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 | |
5c72ca61 |
9 | #include "misc.h" |
98ba26b9 |
10 | |
a3412f52 |
11 | #if defined __GNUC__ && defined __i386__ |
12 | typedef unsigned long BignumInt; |
13 | typedef unsigned long long BignumDblInt; |
14 | #define BIGNUM_INT_MASK 0xFFFFFFFFUL |
15 | #define BIGNUM_TOP_BIT 0x80000000UL |
16 | #define BIGNUM_INT_BITS 32 |
17 | #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) |
18 | #else |
19 | typedef unsigned short BignumInt; |
20 | typedef unsigned long BignumDblInt; |
21 | #define BIGNUM_INT_MASK 0xFFFFU |
22 | #define BIGNUM_TOP_BIT 0x8000U |
23 | #define BIGNUM_INT_BITS 16 |
24 | #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) |
25 | #endif |
26 | |
27 | #define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8) |
28 | |
3709bfe9 |
29 | #define BIGNUM_INTERNAL |
a3412f52 |
30 | typedef BignumInt *Bignum; |
3709bfe9 |
31 | |
e5574168 |
32 | #include "ssh.h" |
33 | |
a3412f52 |
34 | BignumInt bnZero[1] = { 0 }; |
35 | BignumInt bnOne[2] = { 1, 1 }; |
e5574168 |
36 | |
7d6ee6ff |
37 | /* |
a3412f52 |
38 | * The Bignum format is an array of `BignumInt'. The first |
7d6ee6ff |
39 | * element of the array counts the remaining elements. The |
a3412f52 |
40 | * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_ |
7d6ee6ff |
41 | * significant digit first. (So it's trivial to extract the bit |
42 | * with value 2^n for any n.) |
43 | * |
44 | * All Bignums in this module are positive. Negative numbers must |
45 | * be dealt with outside it. |
46 | * |
47 | * INVARIANT: the most significant word of any Bignum must be |
48 | * nonzero. |
49 | */ |
50 | |
7cca0d81 |
51 | Bignum Zero = bnZero, One = bnOne; |
e5574168 |
52 | |
32874aea |
53 | static Bignum newbn(int length) |
54 | { |
a3412f52 |
55 | Bignum b = snewn(length + 1, BignumInt); |
e5574168 |
56 | if (!b) |
57 | abort(); /* FIXME */ |
32874aea |
58 | memset(b, 0, (length + 1) * sizeof(*b)); |
e5574168 |
59 | b[0] = length; |
60 | return b; |
61 | } |
62 | |
32874aea |
63 | void bn_restore_invariant(Bignum b) |
64 | { |
65 | while (b[0] > 1 && b[b[0]] == 0) |
66 | b[0]--; |
3709bfe9 |
67 | } |
68 | |
32874aea |
69 | Bignum copybn(Bignum orig) |
70 | { |
a3412f52 |
71 | Bignum b = snewn(orig[0] + 1, BignumInt); |
7cca0d81 |
72 | if (!b) |
73 | abort(); /* FIXME */ |
32874aea |
74 | memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); |
7cca0d81 |
75 | return b; |
76 | } |
77 | |
32874aea |
78 | void freebn(Bignum b) |
79 | { |
e5574168 |
80 | /* |
81 | * Burn the evidence, just in case. |
82 | */ |
83 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
dcbde236 |
84 | sfree(b); |
e5574168 |
85 | } |
86 | |
32874aea |
87 | Bignum bn_power_2(int n) |
88 | { |
a3412f52 |
89 | Bignum ret = newbn(n / BIGNUM_INT_BITS + 1); |
3709bfe9 |
90 | bignum_set_bit(ret, n, 1); |
91 | return ret; |
92 | } |
93 | |
e5574168 |
94 | /* |
95 | * Compute c = a * b. |
96 | * Input is in the first len words of a and b. |
97 | * Result is returned in the first 2*len words of c. |
98 | */ |
a3412f52 |
99 | static void internal_mul(BignumInt *a, BignumInt *b, |
100 | BignumInt *c, int len) |
e5574168 |
101 | { |
102 | int i, j; |
a3412f52 |
103 | BignumDblInt t; |
e5574168 |
104 | |
32874aea |
105 | for (j = 0; j < 2 * len; j++) |
9400cf6f |
106 | c[j] = 0; |
e5574168 |
107 | |
108 | for (i = len - 1; i >= 0; i--) { |
e5574168 |
109 | t = 0; |
110 | for (j = len - 1; j >= 0; j--) { |
a3412f52 |
111 | t += MUL_WORD(a[i], (BignumDblInt) b[j]); |
112 | t += (BignumDblInt) c[i + j + 1]; |
113 | c[i + j + 1] = (BignumInt) t; |
114 | t = t >> BIGNUM_INT_BITS; |
e5574168 |
115 | } |
a3412f52 |
116 | c[i] = (BignumInt) t; |
e5574168 |
117 | } |
118 | } |
119 | |
a3412f52 |
120 | static void internal_add_shifted(BignumInt *number, |
32874aea |
121 | unsigned n, int shift) |
122 | { |
a3412f52 |
123 | int word = 1 + (shift / BIGNUM_INT_BITS); |
124 | int bshift = shift % BIGNUM_INT_BITS; |
125 | BignumDblInt addend; |
9400cf6f |
126 | |
127 | addend = n << bshift; |
128 | |
129 | while (addend) { |
32874aea |
130 | addend += number[word]; |
a3412f52 |
131 | number[word] = (BignumInt) addend & BIGNUM_INT_MASK; |
