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 | |
3709bfe9 |
9 | #define BIGNUM_INTERNAL |
10 | typedef unsigned short *Bignum; |
11 | |
e5574168 |
12 | #include "ssh.h" |
13 | |
7cca0d81 |
14 | unsigned short bnZero[1] = { 0 }; |
15 | unsigned short bnOne[2] = { 1, 1 }; |
e5574168 |
16 | |
7d6ee6ff |
17 | /* |
18 | * The Bignum format is an array of `unsigned short'. The first |
19 | * element of the array counts the remaining elements. The |
20 | * remaining elements express the actual number, base 2^16, _least_ |
21 | * significant digit first. (So it's trivial to extract the bit |
22 | * with value 2^n for any n.) |
23 | * |
24 | * All Bignums in this module are positive. Negative numbers must |
25 | * be dealt with outside it. |
26 | * |
27 | * INVARIANT: the most significant word of any Bignum must be |
28 | * nonzero. |
29 | */ |
30 | |
7cca0d81 |
31 | Bignum Zero = bnZero, One = bnOne; |
e5574168 |
32 | |
3709bfe9 |
33 | static Bignum newbn(int length) { |
dcbde236 |
34 | Bignum b = smalloc((length+1)*sizeof(unsigned short)); |
e5574168 |
35 | if (!b) |
36 | abort(); /* FIXME */ |
37 | memset(b, 0, (length+1)*sizeof(*b)); |
38 | b[0] = length; |
39 | return b; |
40 | } |
41 | |
3709bfe9 |
42 | void bn_restore_invariant(Bignum b) { |
43 | while (b[0] > 1 && b[b[0]] == 0) b[0]--; |
44 | } |
45 | |
7cca0d81 |
46 | Bignum copybn(Bignum orig) { |
dcbde236 |
47 | Bignum b = smalloc((orig[0]+1)*sizeof(unsigned short)); |
7cca0d81 |
48 | if (!b) |
49 | abort(); /* FIXME */ |
50 | memcpy(b, orig, (orig[0]+1)*sizeof(*b)); |
51 | return b; |
52 | } |
53 | |
e5574168 |
54 | void freebn(Bignum b) { |
55 | /* |
56 | * Burn the evidence, just in case. |
57 | */ |
58 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
dcbde236 |
59 | sfree(b); |
e5574168 |
60 | } |
61 | |
3709bfe9 |
62 | Bignum bn_power_2(int n) { |
63 | Bignum ret = newbn((n+15)/16); |
64 | bignum_set_bit(ret, n, 1); |
65 | return ret; |
66 | } |
67 | |
e5574168 |
68 | /* |
69 | * Compute c = a * b. |
70 | * Input is in the first len words of a and b. |
71 | * Result is returned in the first 2*len words of c. |
72 | */ |
9400cf6f |
73 | static void internal_mul(unsigned short *a, unsigned short *b, |
74 | unsigned short *c, int len) |
e5574168 |
75 | { |
76 | int i, j; |
77 | unsigned long ai, t; |
78 | |
9400cf6f |
79 | for (j = 0; j < 2*len; j++) |
80 | c[j] = 0; |
e5574168 |
81 | |
82 | for (i = len - 1; i >= 0; i--) { |
83 | ai = a[i]; |
84 | t = 0; |
85 | for (j = len - 1; j >= 0; j--) { |
86 | t += ai * (unsigned long) b[j]; |
87 | t += (unsigned long) c[i+j+1]; |
88 | c[i+j+1] = (unsigned short)t; |
89 | t = t >> 16; |
90 | } |
91 | c[i] = (unsigned short)t; |
92 | } |
93 | } |
94 | |
6e522441 |
95 | static void internal_add_shifted(unsigned short *number, |
96 | unsigned n, int shift) { |
9400cf6f |
97 | int word = 1 + (shift / 16); |
98 | int bshift = shift % 16; |
6e522441 |
99 | unsigned long addend; |
9400cf6f |
100 | |
101 | addend = n << bshift; |
102 | |
103 | while (addend) { |
104 | addend += number[word]; |
6e522441 |
105 | number[word] = (unsigned short) addend & 0xFFFF; |
9400cf6f |
106 | addend >>= 16; |
107 | word++; |
108 | } |
109 | } |
110 | |
e5574168 |
111 | /* |
112 | * Compute a = a % m. |
9400cf6f |
113 | * Input in first alen words of a and first mlen words of m. |
114 | * Output in first alen words of a |
115 | * (of which first alen-mlen words will be zero). |
e5574168 |
116 | * The MSW of m MUST have its high bit set. |
