e5574168 |
1 | /* |
2 | * Bignum routines for RSA and DH and stuff. |
3 | */ |
4 | |
5 | #include <stdio.h> |
6 | #include <stdlib.h> |
7 | #include <string.h> |
8 | |
9 | #include "ssh.h" |
10 | |
7cca0d81 |
11 | unsigned short bnZero[1] = { 0 }; |
12 | unsigned short bnOne[2] = { 1, 1 }; |
e5574168 |
13 | |
7cca0d81 |
14 | Bignum Zero = bnZero, One = bnOne; |
e5574168 |
15 | |
16 | Bignum newbn(int length) { |
17 | Bignum b = malloc((length+1)*sizeof(unsigned short)); |
18 | if (!b) |
19 | abort(); /* FIXME */ |
20 | memset(b, 0, (length+1)*sizeof(*b)); |
21 | b[0] = length; |
22 | return b; |
23 | } |
24 | |
7cca0d81 |
25 | Bignum copybn(Bignum orig) { |
26 | Bignum b = malloc((orig[0]+1)*sizeof(unsigned short)); |
27 | if (!b) |
28 | abort(); /* FIXME */ |
29 | memcpy(b, orig, (orig[0]+1)*sizeof(*b)); |
30 | return b; |
31 | } |
32 | |
e5574168 |
33 | void freebn(Bignum b) { |
34 | /* |
35 | * Burn the evidence, just in case. |
36 | */ |
37 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
38 | free(b); |
39 | } |
40 | |
41 | /* |
42 | * Compute c = a * b. |
43 | * Input is in the first len words of a and b. |
44 | * Result is returned in the first 2*len words of c. |
45 | */ |
9400cf6f |
46 | static void internal_mul(unsigned short *a, unsigned short *b, |
47 | unsigned short *c, int len) |
e5574168 |
48 | { |
49 | int i, j; |
50 | unsigned long ai, t; |
51 | |
9400cf6f |
52 | for (j = 0; j < 2*len; j++) |
53 | c[j] = 0; |
e5574168 |
54 | |
55 | for (i = len - 1; i >= 0; i--) { |
56 | ai = a[i]; |
57 | t = 0; |
58 | for (j = len - 1; j >= 0; j--) { |
59 | t += ai * (unsigned long) b[j]; |
60 | t += (unsigned long) c[i+j+1]; |
61 | c[i+j+1] = (unsigned short)t; |
62 | t = t >> 16; |
63 | } |
64 | c[i] = (unsigned short)t; |
65 | } |
66 | } |
67 | |
6e522441 |
68 | static void internal_add_shifted(unsigned short *number, |
69 | unsigned n, int shift) { |
9400cf6f |
70 | int word = 1 + (shift / 16); |
71 | int bshift = shift % 16; |
6e522441 |
72 | unsigned long addend; |
9400cf6f |
73 | |
74 | addend = n << bshift; |
75 | |
76 | while (addend) { |
77 | addend += number[word]; |
6e522441 |
78 | number[word] = (unsigned short) addend & 0xFFFF; |
9400cf6f |
79 | addend >>= 16; |
80 | word++; |
81 | } |
82 | } |
83 | |
e5574168 |
84 | /* |
85 | * Compute a = a % m. |
9400cf6f |
86 | * Input in first alen words of a and first mlen words of m. |
87 | * Output in first alen words of a |
88 | * (of which first alen-mlen words will be zero). |
e5574168 |
89 | * The MSW of m MUST have its high bit set. |
9400cf6f |
90 | * Quotient is accumulated in the `quotient' array, which is a Bignum |
91 | * rather than the internal bigendian format. Quotient parts are shifted |
92 | * left by `qshift' before adding into quot. |
e5574168 |
93 | */ |
9400cf6f |
94 | static void internal_mod(unsigned short *a, int alen, |
95 | unsigned short *m, int mlen, |
96 | unsigned short *quot, int qshift) |
e5574168 |
97 | { |
98 | unsigned short m0, m1; |
99 | unsigned int h; |
100 | int i, k; |
101 | |
e5574168 |
102 | m0 = m[0]; |
9400cf6f |
103 | if (mlen > 1) |
104 | m1 = m[1]; |
