(("%s0x", prefix ? prefix : ""));\r
1590 \r
1591 nibbles = (3 + bignum_bitcount(md)) / 4;\r
1592 if (nibbles < 1)\r
1593 nibbles = 1;\r
1594 morenibbles = 4 * md[0] - nibbles;\r
1595 for (i = 0; i < morenibbles; i++)\r
1596 debug(("-"));\r
1597 for (i = nibbles; i--;)\r
1598 debug(("%c",\r
1599 hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));\r
1600 \r
1601 if (prefix)\r
1602 debug(("\n"));\r
1603 }\r
1604 #endif\r
1605 \r
1606 /*\r
1607 * Simple division.\r
1608 */\r
1609 Bignum bigdiv(Bignum a, Bignum b)\r
1610 {\r
1611 Bignum q = newbn(a[0]);\r
1612 bigdivmod(a, b, NULL, q);\r
1613 while (q[0] > 1 && q[q[0]] == 0)\r
1614 q[0]--;\r
1615 return q;\r
1616 }\r
1617 \r
1618 /*\r
1619 * Simple remainder.\r
1620 */\r
1621 Bignum bigmod(Bignum a, Bignum b)\r
1622 {\r
1623 Bignum r = newbn(b[0]);\r
1624 bigdivmod(a, b, r, NULL);\r
1625 while (r[0] > 1 && r[r[0]] == 0)\r
1626 r[0]--;\r
1627 return r;\r
1628 }\r
1629 \r
1630 /*\r
1631 * Greatest common divisor.\r
1632 */\r
1633 Bignum biggcd(Bignum av, Bignum bv)\r
1634 {\r
1635 Bignum a = copybn(av);\r
1636 Bignum b = copybn(bv);\r
1637 \r
1638 while (bignum_cmp(b, Zero) != 0) {\r
1639 Bignum t = newbn(b[0]);\r
1640 bigdivmod(a, b, t, NULL);\r
1641 while (t[0] > 1 && t[t[0]] == 0)\r
1642 t[0]--;\r
1643 freebn(a);\r
1644 a = b;\r
1645 b = t;\r
1646 }\r
1647 \r
1648 freebn(b);\r
1649 return a;\r
1650 }\r
1651 \r
1652 /*\r
1653 * Modular inverse, using Euclid's extended algorithm.\r
1654 */\r
1655 Bignum modinv(Bignum number, Bignum modulus)\r
1656 {\r
1657 Bignum a = copybn(modulus);\r
1658 Bignum b = copybn(number);\r
1659 Bignum xp = copybn(Zero);\r
1660 Bignum x = copybn(One);\r
1661 int sign = +1;\r
1662 \r
1663 assert(number[number[0]] != 0);\r
1664 assert(modulus[modulus[0]] != 0);\r
1665 \r
1666 while (bignum_cmp(b, One) != 0) {\r
1667 Bignum t, q;\r
1668 \r
1669 if (bignum_cmp(b, Zero) == 0) {\r
1670 /*\r
1671 * Found a common factor between the inputs, so we cannot\r
1672 * return a modular inverse at all.\r
1673 */\r
1674 freebn(b);\r
1675 freebn(a);\r
1676 freebn(xp);\r
1677 freebn(x);\r
1678 return NULL;\r
1679 }\r
1680 \r
1681 t = newbn(b[0]);\r
1682 q = newbn(a[0]);\r
1683 bigdivmod(a, b, t, q);\r
1684 while (t[0] > 1 && t[t[0]] == 0)\r
1685 t[0]--;\r
1686 while (q[0] > 1 && q[q[0]] == 0)\r
1687 q[0]--;\r
1688 freebn(a);\r
1689 a = b;\r
1690 b = t;\r
1691 t = xp;\r
1692 xp = x;\r
1693 x = bigmuladd(q, xp, t);\r
1694 sign = -sign;\r
1695 freebn(t);\r
1696 freebn(q);\r
1697 }\r
1698 \r
1699 freebn(b);\r
1700 freebn(a);\r
1701 freebn(xp);\r
1702 \r
1703 /* now we know that sign * x == 1, and that x < modulus */\r
1704 if (sign < 0) {\r
1705 /* set a new x to be modulus - x */\r
1706 Bignum newx = newbn(modulus[0]);\r
1707 BignumInt carry = 0;\r
1708 int maxspot = 1;\r
1709 int i;\r
1710 \r