9400cf6f |
117 | * Quotient is accumulated in the `quotient' array, which is a Bignum |
118 | * rather than the internal bigendian format. Quotient parts are shifted |
119 | * left by `qshift' before adding into quot. |
e5574168 |
120 | */ |
9400cf6f |
121 | static void internal_mod(unsigned short *a, int alen, |
122 | unsigned short *m, int mlen, |
123 | unsigned short *quot, int qshift) |
e5574168 |
124 | { |
125 | unsigned short m0, m1; |
126 | unsigned int h; |
127 | int i, k; |
128 | |
e5574168 |
129 | m0 = m[0]; |
9400cf6f |
130 | if (mlen > 1) |
131 | m1 = m[1]; |
132 | else |
133 | m1 = 0; |
e5574168 |
134 | |
9400cf6f |
135 | for (i = 0; i <= alen-mlen; i++) { |
e5574168 |
136 | unsigned long t; |
9400cf6f |
137 | unsigned int q, r, c, ai1; |
e5574168 |
138 | |
139 | if (i == 0) { |
140 | h = 0; |
141 | } else { |
142 | h = a[i-1]; |
143 | a[i-1] = 0; |
144 | } |
145 | |
9400cf6f |
146 | if (i == alen-1) |
147 | ai1 = 0; |
148 | else |
149 | ai1 = a[i+1]; |
150 | |
e5574168 |
151 | /* Find q = h:a[i] / m0 */ |
152 | t = ((unsigned long) h << 16) + a[i]; |
153 | q = t / m0; |
154 | r = t % m0; |
155 | |
156 | /* Refine our estimate of q by looking at |
157 | h:a[i]:a[i+1] / m0:m1 */ |
158 | t = (long) m1 * (long) q; |
9400cf6f |
159 | if (t > ((unsigned long) r << 16) + ai1) { |
e5574168 |
160 | q--; |
161 | t -= m1; |
162 | r = (r + m0) & 0xffff; /* overflow? */ |
163 | if (r >= (unsigned long)m0 && |
9400cf6f |
164 | t > ((unsigned long) r << 16) + ai1) |
e5574168 |
165 | q--; |
166 | } |
167 | |
9400cf6f |
168 | /* Subtract q * m from a[i...] */ |
e5574168 |
169 | c = 0; |
9400cf6f |
170 | for (k = mlen - 1; k >= 0; k--) { |
e5574168 |
171 | t = (long) q * (long) m[k]; |
172 | t += c; |
173 | c = t >> 16; |
174 | if ((unsigned short) t > a[i+k]) c++; |
175 | a[i+k] -= (unsigned short) t; |
176 | } |
177 | |
178 | /* Add back m in case of borrow */ |
179 | if (c != h) { |
180 | t = 0; |
9400cf6f |
181 | for (k = mlen - 1; k >= 0; k--) { |
e5574168 |
182 | t += m[k]; |
183 | t += a[i+k]; |
184 | a[i+k] = (unsigned short)t; |
185 | t = t >> 16; |
186 | } |
9400cf6f |
187 | q--; |
e5574168 |
188 | } |
9400cf6f |
189 | if (quot) |
190 | internal_add_shifted(quot, q, qshift + 16 * (alen-mlen-i)); |
e5574168 |
191 | } |
192 | } |
193 | |
194 | /* |
195 | * Compute (base ^ exp) % mod. |
196 | * The base MUST be smaller than the modulus. |
197 | * The most significant word of mod MUST be non-zero. |
198 | * We assume that the result array is the same size as the mod array. |
199 | */ |
59600f67 |
200 | Bignum modpow(Bignum base, Bignum exp, Bignum mod) |
e5574168 |
201 | { |
202 | unsigned short *a, *b, *n, *m; |
203 | int mshift; |
204 | int mlen, i, j; |
59600f67 |
205 | Bignum result; |
e5574168 |
206 | |
207 | /* Allocate m of size mlen, copy mod to m */ |
208 | /* We use big endian internally */ |
209 | mlen = mod[0]; |
dcbde236 |
210 | m = smalloc(mlen * sizeof(unsigned short)); |
e5574168 |
211 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
212 | |
213 | /* Shift m left to make msb bit set */ |
214 | for (mshift = 0; mshift < 15; mshift++) |
215 | if ((m[0] << mshift) & 0x8000) break; |
216 | if (mshift) { |
217 | for (i = 0; i < mlen - 1; i++) |
218 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
219 | m[mlen-1] = m[mlen-1] << mshift; |
220 | } |
221 | |
222 | /* Allocate n of size mlen, copy base to n */ |
dcbde236 |
223 | n = smalloc(mlen * sizeof(unsigned short)); |
e5574168 |