105 | else |
106 | m1 = 0; |
e5574168 |
107 | |
9400cf6f |
108 | for (i = 0; i <= alen-mlen; i++) { |
e5574168 |
109 | unsigned long t; |
9400cf6f |
110 | unsigned int q, r, c, ai1; |
e5574168 |
111 | |
112 | if (i == 0) { |
113 | h = 0; |
114 | } else { |
115 | h = a[i-1]; |
116 | a[i-1] = 0; |
117 | } |
118 | |
9400cf6f |
119 | if (i == alen-1) |
120 | ai1 = 0; |
121 | else |
122 | ai1 = a[i+1]; |
123 | |
e5574168 |
124 | /* Find q = h:a[i] / m0 */ |
125 | t = ((unsigned long) h << 16) + a[i]; |
126 | q = t / m0; |
127 | r = t % m0; |
128 | |
129 | /* Refine our estimate of q by looking at |
130 | h:a[i]:a[i+1] / m0:m1 */ |
131 | t = (long) m1 * (long) q; |
9400cf6f |
132 | if (t > ((unsigned long) r << 16) + ai1) { |
e5574168 |
133 | q--; |
134 | t -= m1; |
135 | r = (r + m0) & 0xffff; /* overflow? */ |
136 | if (r >= (unsigned long)m0 && |
9400cf6f |
137 | t > ((unsigned long) r << 16) + ai1) |
e5574168 |
138 | q--; |
139 | } |
140 | |
9400cf6f |
141 | /* Subtract q * m from a[i...] */ |
e5574168 |
142 | c = 0; |
9400cf6f |
143 | for (k = mlen - 1; k >= 0; k--) { |
e5574168 |
144 | t = (long) q * (long) m[k]; |
145 | t += c; |
146 | c = t >> 16; |
147 | if ((unsigned short) t > a[i+k]) c++; |
148 | a[i+k] -= (unsigned short) t; |
149 | } |
150 | |
151 | /* Add back m in case of borrow */ |
152 | if (c != h) { |
153 | t = 0; |
9400cf6f |
154 | for (k = mlen - 1; k >= 0; k--) { |
e5574168 |
155 | t += m[k]; |
156 | t += a[i+k]; |
157 | a[i+k] = (unsigned short)t; |
158 | t = t >> 16; |
159 | } |
9400cf6f |
160 | q--; |
e5574168 |
161 | } |
9400cf6f |
162 | if (quot) |
163 | internal_add_shifted(quot, q, qshift + 16 * (alen-mlen-i)); |
e5574168 |
164 | } |
165 | } |
166 | |
167 | /* |
168 | * Compute (base ^ exp) % mod. |
169 | * The base MUST be smaller than the modulus. |
170 | * The most significant word of mod MUST be non-zero. |
171 | * We assume that the result array is the same size as the mod array. |
172 | */ |
173 | void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) |
174 | { |
175 | unsigned short *a, *b, *n, *m; |
176 | int mshift; |
177 | int mlen, i, j; |
178 | |
179 | /* Allocate m of size mlen, copy mod to m */ |
180 | /* We use big endian internally */ |
181 | mlen = mod[0]; |
182 | m = malloc(mlen * sizeof(unsigned short)); |
183 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
184 | |
185 | /* Shift m left to make msb bit set */ |
186 | for (mshift = 0; mshift < 15; mshift++) |
187 | if ((m[0] << mshift) & 0x8000) break; |
188 | if (mshift) { |
189 | for (i = 0; i < mlen - 1; i++) |
190 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
191 | m[mlen-1] = m[mlen-1] << mshift; |
192 | } |
193 | |
194 | /* Allocate n of size mlen, copy base to n */ |
195 | n = malloc(mlen * sizeof(unsigned short)); |
196 | i = mlen - base[0]; |
197 | for (j = 0; j < i; j++) n[j] = 0; |
198 | for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; |
199 | |
200 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
201 | a = malloc(2 * mlen * sizeof(unsigned short)); |
202 | b = malloc(2 * mlen * sizeof(unsigned short)); |