1711 for (i = 1; i <= (int)newx[0]; i++) {\r
1712 BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0);\r
1713 BignumInt bword = (i <= (int)x[0] ? x[i] : 0);\r
1714 newx[i] = aword - bword - carry;\r
1715 bword = ~bword;\r
1716 carry = carry ? (newx[i] >= bword) : (newx[i] > bword);\r
1717 if (newx[i] != 0)\r
1718 maxspot = i;\r
1719 }\r
1720 newx[0] = maxspot;\r
1721 freebn(x);\r
1722 x = newx;\r
1723 }\r
1724 \r
1725 /* and return. */\r
1726 return x;\r
1727 }\r
1728 \r
1729 /*\r
1730 * Render a bignum into decimal. Return a malloced string holding\r
1731 * the decimal representation.\r
1732 */\r
1733 char *bignum_decimal(Bignum x)\r
1734 {\r
1735 int ndigits, ndigit;\r
1736 int i, iszero;\r
1737 BignumDblInt carry;\r
1738 char *ret;\r
1739 BignumInt *workspace;\r
1740 \r
1741 /*\r
1742 * First, estimate the number of digits. Since log(10)/log(2)\r
1743 * is just greater than 93/28 (the joys of continued fraction\r
1744 * approximations...) we know that for every 93 bits, we need\r
1745 * at most 28 digits. This will tell us how much to malloc.\r
1746 *\r
1747 * Formally: if x has i bits, that means x is strictly less\r
1748 * than 2^i. Since 2 is less than 10^(28/93), this is less than\r
1749 * 10^(28i/93). We need an integer power of ten, so we must\r
1750 * round up (rounding down might make it less than x again).\r
1751 * Therefore if we multiply the bit count by 28/93, rounding\r
1752 * up, we will have enough digits.\r
1753 *\r
1754 * i=0 (i.e., x=0) is an irritating special case.\r
1755 */\r
1756 i = bignum_bitcount(x);\r
1757 if (!i)\r
1758 ndigits = 1; /* x = 0 */\r
1759 else\r
1760 ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */\r
1761 ndigits++; /* allow for trailing \0 */\r
1762 ret = snewn(ndigits, char);\r
1763 \r
1764 /*\r
1765 * Now allocate some workspace to hold the binary form as we\r
1766 * repeatedly divide it by ten. Initialise this to the\r
1767 * big-endian form of the number.\r
1768 */\r
1769 workspace = snewn(x[0], BignumInt);\r
1770 for (i = 0; i < (int)x[0]; i++)\r
1771 workspace[i] = x[x[0] - i];\r
1772 \r
1773 /*\r
1774 * Next, write the decimal number starting with the last digit.\r
1775 * We use ordinary short division, dividing 10 into the\r
1776 * workspace.\r
1777 */\r
1778 ndigit = ndigits - 1;\r
1779 ret[ndigit] = '\0';\r
1780 do {\r
1781 iszero = 1;\r
1782 carry = 0;\r
1783 for (i = 0; i < (int)x[0]; i++) {\r
1784 carry = (carry << BIGNUM_INT_BITS) + workspace[i];\r
1785 workspace[i] = (BignumInt) (carry / 10);\r
1786 if (workspace[i])\r
1787 iszero = 0;\r
1788 carry %= 10;\r
1789 }\r
1790 ret[--ndigit] = (char) (carry + '0');\r
1791 } while (!iszero);\r
1792 \r
1793 /*\r
1794 * There's a chance we've fallen short of the start of the\r
1795 * string. Correct if so.\r
1796 */\r
1797 if (ndigit > 0)\r