224 | i = mlen - base[0]; |
225 | for (j = 0; j < i; j++) n[j] = 0; |
226 | for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; |
227 | |
228 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
dcbde236 |
229 | a = smalloc(2 * mlen * sizeof(unsigned short)); |
230 | b = smalloc(2 * mlen * sizeof(unsigned short)); |
e5574168 |
231 | for (i = 0; i < 2*mlen; i++) a[i] = 0; |
232 | a[2*mlen-1] = 1; |
233 | |
234 | /* Skip leading zero bits of exp. */ |
235 | i = 0; j = 15; |
236 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
237 | j--; |
238 | if (j < 0) { i++; j = 15; } |
239 | } |
240 | |
241 | /* Main computation */ |
242 | while (i < exp[0]) { |
243 | while (j >= 0) { |
9400cf6f |
244 | internal_mul(a + mlen, a + mlen, b, mlen); |
245 | internal_mod(b, mlen*2, m, mlen, NULL, 0); |
e5574168 |
246 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
9400cf6f |
247 | internal_mul(b + mlen, n, a, mlen); |
248 | internal_mod(a, mlen*2, m, mlen, NULL, 0); |
e5574168 |
249 | } else { |
250 | unsigned short *t; |
251 | t = a; a = b; b = t; |
252 | } |
253 | j--; |
254 | } |
255 | i++; j = 15; |
256 | } |
257 | |
258 | /* Fixup result in case the modulus was shifted */ |
259 | if (mshift) { |
260 | for (i = mlen - 1; i < 2*mlen - 1; i++) |
261 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
262 | a[2*mlen-1] = a[2*mlen-1] << mshift; |
9400cf6f |
263 | internal_mod(a, mlen*2, m, mlen, NULL, 0); |
e5574168 |
264 | for (i = 2*mlen - 1; i >= mlen; i--) |
265 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
266 | } |
267 | |
268 | /* Copy result to buffer */ |
59600f67 |
269 | result = newbn(mod[0]); |
e5574168 |
270 | for (i = 0; i < mlen; i++) |
271 | result[result[0] - i] = a[i+mlen]; |
59600f67 |
272 | while (result[0] > 1 && result[result[0]] == 0) result[0]--; |
e5574168 |
273 | |
274 | /* Free temporary arrays */ |
dcbde236 |
275 | for (i = 0; i < 2*mlen; i++) a[i] = 0; sfree(a); |
276 | for (i = 0; i < 2*mlen; i++) b[i] = 0; sfree(b); |
277 | for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); |
278 | for (i = 0; i < mlen; i++) n[i] = 0; sfree(n); |
59600f67 |
279 | |
280 | return result; |
e5574168 |
281 | } |
7cca0d81 |
282 | |
283 | /* |
284 | * Compute (p * q) % mod. |
285 | * The most significant word of mod MUST be non-zero. |
286 | * We assume that the result array is the same size as the mod array. |
287 | */ |
59600f67 |
288 | Bignum modmul(Bignum p, Bignum q, Bignum mod) |
7cca0d81 |
289 | { |
290 | unsigned short *a, *n, *m, *o; |
291 | int mshift; |
80b10571 |
292 | int pqlen, mlen, rlen, i, j; |
59600f67 |
293 | Bignum result; |
7cca0d81 |
294 | |
295 | /* Allocate m of size mlen, copy mod to m */ |
296 | /* We use big endian internally */ |
297 | mlen = mod[0]; |
dcbde236 |
298 | m = smalloc(mlen * sizeof(unsigned short)); |
7cca0d81 |
299 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
300 | |
301 | /* Shift m left to make msb bit set */ |
302 | for (mshift = 0; mshift < 15; mshift++) |
303 | if ((m[0] << mshift) & 0x8000) break; |
304 | if (mshift) { |
305 | for (i = 0; i < mlen - 1; i++) |
306 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
307 | m[mlen-1] = m[mlen-1] << mshift; |
308 | } |
309 | |
310 | pqlen = (p[0] > q[0] ? p[0] : q[0]); |
311 | |
312 | /* Allocate n of size pqlen, copy p to n */ |
dcbde236 |
313 | n = smalloc(pqlen * sizeof(unsigned short)); |
7cca0d81 |
314 | i = pqlen - p[0]; |
315 | for (j = 0; j < i; j++) n[j] = 0; |