203 | for (i = 0; i < 2*mlen; i++) a[i] = 0; |
204 | a[2*mlen-1] = 1; |
205 | |
206 | /* Skip leading zero bits of exp. */ |
207 | i = 0; j = 15; |
208 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
209 | j--; |
210 | if (j < 0) { i++; j = 15; } |
211 | } |
212 | |
213 | /* Main computation */ |
214 | while (i < exp[0]) { |
215 | while (j >= 0) { |
9400cf6f |
216 | internal_mul(a + mlen, a + mlen, b, mlen); |
217 | internal_mod(b, mlen*2, m, mlen, NULL, 0); |
e5574168 |
218 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
9400cf6f |
219 | internal_mul(b + mlen, n, a, mlen); |
220 | internal_mod(a, mlen*2, m, mlen, NULL, 0); |
e5574168 |
221 | } else { |
222 | unsigned short *t; |
223 | t = a; a = b; b = t; |
224 | } |
225 | j--; |
226 | } |
227 | i++; j = 15; |
228 | } |
229 | |
230 | /* Fixup result in case the modulus was shifted */ |
231 | if (mshift) { |
232 | for (i = mlen - 1; i < 2*mlen - 1; i++) |
233 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
234 | a[2*mlen-1] = a[2*mlen-1] << mshift; |
9400cf6f |
235 | internal_mod(a, mlen*2, m, mlen, NULL, 0); |
e5574168 |
236 | for (i = 2*mlen - 1; i >= mlen; i--) |
237 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
238 | } |
239 | |
240 | /* Copy result to buffer */ |
241 | for (i = 0; i < mlen; i++) |
242 | result[result[0] - i] = a[i+mlen]; |
243 | |
244 | /* Free temporary arrays */ |
245 | for (i = 0; i < 2*mlen; i++) a[i] = 0; free(a); |
246 | for (i = 0; i < 2*mlen; i++) b[i] = 0; free(b); |
247 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
248 | for (i = 0; i < mlen; i++) n[i] = 0; free(n); |
249 | } |
7cca0d81 |
250 | |
251 | /* |
252 | * Compute (p * q) % mod. |
253 | * The most significant word of mod MUST be non-zero. |
254 | * We assume that the result array is the same size as the mod array. |
255 | */ |
256 | void modmul(Bignum p, Bignum q, Bignum mod, Bignum result) |
257 | { |
258 | unsigned short *a, *n, *m, *o; |
259 | int mshift; |
260 | int pqlen, mlen, i, j; |
261 | |
262 | /* Allocate m of size mlen, copy mod to m */ |
263 | /* We use big endian internally */ |
264 | mlen = mod[0]; |
265 | m = malloc(mlen * sizeof(unsigned short)); |
266 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
267 | |
268 | /* Shift m left to make msb bit set */ |
269 | for (mshift = 0; mshift < 15; mshift++) |
270 | if ((m[0] << mshift) & 0x8000) break; |
271 | if (mshift) { |
272 | for (i = 0; i < mlen - 1; i++) |
273 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
274 | m[mlen-1] = m[mlen-1] << mshift; |
275 | } |
276 | |
277 | pqlen = (p[0] > q[0] ? p[0] : q[0]); |
278 | |
279 | /* Allocate n of size pqlen, copy p to n */ |
280 | n = malloc(pqlen * sizeof(unsigned short)); |
281 | i = pqlen - p[0]; |
282 | for (j = 0; j < i; j++) n[j] = 0; |
283 | for (j = 0; j < p[0]; j++) n[i+j] = p[p[0] - j]; |
284 | |
285 | /* Allocate o of size pqlen, copy q to o */ |
286 | o = malloc(pqlen * sizeof(unsigned short)); |
287 | i = pqlen - q[0]; |
288 | for (j = 0; j < i; j++) o[j] = 0; |
289 | for (j = 0; j < q[0]; j++) o[i+j] = q[q[0] - j]; |
290 | |
291 | /* Allocate a of size 2*pqlen for result */ |