1798 memmove(ret, ret + ndigit, ndigits - ndigit);\r
1799 \r
1800 /*\r
1801 * Done.\r
1802 */\r
1803 smemclr(workspace, x[0] * sizeof(*workspace));\r
1804 sfree(workspace);\r
1805 return ret;\r
1806 }\r
1807 \r
1808 #ifdef TESTBN\r
1809 \r
1810 #include <stdio.h>\r
1811 #include <stdlib.h>\r
1812 #include <ctype.h>\r
1813 \r
1814 /*\r
1815 * gcc -Wall -g -O0 -DTESTBN -o testbn sshbn.c misc.c conf.c tree234.c unix/uxmisc.c -I. -I unix -I charset\r
1816 *\r
1817 * Then feed to this program's standard input the output of\r
1818 * testdata/bignum.py .\r
1819 */\r
1820 \r
1821 void modalfatalbox(char *p, ...)\r
1822 {\r
1823 va_list ap;\r
1824 fprintf(stderr, "FATAL ERROR: ");\r
1825 va_start(ap, p);\r
1826 vfprintf(stderr, p, ap);\r
1827 va_end(ap);\r
1828 fputc('\n', stderr);\r
1829 exit(1);\r
1830 }\r
1831 \r
1832 #define fromxdigit(c) ( (c)>'9' ? ((c)&0xDF) - 'A' + 10 : (c) - '0' )\r
1833 \r
1834 int main(int argc, char **argv)\r
1835 {\r
1836 char *buf;\r
1837 int line = 0;\r
1838 int passes = 0, fails = 0;\r
1839 \r
1840 while ((buf = fgetline(stdin)) != NULL) {\r
1841 int maxlen = strlen(buf);\r
1842 unsigned char *data = snewn(maxlen, unsigned char);\r
1843 unsigned char *ptrs[5], *q;\r
1844 int ptrnum;\r
1845 char *bufp = buf;\r
1846 \r
1847 line++;\r
1848 \r
1849 q = data;\r
1850 ptrnum = 0;\r
1851 \r
1852 while (*bufp && !isspace((unsigned char)*bufp))\r
1853 bufp++;\r
1854 if (bufp)\r
1855 *bufp++ = '\0';\r
1856 \r
1857 while (*bufp) {\r
1858 char *start, *end;\r
1859 int i;\r
1860 \r
1861 while (*bufp && !isxdigit((unsigned char)*bufp))\r
1862 bufp++;\r
1863 start = bufp;\r
1864 \r
1865 if (!*bufp)\r
1866 break;\r
1867 \r
1868 while (*bufp && isxdigit((unsigned char)*bufp))\r
1869 bufp++;\r
1870 end = bufp;\r
1871 \r
1872 if (ptrnum >= lenof(ptrs))\r
1873 break;\r
1874 ptrs[ptrnum++] = q;\r
1875 \r
1876 for (i = -((end - start) & 1); i < end-start; i += 2) {\r
1877 unsigned char val = (i < 0 ? 0 : fromxdigit(start[i]));\r
1878 val = val * 16 + fromxdigit(start[i+1]);\r
1879 *q++ = val;\r
1880 }\r
1881 \r
1882 ptrs[ptrnum] = q;\r
1883 }\r
1884 \r
1885 if (!strcmp(buf, "mul")) {\r
1886 Bignum a, b, c, p;\r
1887 \r
1888 if (ptrnum != 3) {\r
1889 printf("%d: mul with %d parameters, expected 3\n", line, ptrnum);\r
1890 exit(1);\r
1891 }\r
1892 a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);\r
1893 b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);\r
1894 c = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);\r
1895 p = bigmul(a, b);\r
1896 \r
1897 if (bignum_cmp(c, p) == 0) {\r
1898 passes++;\r
1899 } else {\r
1900 char *as = bignum_decimal(a);\r
1901 char *bs = bignum_decimal(b);\r
1902 char *cs = bignum_decimal(c);\r
1903 char *ps = bignum_decimal(p);\r
1904 \r
1905 printf("%d: fail: %s * %s gave %s expected %s\n",\r