316 | for (j = 0; j < p[0]; j++) n[i+j] = p[p[0] - j]; |
317 | |
318 | /* Allocate o of size pqlen, copy q to o */ |
dcbde236 |
319 | o = smalloc(pqlen * sizeof(unsigned short)); |
7cca0d81 |
320 | i = pqlen - q[0]; |
321 | for (j = 0; j < i; j++) o[j] = 0; |
322 | for (j = 0; j < q[0]; j++) o[i+j] = q[q[0] - j]; |
323 | |
324 | /* Allocate a of size 2*pqlen for result */ |
dcbde236 |
325 | a = smalloc(2 * pqlen * sizeof(unsigned short)); |
7cca0d81 |
326 | |
327 | /* Main computation */ |
9400cf6f |
328 | internal_mul(n, o, a, pqlen); |
329 | internal_mod(a, pqlen*2, m, mlen, NULL, 0); |
7cca0d81 |
330 | |
331 | /* Fixup result in case the modulus was shifted */ |
332 | if (mshift) { |
333 | for (i = 2*pqlen - mlen - 1; i < 2*pqlen - 1; i++) |
334 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
335 | a[2*pqlen-1] = a[2*pqlen-1] << mshift; |
9400cf6f |
336 | internal_mod(a, pqlen*2, m, mlen, NULL, 0); |
7cca0d81 |
337 | for (i = 2*pqlen - 1; i >= 2*pqlen - mlen; i--) |
338 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
339 | } |
340 | |
341 | /* Copy result to buffer */ |
80b10571 |
342 | rlen = (mlen < pqlen*2 ? mlen : pqlen*2); |
343 | result = newbn(rlen); |
344 | for (i = 0; i < rlen; i++) |
345 | result[result[0] - i] = a[i+2*pqlen-rlen]; |
59600f67 |
346 | while (result[0] > 1 && result[result[0]] == 0) result[0]--; |
7cca0d81 |
347 | |
348 | /* Free temporary arrays */ |
dcbde236 |
349 | for (i = 0; i < 2*pqlen; i++) a[i] = 0; sfree(a); |
350 | for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); |
351 | for (i = 0; i < pqlen; i++) n[i] = 0; sfree(n); |
352 | for (i = 0; i < pqlen; i++) o[i] = 0; sfree(o); |
59600f67 |
353 | |
354 | return result; |
7cca0d81 |
355 | } |
356 | |
357 | /* |
9400cf6f |
358 | * Compute p % mod. |
359 | * The most significant word of mod MUST be non-zero. |
360 | * We assume that the result array is the same size as the mod array. |
361 | * We optionally write out a quotient. |
362 | */ |
363 | void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) |
364 | { |
365 | unsigned short *n, *m; |
366 | int mshift; |
367 | int plen, mlen, i, j; |
368 | |
369 | /* Allocate m of size mlen, copy mod to m */ |
370 | /* We use big endian internally */ |
371 | mlen = mod[0]; |
dcbde236 |
372 | m = smalloc(mlen * sizeof(unsigned short)); |
9400cf6f |
373 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
374 | |
375 | /* Shift m left to make msb bit set */ |
376 | for (mshift = 0; mshift < 15; mshift++) |
377 | if ((m[0] << mshift) & 0x8000) break; |
378 | if (mshift) { |
379 | for (i = 0; i < mlen - 1; i++) |
380 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
381 | m[mlen-1] = m[mlen-1] << mshift; |
382 | } |
383 | |
384 | plen = p[0]; |
385 | /* Ensure plen > mlen */ |
386 | if (plen <= mlen) plen = mlen+1; |
387 | |
388 | /* Allocate n of size plen, copy p to n */ |
dcbde236 |
389 | n = smalloc(plen * sizeof(unsigned short)); |
9400cf6f |
390 | for (j = 0; j < plen; j++) n[j] = 0; |
391 | for (j = 1; j <= p[0]; j++) n[plen-j] = p[j]; |
392 | |
393 | /* Main computation */ |
394 | internal_mod(n, plen, m, mlen, quotient, mshift); |
395 | |
396 | /* Fixup result in case the modulus was shifted */ |
397 | if (mshift) { |
398 | for (i = plen - mlen - 1; i < plen - 1; i++) |
399 | n[i] = (n[i] << mshift) | (n[i+1] >> (16-mshift)); |
400 | n[plen-1] = n[plen-1] << mshift; |
401 | internal_mod(n, plen, m, mlen, quotient, 0); |
402 | for (i = plen - 1; i >= plen - mlen; i--) |