292 | a = malloc(2 * pqlen * sizeof(unsigned short)); |
293 | |
294 | /* Main computation */ |
9400cf6f |
295 | internal_mul(n, o, a, pqlen); |
296 | internal_mod(a, pqlen*2, m, mlen, NULL, 0); |
7cca0d81 |
297 | |
298 | /* Fixup result in case the modulus was shifted */ |
299 | if (mshift) { |
300 | for (i = 2*pqlen - mlen - 1; i < 2*pqlen - 1; i++) |
301 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
302 | a[2*pqlen-1] = a[2*pqlen-1] << mshift; |
9400cf6f |
303 | internal_mod(a, pqlen*2, m, mlen, NULL, 0); |
7cca0d81 |
304 | for (i = 2*pqlen - 1; i >= 2*pqlen - mlen; i--) |
305 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
306 | } |
307 | |
308 | /* Copy result to buffer */ |
309 | for (i = 0; i < mlen; i++) |
310 | result[result[0] - i] = a[i+2*pqlen-mlen]; |
311 | |
312 | /* Free temporary arrays */ |
313 | for (i = 0; i < 2*pqlen; i++) a[i] = 0; free(a); |
314 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
315 | for (i = 0; i < pqlen; i++) n[i] = 0; free(n); |
316 | for (i = 0; i < pqlen; i++) o[i] = 0; free(o); |
317 | } |
318 | |
319 | /* |
9400cf6f |
320 | * Compute p % mod. |
321 | * The most significant word of mod MUST be non-zero. |
322 | * We assume that the result array is the same size as the mod array. |
323 | * We optionally write out a quotient. |
324 | */ |
325 | void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) |
326 | { |
327 | unsigned short *n, *m; |
328 | int mshift; |
329 | int plen, mlen, i, j; |
330 | |
331 | /* Allocate m of size mlen, copy mod to m */ |
332 | /* We use big endian internally */ |
333 | mlen = mod[0]; |
334 | m = malloc(mlen * sizeof(unsigned short)); |
335 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
336 | |
337 | /* Shift m left to make msb bit set */ |
338 | for (mshift = 0; mshift < 15; mshift++) |
339 | if ((m[0] << mshift) & 0x8000) break; |
340 | if (mshift) { |
341 | for (i = 0; i < mlen - 1; i++) |
342 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
343 | m[mlen-1] = m[mlen-1] << mshift; |
344 | } |
345 | |
346 | plen = p[0]; |
347 | /* Ensure plen > mlen */ |
348 | if (plen <= mlen) plen = mlen+1; |
349 | |
350 | /* Allocate n of size plen, copy p to n */ |
351 | n = malloc(plen * sizeof(unsigned short)); |
352 | for (j = 0; j < plen; j++) n[j] = 0; |
353 | for (j = 1; j <= p[0]; j++) n[plen-j] = p[j]; |
354 | |
355 | /* Main computation */ |
356 | internal_mod(n, plen, m, mlen, quotient, mshift); |
357 | |
358 | /* Fixup result in case the modulus was shifted */ |
359 | if (mshift) { |
360 | for (i = plen - mlen - 1; i < plen - 1; i++) |
361 | n[i] = (n[i] << mshift) | (n[i+1] >> (16-mshift)); |
362 | n[plen-1] = n[plen-1] << mshift; |
363 | internal_mod(n, plen, m, mlen, quotient, 0); |
364 | for (i = plen - 1; i >= plen - mlen; i--) |
365 | n[i] = (n[i] >> mshift) | (n[i-1] << (16-mshift)); |
366 | } |
367 | |
368 | /* Copy result to buffer */ |
369 | for (i = 1; i <= result[0]; i++) { |
370 | int j = plen-i; |
371 | result[i] = j>=0 ? n[j] : 0; |
372 | } |
373 | |
374 | /* Free temporary arrays */ |
375 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