1906 line, as, bs, ps, cs);\r
1907 fails++;\r
1908 \r
1909 sfree(as);\r
1910 sfree(bs);\r
1911 sfree(cs);\r
1912 sfree(ps);\r
1913 }\r
1914 freebn(a);\r
1915 freebn(b);\r
1916 freebn(c);\r
1917 freebn(p);\r
1918 } else if (!strcmp(buf, "modmul")) {\r
1919 Bignum a, b, m, c, p;\r
1920 \r
1921 if (ptrnum != 4) {\r
1922 printf("%d: modmul with %d parameters, expected 4\n",\r
1923 line, ptrnum);\r
1924 exit(1);\r
1925 }\r
1926 a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);\r
1927 b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);\r
1928 m = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);\r
1929 c = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);\r
1930 p = modmul(a, b, m);\r
1931 \r
1932 if (bignum_cmp(c, p) == 0) {\r
1933 passes++;\r
1934 } else {\r
1935 char *as = bignum_decimal(a);\r
1936 char *bs = bignum_decimal(b);\r
1937 char *ms = bignum_decimal(m);\r
1938 char *cs = bignum_decimal(c);\r
1939 char *ps = bignum_decimal(p);\r
1940 \r
1941 printf("%d: fail: %s * %s mod %s gave %s expected %s\n",\r
1942 line, as, bs, ms, ps, cs);\r
1943 fails++;\r
1944 \r
1945 sfree(as);\r
1946 sfree(bs);\r
1947 sfree(ms);\r
1948 sfree(cs);\r
1949 sfree(ps);\r
1950 }\r
1951 freebn(a);\r
1952 freebn(b);\r
1953 freebn(m);\r
1954 freebn(c);\r
1955 freebn(p);\r
1956 } else if (!strcmp(buf, "pow")) {\r
1957 Bignum base, expt, modulus, expected, answer;\r
1958 \r
1959 if (ptrnum != 4) {\r
1960 printf("%d: mul with %d parameters, expected 4\n", line, ptrnum);\r
1961 exit(1);\r
1962 }\r
1963 \r
1964 base = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);\r
1965 expt = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);\r
1966 modulus = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);\r
1967 expected = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);\r
1968 answer = modpow(base, expt, modulus);\r
1969 \r
1970 if (bignum_cmp(expected, answer) == 0) {\r
1971 passes++;\r
1972 } else {\r
1973 char *as = bignum_decimal(base);\r
1974 char *bs = bignum_decimal(expt);\r
1975 char *cs = bignum_decimal(modulus);\r
1976 char *ds = bignum_decimal(answer);\r
1977 char *ps = bignum_decimal(expected);\r
1978 \r
1979 printf("%d: fail: %s ^ %s mod %s gave %s expected %s\n",\r
1980 line, as, bs, cs, ds, ps);\r
1981 fails++;\r
1982 \r
1983 sfree(as);\r
1984 sfree(bs);\r
1985 sfree(cs);\r
1986 sfree(ds);\r
1987 sfree(ps);\r
1988 }\r
1989 freebn(base);\r
1990 freebn(expt);\r
1991 freebn(modulus);\r
1992 freebn(expected);\r
1993 freebn(answer);\r
1994 } else {\r
1995 printf("%d: unrecognised test keyword: '%s'\n", line, buf);\r
1996 exit(1);\r
1997 }\r
1998 \r
1999 sfree(buf);\r
2000 sfree(data);\r
2001 }\r
2002 \r
2003 printf("passed %d failed %d total %d\n", passes, fails, passes+fails);\r
2004 return fails != 0;\r
2005 }\r
2006 \r
2007 #endif\r