403 | n[i] = (n[i] >> mshift) | (n[i-1] << (16-mshift)); |
404 | } |
405 | |
406 | /* Copy result to buffer */ |
407 | for (i = 1; i <= result[0]; i++) { |
408 | int j = plen-i; |
409 | result[i] = j>=0 ? n[j] : 0; |
410 | } |
411 | |
412 | /* Free temporary arrays */ |
dcbde236 |
413 | for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); |
414 | for (i = 0; i < plen; i++) n[i] = 0; sfree(n); |
9400cf6f |
415 | } |
416 | |
417 | /* |
7cca0d81 |
418 | * Decrement a number. |
419 | */ |
420 | void decbn(Bignum bn) { |
421 | int i = 1; |
422 | while (i < bn[0] && bn[i] == 0) |
423 | bn[i++] = 0xFFFF; |
424 | bn[i]--; |
425 | } |
426 | |
3709bfe9 |
427 | Bignum bignum_from_bytes(unsigned char *data, int nbytes) { |
428 | Bignum result; |
429 | int w, i; |
430 | |
431 | w = (nbytes+1)/2; /* bytes -> words */ |
432 | |
433 | result = newbn(w); |
434 | for (i=1; i<=w; i++) |
435 | result[i] = 0; |
436 | for (i=nbytes; i-- ;) { |
437 | unsigned char byte = *data++; |
438 | if (i & 1) |
439 | result[1+i/2] |= byte<<8; |
440 | else |
441 | result[1+i/2] |= byte; |
442 | } |
443 | |
444 | while (result[0] > 1 && result[result[0]] == 0) result[0]--; |
445 | return result; |
446 | } |
447 | |
7cca0d81 |
448 | /* |
449 | * Read an ssh1-format bignum from a data buffer. Return the number |
450 | * of bytes consumed. |
451 | */ |
452 | int ssh1_read_bignum(unsigned char *data, Bignum *result) { |
453 | unsigned char *p = data; |
7cca0d81 |
454 | int i; |
455 | int w, b; |
456 | |
457 | w = 0; |
458 | for (i=0; i<2; i++) |
459 | w = (w << 8) + *p++; |
7cca0d81 |
460 | b = (w+7)/8; /* bits -> bytes */ |
7cca0d81 |
461 | |
a52f067e |
462 | if (!result) /* just return length */ |
463 | return b + 2; |
464 | |
3709bfe9 |
465 | *result = bignum_from_bytes(p, b); |
7cca0d81 |
466 | |
3709bfe9 |
467 | return p + b - data; |
7cca0d81 |
468 | } |
5c58ad2d |
469 | |
470 | /* |
471 | * Return the bit count of a bignum, for ssh1 encoding. |
472 | */ |
473 | int ssh1_bignum_bitcount(Bignum bn) { |
474 | int bitcount = bn[0] * 16 - 1; |
5c58ad2d |
475 | while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0) |
476 | bitcount--; |
477 | return bitcount + 1; |
478 | } |
479 | |
480 | /* |
481 | * Return the byte length of a bignum when ssh1 encoded. |
482 | */ |
483 | int ssh1_bignum_length(Bignum bn) { |
484 | return 2 + (ssh1_bignum_bitcount(bn)+7)/8; |
485 | } |
486 | |
487 | /* |
488 | * Return a byte from a bignum; 0 is least significant, etc. |
489 | */ |
490 | int bignum_byte(Bignum bn, int i) { |
491 | if (i >= 2*bn[0]) |
492 | return 0; /* beyond the end */ |
493 | else if (i & 1) |
494 | return (bn[i/2+1] >> 8) & 0xFF; |
495 | else |
496 | return (bn[i/2+1] ) & 0xFF; |
497 | } |
498 | |
499 | /* |
9400cf6f |
500 | * Return a bit from a bignum; 0 is least significant, etc. |
501 | */ |
502 | int bignum_bit(Bignum bn, int i) { |
503 | if (i >= 16*bn[0]) |
504 | return 0; /* beyond the end */ |
505 | else |
506 | return (bn[i/16+1] >> (i%16)) & 1; |
507 | } |
508 | |
509 | /* |
510 | * Set a bit in a bignum; 0 is least significant, etc. |
511 | */ |
512 | void bignum_set_bit(Bignum bn, int bitnum, int value) { |
513 | if (bitnum >= 16*bn[0]) |
514 | abort(); /* beyond the end */ |
515 | else { |
516 | int v = bitnum/16+1; |
517 | int mask = 1 << (bitnum%16); |
518 | if (value) |
519 | bn[v] |= mask; |
520 | else |
521 | bn[v] &= ~mask; |
522 | } |
523 | } |
524 | |
525 | /* |
5c58ad2d |