376 | for (i = 0; i < plen; i++) n[i] = 0; free(n); |
377 | } |
378 | |
379 | /* |
7cca0d81 |
380 | * Decrement a number. |
381 | */ |
382 | void decbn(Bignum bn) { |
383 | int i = 1; |
384 | while (i < bn[0] && bn[i] == 0) |
385 | bn[i++] = 0xFFFF; |
386 | bn[i]--; |
387 | } |
388 | |
389 | /* |
390 | * Read an ssh1-format bignum from a data buffer. Return the number |
391 | * of bytes consumed. |
392 | */ |
393 | int ssh1_read_bignum(unsigned char *data, Bignum *result) { |
394 | unsigned char *p = data; |
395 | Bignum bn; |
396 | int i; |
397 | int w, b; |
398 | |
399 | w = 0; |
400 | for (i=0; i<2; i++) |
401 | w = (w << 8) + *p++; |
402 | |
403 | b = (w+7)/8; /* bits -> bytes */ |
404 | w = (w+15)/16; /* bits -> words */ |
405 | |
a52f067e |
406 | if (!result) /* just return length */ |
407 | return b + 2; |
408 | |
7cca0d81 |
409 | bn = newbn(w); |
410 | |
411 | for (i=1; i<=w; i++) |
412 | bn[i] = 0; |
413 | for (i=b; i-- ;) { |
414 | unsigned char byte = *p++; |
415 | if (i & 1) |
416 | bn[1+i/2] |= byte<<8; |
417 | else |
418 | bn[1+i/2] |= byte; |
419 | } |
420 | |
421 | *result = bn; |
422 | |
423 | return p - data; |
424 | } |
5c58ad2d |
425 | |
426 | /* |
427 | * Return the bit count of a bignum, for ssh1 encoding. |
428 | */ |
429 | int ssh1_bignum_bitcount(Bignum bn) { |
430 | int bitcount = bn[0] * 16 - 1; |
431 | |
432 | while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0) |
433 | bitcount--; |
434 | return bitcount + 1; |
435 | } |
436 | |
437 | /* |
438 | * Return the byte length of a bignum when ssh1 encoded. |
439 | */ |
440 | int ssh1_bignum_length(Bignum bn) { |
441 | return 2 + (ssh1_bignum_bitcount(bn)+7)/8; |
442 | } |
443 | |
444 | /* |
445 | * Return a byte from a bignum; 0 is least significant, etc. |
446 | */ |
447 | int bignum_byte(Bignum bn, int i) { |
448 | if (i >= 2*bn[0]) |
449 | return 0; /* beyond the end */ |
450 | else if (i & 1) |
451 | return (bn[i/2+1] >> 8) & 0xFF; |
452 | else |
453 | return (bn[i/2+1] ) & 0xFF; |
454 | } |
455 | |
456 | /* |
9400cf6f |
457 | * Return a bit from a bignum; 0 is least significant, etc. |
458 | */ |
459 | int bignum_bit(Bignum bn, int i) { |
460 | if (i >= 16*bn[0]) |
461 | return 0; /* beyond the end */ |
462 | else |
463 | return (bn[i/16+1] >> (i%16)) & 1; |
464 | } |
465 | |
466 | /* |
467 | * Set a bit in a bignum; 0 is least significant, etc. |
468 | */ |
469 | void bignum_set_bit(Bignum bn, int bitnum, int value) { |
470 | if (bitnum >= 16*bn[0]) |
471 | abort(); /* beyond the end */ |
472 | else { |
473 | int v = bitnum/16+1; |
474 | int mask = 1 << (bitnum%16); |
475 | if (value) |
476 | bn[v] |= mask; |
477 | else |
478 | bn[v] &= ~mask; |
479 | } |
480 | } |
481 | |
482 | /* |
5c58ad2d |
483 | * Write a ssh1-format bignum into a buffer. It is assumed the |
484 | * buffer is big enough. Returns the number of bytes used. |
485 | */ |
486 | int ssh1_write_bignum(void *data, Bignum bn) { |
487 | unsigned char *p = data; |
488 | int len = ssh1_bignum_length(bn); |
489 | int i; |
490 | int bitc = ssh1_bignum_bitcount(bn); |
491 | |
492 | *p++ = (bitc >> 8) & 0xFF; |
