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