526 | * Write a ssh1-format bignum into a buffer. It is assumed the |
527 | * buffer is big enough. Returns the number of bytes used. |
528 | */ |
529 | int ssh1_write_bignum(void *data, Bignum bn) { |
530 | unsigned char *p = data; |
531 | int len = ssh1_bignum_length(bn); |
532 | int i; |
533 | int bitc = ssh1_bignum_bitcount(bn); |
534 | |
535 | *p++ = (bitc >> 8) & 0xFF; |
536 | *p++ = (bitc ) & 0xFF; |
537 | for (i = len-2; i-- ;) |
538 | *p++ = bignum_byte(bn, i); |
539 | return len; |
540 | } |
9400cf6f |
541 | |
542 | /* |
543 | * Compare two bignums. Returns like strcmp. |
544 | */ |
545 | int bignum_cmp(Bignum a, Bignum b) { |
546 | int amax = a[0], bmax = b[0]; |
547 | int i = (amax > bmax ? amax : bmax); |
548 | while (i) { |
549 | unsigned short aval = (i > amax ? 0 : a[i]); |
550 | unsigned short bval = (i > bmax ? 0 : b[i]); |
551 | if (aval < bval) return -1; |
552 | if (aval > bval) return +1; |
553 | i--; |
554 | } |
555 | return 0; |
556 | } |
557 | |
558 | /* |
559 | * Right-shift one bignum to form another. |
560 | */ |
561 | Bignum bignum_rshift(Bignum a, int shift) { |
562 | Bignum ret; |
563 | int i, shiftw, shiftb, shiftbb, bits; |
564 | unsigned short ai, ai1; |
565 | |
566 | bits = ssh1_bignum_bitcount(a) - shift; |
567 | ret = newbn((bits+15)/16); |
568 | |
569 | if (ret) { |
570 | shiftw = shift / 16; |
571 | shiftb = shift % 16; |
572 | shiftbb = 16 - shiftb; |
573 | |
574 | ai1 = a[shiftw+1]; |
575 | for (i = 1; i <= ret[0]; i++) { |
576 | ai = ai1; |
577 | ai1 = (i+shiftw+1 <= a[0] ? a[i+shiftw+1] : 0); |
578 | ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & 0xFFFF; |
579 | } |
580 | } |
581 | |
582 | return ret; |
583 | } |
584 | |
585 | /* |
586 | * Non-modular multiplication and addition. |
587 | */ |
588 | Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { |
589 | int alen = a[0], blen = b[0]; |
590 | int mlen = (alen > blen ? alen : blen); |
591 | int rlen, i, maxspot; |
592 | unsigned short *workspace; |
593 | Bignum ret; |
594 | |
595 | /* mlen space for a, mlen space for b, 2*mlen for result */ |
dcbde236 |
596 | workspace = smalloc(mlen * 4 * sizeof(unsigned short)); |
9400cf6f |
597 | for (i = 0; i < mlen; i++) { |
598 | workspace[0*mlen + i] = (mlen-i <= a[0] ? a[mlen-i] : 0); |
599 | workspace[1*mlen + i] = (mlen-i <= b[0] ? b[mlen-i] : 0); |
600 | } |
601 | |
602 | internal_mul(workspace+0*mlen, workspace+1*mlen, workspace+2*mlen, mlen); |
603 | |
604 | /* now just copy the result back */ |
605 | rlen = alen + blen + 1; |
606 | if (addend && rlen <= addend[0]) |
607 | rlen = addend[0] + 1; |
608 | ret = newbn(rlen); |
609 | maxspot = 0; |
610 | for (i = 1; i <= ret[0]; i++) { |
611 | ret[i] = (i <= 2*mlen ? workspace[4*mlen - i] : 0); |
612 | if (ret[i] != 0) |
613 | maxspot = i; |
614 | } |
615 | ret[0] = maxspot; |
616 | |
617 | /* now add in the addend, if any */ |
618 | if (addend) { |
619 | unsigned long carry = 0; |
620 | for (i = 1; i <= rlen; i++) { |
621 | carry += (i <= ret[0] ? ret[i] : 0); |
622 | carry += (i <= addend[0] ? addend[i] : 0); |
6e522441 |
623 | ret[i] = (unsigned short) carry & 0xFFFF; |
9400cf6f |
624 | carry >>= 16; |
625 | if (ret[i] != 0 && i > maxspot) |
626 | maxspot = i; |
627 | } |
628 | } |
629 | ret[0] = maxspot; |
630 | |
631 | return ret; |
632 | } |
633 | |
634 | /* |
635 | * Non-modular multiplication. |
636 | */ |
637 | Bignum bigmul(Bignum a, Bignum b) { |
638 | return bigmuladd(a, b, NULL); |
639 | } |
640 | |
641 | /* |
3709bfe9 |