493 | *p++ = (bitc ) & 0xFF; |
494 | for (i = len-2; i-- ;) |
495 | *p++ = bignum_byte(bn, i); |
496 | return len; |
497 | } |
9400cf6f |
498 | |
499 | /* |
500 | * Compare two bignums. Returns like strcmp. |
501 | */ |
502 | int bignum_cmp(Bignum a, Bignum b) { |
503 | int amax = a[0], bmax = b[0]; |
504 | int i = (amax > bmax ? amax : bmax); |
505 | while (i) { |
506 | unsigned short aval = (i > amax ? 0 : a[i]); |
507 | unsigned short bval = (i > bmax ? 0 : b[i]); |
508 | if (aval < bval) return -1; |
509 | if (aval > bval) return +1; |
510 | i--; |
511 | } |
512 | return 0; |
513 | } |
514 | |
515 | /* |
516 | * Right-shift one bignum to form another. |
517 | */ |
518 | Bignum bignum_rshift(Bignum a, int shift) { |
519 | Bignum ret; |
520 | int i, shiftw, shiftb, shiftbb, bits; |
521 | unsigned short ai, ai1; |
522 | |
523 | bits = ssh1_bignum_bitcount(a) - shift; |
524 | ret = newbn((bits+15)/16); |
525 | |
526 | if (ret) { |
527 | shiftw = shift / 16; |
528 | shiftb = shift % 16; |
529 | shiftbb = 16 - shiftb; |
530 | |
531 | ai1 = a[shiftw+1]; |
532 | for (i = 1; i <= ret[0]; i++) { |
533 | ai = ai1; |
534 | ai1 = (i+shiftw+1 <= a[0] ? a[i+shiftw+1] : 0); |
535 | ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & 0xFFFF; |
536 | } |
537 | } |
538 | |
539 | return ret; |
540 | } |
541 | |
542 | /* |
543 | * Non-modular multiplication and addition. |
544 | */ |
545 | Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { |
546 | int alen = a[0], blen = b[0]; |
547 | int mlen = (alen > blen ? alen : blen); |
548 | int rlen, i, maxspot; |
549 | unsigned short *workspace; |
550 | Bignum ret; |
551 | |
552 | /* mlen space for a, mlen space for b, 2*mlen for result */ |
553 | workspace = malloc(mlen * 4 * sizeof(unsigned short)); |
554 | for (i = 0; i < mlen; i++) { |
555 | workspace[0*mlen + i] = (mlen-i <= a[0] ? a[mlen-i] : 0); |
556 | workspace[1*mlen + i] = (mlen-i <= b[0] ? b[mlen-i] : 0); |
557 | } |
558 | |
559 | internal_mul(workspace+0*mlen, workspace+1*mlen, workspace+2*mlen, mlen); |
560 | |
561 | /* now just copy the result back */ |
562 | rlen = alen + blen + 1; |
563 | if (addend && rlen <= addend[0]) |
564 | rlen = addend[0] + 1; |
565 | ret = newbn(rlen); |
566 | maxspot = 0; |
567 | for (i = 1; i <= ret[0]; i++) { |
568 | ret[i] = (i <= 2*mlen ? workspace[4*mlen - i] : 0); |
569 | if (ret[i] != 0) |
570 | maxspot = i; |
571 | } |
572 | ret[0] = maxspot; |
573 | |
574 | /* now add in the addend, if any */ |
575 | if (addend) { |
576 | unsigned long carry = 0; |
577 | for (i = 1; i <= rlen; i++) { |
578 | carry += (i <= ret[0] ? ret[i] : 0); |
579 | carry += (i <= addend[0] ? addend[i] : 0); |
6e522441 |
580 | ret[i] = (unsigned short) carry & 0xFFFF; |
9400cf6f |
581 | carry >>= 16; |
582 | if (ret[i] != 0 && i > maxspot) |
583 | maxspot = i; |
584 | } |
585 | } |
586 | ret[0] = maxspot; |
587 | |
588 | return ret; |
589 | } |
590 | |
591 | /* |
592 | * Non-modular multiplication. |
593 | */ |
594 | Bignum bigmul(Bignum a, Bignum b) { |
595 | return bigmuladd(a, b, NULL); |
596 | } |
597 | |
598 | /* |
599 | * Convert a (max 16-bit) short into a bignum. |