642 | * Create a bignum which is the bitmask covering another one. That |
643 | * is, the smallest integer which is >= N and is also one less than |
644 | * a power of two. |
645 | */ |
646 | Bignum bignum_bitmask(Bignum n) { |
647 | Bignum ret = copybn(n); |
648 | int i; |
649 | unsigned short j; |
650 | |
651 | i = ret[0]; |
652 | while (n[i] == 0 && i > 0) |
653 | i--; |
654 | if (i <= 0) |
655 | return ret; /* input was zero */ |
656 | j = 1; |
657 | while (j < n[i]) |
658 | j = 2*j+1; |
659 | ret[i] = j; |
660 | while (--i > 0) |
661 | ret[i] = 0xFFFF; |
662 | return ret; |
663 | } |
664 | |
665 | /* |
9400cf6f |
666 | * Convert a (max 16-bit) short into a bignum. |
667 | */ |
668 | Bignum bignum_from_short(unsigned short n) { |
669 | Bignum ret; |
670 | |
671 | ret = newbn(2); |
672 | ret[1] = n & 0xFFFF; |
673 | ret[2] = (n >> 16) & 0xFFFF; |
674 | ret[0] = (ret[2] ? 2 : 1); |
675 | return ret; |
676 | } |
677 | |
678 | /* |
679 | * Add a long to a bignum. |
680 | */ |
681 | Bignum bignum_add_long(Bignum number, unsigned long addend) { |
682 | Bignum ret = newbn(number[0]+1); |
683 | int i, maxspot = 0; |
684 | unsigned long carry = 0; |
685 | |
686 | for (i = 1; i <= ret[0]; i++) { |
687 | carry += addend & 0xFFFF; |
688 | carry += (i <= number[0] ? number[i] : 0); |
689 | addend >>= 16; |
6e522441 |
690 | ret[i] = (unsigned short) carry & 0xFFFF; |
9400cf6f |
691 | carry >>= 16; |
692 | if (ret[i] != 0) |
693 | maxspot = i; |
694 | } |
695 | ret[0] = maxspot; |
696 | return ret; |
697 | } |
698 | |
699 | /* |
700 | * Compute the residue of a bignum, modulo a (max 16-bit) short. |
701 | */ |
702 | unsigned short bignum_mod_short(Bignum number, unsigned short modulus) { |
9400cf6f |
703 | unsigned long mod, r; |
704 | int i; |
705 | |
706 | r = 0; |
707 | mod = modulus; |
708 | for (i = number[0]; i > 0; i--) |
709 | r = (r * 65536 + number[i]) % mod; |
6e522441 |
710 | return (unsigned short) r; |
9400cf6f |
711 | } |
712 | |
3709bfe9 |
713 | void diagbn(char *prefix, Bignum md) { |
9400cf6f |
714 | int i, nibbles, morenibbles; |
715 | static const char hex[] = "0123456789ABCDEF"; |
716 | |
717 | printf("%s0x", prefix ? prefix : ""); |
718 | |
719 | nibbles = (3 + ssh1_bignum_bitcount(md))/4; if (nibbles<1) nibbles=1; |
720 | morenibbles = 4*md[0] - nibbles; |
721 | for (i=0; i<morenibbles; i++) putchar('-'); |
722 | for (i=nibbles; i-- ;) |
723 | putchar(hex[(bignum_byte(md, i/2) >> (4*(i%2))) & 0xF]); |
724 | |
725 | if (prefix) putchar('\n'); |
726 | } |
727 | |
728 | /* |
729 | * Greatest common divisor. |
730 | */ |
731 | Bignum biggcd(Bignum av, Bignum bv) { |
732 | Bignum a = copybn(av); |
733 | Bignum b = copybn(bv); |
734 | |
735 | diagbn("a = ", a); |
736 | diagbn("b = ", b); |
737 | while (bignum_cmp(b, Zero) != 0) { |
738 | Bignum t = newbn(b[0]); |
739 | bigmod(a, b, t, NULL); |
740 | diagbn("t = ", t); |
741 | while (t[0] > 1 && t[t[0]] == 0) t[0]--; |
742 | freebn(a); |
743 | a = b; |
744 | b = t; |
745 | } |
746 | |
747 | freebn(b); |
748 | return a; |
749 | } |
750 | |
751 | /* |
752 | * Modular inverse, using Euclid's extended algorithm. |
753 | */ |
754 | Bignum modinv(Bignum number, Bignum modulus) { |
755 | Bignum a = copybn(modulus); |
756 | Bignum b = copybn(number); |
757 | Bignum xp = copybn(Zero); |
758 | Bignum x = copybn(One); |
759 | int sign = +1; |
760 | |
761 | while (bignum_cmp(b, One) != 0) { |
762 | Bignum t = newbn(b[0]); |
763 | Bignum q = newbn(a[0]); |
764 | bigmod(a, b, t, q); |