600 | */ |
601 | Bignum bignum_from_short(unsigned short n) { |
602 | Bignum ret; |
603 | |
604 | ret = newbn(2); |
605 | ret[1] = n & 0xFFFF; |
606 | ret[2] = (n >> 16) & 0xFFFF; |
607 | ret[0] = (ret[2] ? 2 : 1); |
608 | return ret; |
609 | } |
610 | |
611 | /* |
612 | * Add a long to a bignum. |
613 | */ |
614 | Bignum bignum_add_long(Bignum number, unsigned long addend) { |
615 | Bignum ret = newbn(number[0]+1); |
616 | int i, maxspot = 0; |
617 | unsigned long carry = 0; |
618 | |
619 | for (i = 1; i <= ret[0]; i++) { |
620 | carry += addend & 0xFFFF; |
621 | carry += (i <= number[0] ? number[i] : 0); |
622 | addend >>= 16; |
6e522441 |
623 | ret[i] = (unsigned short) carry & 0xFFFF; |
9400cf6f |
624 | carry >>= 16; |
625 | if (ret[i] != 0) |
626 | maxspot = i; |
627 | } |
628 | ret[0] = maxspot; |
629 | return ret; |
630 | } |
631 | |
632 | /* |
633 | * Compute the residue of a bignum, modulo a (max 16-bit) short. |
634 | */ |
635 | unsigned short bignum_mod_short(Bignum number, unsigned short modulus) { |
9400cf6f |
636 | unsigned long mod, r; |
637 | int i; |
638 | |
639 | r = 0; |
640 | mod = modulus; |
641 | for (i = number[0]; i > 0; i--) |
642 | r = (r * 65536 + number[i]) % mod; |
6e522441 |
643 | return (unsigned short) r; |
9400cf6f |
644 | } |
645 | |
646 | static void diagbn(char *prefix, Bignum md) { |
647 | int i, nibbles, morenibbles; |
648 | static const char hex[] = "0123456789ABCDEF"; |
649 | |
650 | printf("%s0x", prefix ? prefix : ""); |
651 | |
652 | nibbles = (3 + ssh1_bignum_bitcount(md))/4; if (nibbles<1) nibbles=1; |
653 | morenibbles = 4*md[0] - nibbles; |
654 | for (i=0; i<morenibbles; i++) putchar('-'); |
655 | for (i=nibbles; i-- ;) |
656 | putchar(hex[(bignum_byte(md, i/2) >> (4*(i%2))) & 0xF]); |
657 | |
658 | if (prefix) putchar('\n'); |
659 | } |
660 | |
661 | /* |
662 | * Greatest common divisor. |
663 | */ |
664 | Bignum biggcd(Bignum av, Bignum bv) { |
665 | Bignum a = copybn(av); |
666 | Bignum b = copybn(bv); |
667 | |
668 | diagbn("a = ", a); |
669 | diagbn("b = ", b); |
670 | while (bignum_cmp(b, Zero) != 0) { |
671 | Bignum t = newbn(b[0]); |
672 | bigmod(a, b, t, NULL); |
673 | diagbn("t = ", t); |
674 | while (t[0] > 1 && t[t[0]] == 0) t[0]--; |
675 | freebn(a); |
676 | a = b; |
677 | b = t; |
678 | } |
679 | |
680 | freebn(b); |
681 | return a; |
682 | } |
683 | |
684 | /* |
685 | * Modular inverse, using Euclid's extended algorithm. |
686 | */ |
687 | Bignum modinv(Bignum number, Bignum modulus) { |
688 | Bignum a = copybn(modulus); |
689 | Bignum b = copybn(number); |
690 | Bignum xp = copybn(Zero); |
691 | Bignum x = copybn(One); |
692 | int sign = +1; |
693 | |
694 | while (bignum_cmp(b, One) != 0) { |
695 | Bignum t = newbn(b[0]); |
696 | Bignum q = newbn(a[0]); |
697 | bigmod(a, b, t, q); |
698 | while (t[0] > 1 && t[t[0]] == 0) t[0]--; |
699 | freebn(a); |
700 | a = b; |
701 | b = t; |
702 | t = xp; |
703 | xp = x; |
704 | x = bigmuladd(q, xp, t); |
705 | sign = -sign; |
706 | freebn(t); |
707 | } |
708 | |
709 | freebn(b); |
710 | freebn(a); |
711 | freebn(xp); |
712 | |