765 | while (t[0] > 1 && t[t[0]] == 0) t[0]--; |
766 | freebn(a); |
767 | a = b; |
768 | b = t; |
769 | t = xp; |
770 | xp = x; |
771 | x = bigmuladd(q, xp, t); |
772 | sign = -sign; |
773 | freebn(t); |
774 | } |
775 | |
776 | freebn(b); |
777 | freebn(a); |
778 | freebn(xp); |
779 | |
780 | /* now we know that sign * x == 1, and that x < modulus */ |
781 | if (sign < 0) { |
782 | /* set a new x to be modulus - x */ |
783 | Bignum newx = newbn(modulus[0]); |
784 | unsigned short carry = 0; |
785 | int maxspot = 1; |
786 | int i; |
787 | |
788 | for (i = 1; i <= newx[0]; i++) { |
789 | unsigned short aword = (i <= modulus[0] ? modulus[i] : 0); |
790 | unsigned short bword = (i <= x[0] ? x[i] : 0); |
791 | newx[i] = aword - bword - carry; |
792 | bword = ~bword; |
793 | carry = carry ? (newx[i] >= bword) : (newx[i] > bword); |
794 | if (newx[i] != 0) |
795 | maxspot = i; |
796 | } |
797 | newx[0] = maxspot; |
798 | freebn(x); |
799 | x = newx; |
800 | } |
801 | |
802 | /* and return. */ |
803 | return x; |
804 | } |
6e522441 |
805 | |
806 | /* |
807 | * Render a bignum into decimal. Return a malloced string holding |
808 | * the decimal representation. |
809 | */ |
810 | char *bignum_decimal(Bignum x) { |
811 | int ndigits, ndigit; |
812 | int i, iszero; |
813 | unsigned long carry; |
814 | char *ret; |
815 | unsigned short *workspace; |
816 | |
817 | /* |
818 | * First, estimate the number of digits. Since log(10)/log(2) |
819 | * is just greater than 93/28 (the joys of continued fraction |
820 | * approximations...) we know that for every 93 bits, we need |
821 | * at most 28 digits. This will tell us how much to malloc. |
822 | * |
823 | * Formally: if x has i bits, that means x is strictly less |
824 | * than 2^i. Since 2 is less than 10^(28/93), this is less than |
825 | * 10^(28i/93). We need an integer power of ten, so we must |
826 | * round up (rounding down might make it less than x again). |
827 | * Therefore if we multiply the bit count by 28/93, rounding |
828 | * up, we will have enough digits. |
829 | */ |
830 | i = ssh1_bignum_bitcount(x); |
831 | ndigits = (28*i + 92)/93; /* multiply by 28/93 and round up */ |
832 | ndigits++; /* allow for trailing \0 */ |
dcbde236 |
833 | ret = smalloc(ndigits); |
6e522441 |
834 | |
835 | /* |
836 | * Now allocate some workspace to hold the binary form as we |
837 | * repeatedly divide it by ten. Initialise this to the |
838 | * big-endian form of the number. |
839 | */ |
dcbde236 |
840 | workspace = smalloc(sizeof(unsigned short) * x[0]); |
6e522441 |
841 | for (i = 0; i < x[0]; i++) |
842 | workspace[i] = x[x[0] - i]; |
843 | |
844 | /* |
845 | * Next, write the decimal number starting with the last digit. |
846 | * We use ordinary short division, dividing 10 into the |
847 | * workspace. |
848 | */ |
849 | ndigit = ndigits-1; |
850 | ret[ndigit] = '\0'; |
851 | do { |
852 | iszero = 1; |
853 | carry = 0; |
854 | for (i = 0; i < x[0]; i++) { |
855 | carry = (carry << 16) + workspace[i]; |
856 | workspace[i] = (unsigned short) (carry / 10); |
857 | if (workspace[i]) |
858 | iszero = 0; |
859 | carry %= 10; |
860 | } |
861 | ret[--ndigit] = (char)(carry + '0'); |
862 | } while (!iszero); |
863 | |
864 | /* |
865 | * There's a chance we've fallen short of the start of the |
866 | * string. Correct if so. |
867 | */ |
868 | if (ndigit > 0) |
869 | memmove(ret, ret+ndigit, ndigits-ndigit); |
870 | |
871 | /* |
872 | * Done. |
873 | */ |
874 | return ret; |
875 | } |