713 | /* now we know that sign * x == 1, and that x < modulus */ |
714 | if (sign < 0) { |
715 | /* set a new x to be modulus - x */ |
716 | Bignum newx = newbn(modulus[0]); |
717 | unsigned short carry = 0; |
718 | int maxspot = 1; |
719 | int i; |
720 | |
721 | for (i = 1; i <= newx[0]; i++) { |
722 | unsigned short aword = (i <= modulus[0] ? modulus[i] : 0); |
723 | unsigned short bword = (i <= x[0] ? x[i] : 0); |
724 | newx[i] = aword - bword - carry; |
725 | bword = ~bword; |
726 | carry = carry ? (newx[i] >= bword) : (newx[i] > bword); |
727 | if (newx[i] != 0) |
728 | maxspot = i; |
729 | } |
730 | newx[0] = maxspot; |
731 | freebn(x); |
732 | x = newx; |
733 | } |
734 | |
735 | /* and return. */ |
736 | return x; |
737 | } |
6e522441 |
738 | |
739 | /* |
740 | * Render a bignum into decimal. Return a malloced string holding |
741 | * the decimal representation. |
742 | */ |
743 | char *bignum_decimal(Bignum x) { |
744 | int ndigits, ndigit; |
745 | int i, iszero; |
746 | unsigned long carry; |
747 | char *ret; |
748 | unsigned short *workspace; |
749 | |
750 | /* |
751 | * First, estimate the number of digits. Since log(10)/log(2) |
752 | * is just greater than 93/28 (the joys of continued fraction |
753 | * approximations...) we know that for every 93 bits, we need |
754 | * at most 28 digits. This will tell us how much to malloc. |
755 | * |
756 | * Formally: if x has i bits, that means x is strictly less |
757 | * than 2^i. Since 2 is less than 10^(28/93), this is less than |
758 | * 10^(28i/93). We need an integer power of ten, so we must |
759 | * round up (rounding down might make it less than x again). |
760 | * Therefore if we multiply the bit count by 28/93, rounding |
761 | * up, we will have enough digits. |
762 | */ |
763 | i = ssh1_bignum_bitcount(x); |
764 | ndigits = (28*i + 92)/93; /* multiply by 28/93 and round up */ |
765 | ndigits++; /* allow for trailing \0 */ |
766 | ret = malloc(ndigits); |
767 | |
768 | /* |
769 | * Now allocate some workspace to hold the binary form as we |
770 | * repeatedly divide it by ten. Initialise this to the |
771 | * big-endian form of the number. |
772 | */ |
773 | workspace = malloc(sizeof(unsigned short) * x[0]); |
774 | for (i = 0; i < x[0]; i++) |
775 | workspace[i] = x[x[0] - i]; |
776 | |
777 | /* |
778 | * Next, write the decimal number starting with the last digit. |
779 | * We use ordinary short division, dividing 10 into the |
780 | * workspace. |
781 | */ |
782 | ndigit = ndigits-1; |
783 | ret[ndigit] = '\0'; |
784 | do { |
785 | iszero = 1; |
786 | carry = 0; |
787 | for (i = 0; i < x[0]; i++) { |
788 | carry = (carry << 16) + workspace[i]; |
789 | workspace[i] = (unsigned short) (carry / 10); |
790 | if (workspace[i]) |
791 | iszero = 0; |
792 | carry %= 10; |
793 | } |
794 | ret[--ndigit] = (char)(carry + '0'); |
795 | } while (!iszero); |
796 | |
797 | /* |
798 | * There's a chance we've fallen short of the start of the |
799 | * string. Correct if so. |
800 | */ |
801 | if (ndigit > 0) |
802 | memmove(ret, ret+ndigit, ndigits-ndigit); |
803 | |
804 | /* |
805 | * Done. |
806 | */ |
807 | return ret; |
808 | } |