132 | addend >>= BIGNUM_INT_BITS; |
32874aea |
133 | word++; |
9400cf6f |
134 | } |
135 | } |
136 | |
e5574168 |
137 | /* |
138 | * Compute a = a % m. |
9400cf6f |
139 | * Input in first alen words of a and first mlen words of m. |
140 | * Output in first alen words of a |
141 | * (of which first alen-mlen words will be zero). |
e5574168 |
142 | * The MSW of m MUST have its high bit set. |
9400cf6f |
143 | * Quotient is accumulated in the `quotient' array, which is a Bignum |
144 | * rather than the internal bigendian format. Quotient parts are shifted |
145 | * left by `qshift' before adding into quot. |
e5574168 |
146 | */ |
a3412f52 |
147 | static void internal_mod(BignumInt *a, int alen, |
148 | BignumInt *m, int mlen, |
149 | BignumInt *quot, int qshift) |
e5574168 |
150 | { |
a3412f52 |
151 | BignumInt m0, m1; |
e5574168 |
152 | unsigned int h; |
153 | int i, k; |
154 | |
e5574168 |
155 | m0 = m[0]; |
9400cf6f |
156 | if (mlen > 1) |
32874aea |
157 | m1 = m[1]; |
9400cf6f |
158 | else |
32874aea |
159 | m1 = 0; |
e5574168 |
160 | |
32874aea |
161 | for (i = 0; i <= alen - mlen; i++) { |
a3412f52 |
162 | BignumDblInt t; |
9400cf6f |
163 | unsigned int q, r, c, ai1; |
e5574168 |
164 | |
165 | if (i == 0) { |
166 | h = 0; |
167 | } else { |
32874aea |
168 | h = a[i - 1]; |
169 | a[i - 1] = 0; |
e5574168 |
170 | } |
171 | |
32874aea |
172 | if (i == alen - 1) |
173 | ai1 = 0; |
174 | else |
175 | ai1 = a[i + 1]; |
9400cf6f |
176 | |
e5574168 |
177 | /* Find q = h:a[i] / m0 */ |
a3412f52 |
178 | t = ((BignumDblInt) h << BIGNUM_INT_BITS) + a[i]; |
e5574168 |
179 | q = t / m0; |
180 | r = t % m0; |
181 | |
182 | /* Refine our estimate of q by looking at |
32874aea |
183 | h:a[i]:a[i+1] / m0:m1 */ |
a3412f52 |
184 | t = (BignumDblInt) m1 * (BignumDblInt) q; |
185 | if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) { |
e5574168 |
186 | q--; |
187 | t -= m1; |
a3412f52 |
188 | r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */ |
189 | if (r >= (BignumDblInt) m0 && |
190 | t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--; |
e5574168 |
191 | } |
192 | |
9400cf6f |
193 | /* Subtract q * m from a[i...] */ |
e5574168 |
194 | c = 0; |
9400cf6f |
195 | for (k = mlen - 1; k >= 0; k--) { |
a3412f52 |
196 | t = (BignumDblInt) q * (BignumDblInt) m[k]; |
e5574168 |
197 | t += c; |
a3412f52 |
198 | c = t >> BIGNUM_INT_BITS; |
199 | if ((BignumInt) t > a[i + k]) |
32874aea |
200 | c++; |
a3412f52 |
201 | a[i + k] -= (BignumInt) t; |
e5574168 |
202 | } |
203 | |
204 | /* Add back m in case of borrow */ |
205 | if (c != h) { |
206 | t = 0; |
9400cf6f |
207 | for (k = mlen - 1; k >= 0; k--) { |
e5574168 |
208 | t += m[k]; |
32874aea |
209 | t += a[i + k]; |
a3412f52 |
210 | a[i + k] = (BignumInt) t; |
211 | t = t >> BIGNUM_INT_BITS; |
e5574168 |
212 | } |
32874aea |
213 | q--; |
e5574168 |
214 | } |
32874aea |
215 | if (quot) |
a3412f52 |
216 | internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); |
e5574168 |
217 | } |
218 | } |
219 | |
220 | /* |
221 | * Compute (base ^ exp) % mod. |
222 | * The base MUST be smaller than the modulus. |
223 | * The most significant word of mod MUST be non-zero. |
224 | * We assume that the result array is the same size as the mod array. |
225 | */ |
59600f67 |
226 | Bignum modpow(Bignum base, Bignum exp, Bignum mod) |
e5574168 |
227 | { |
a3412f52 |
228 | BignumInt *a, *b, *n, *m; |
e5574168 |
229 | int mshift; |
230 | int mlen, i, j; |
59600f67 |
231 | Bignum result; |
e5574168 |
232 | |
233 | /* Allocate m of size mlen, copy mod to m */ |
234 | /* We use big endian internally */ |
235 | mlen = mod[0]; |
a3412f52 |
236 | m = snewn(mlen, BignumInt); |
32874aea |
237 | for (j = 0; j < mlen; j++) |
238 | m[j] = mod[mod[0] - j]; |
e5574168 |
239 | |
240 | /* Shift m left to make msb bit set */ |
a3412f52 |
241 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
242 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
32874aea |
243 | break; |
e5574168 |
244 | if (mshift) { |
245 | for (i = 0; i < mlen - 1; i++) |
a3412f52 |
246 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
247 | m[mlen - 1] = m[mlen - 1] << mshift; |
e5574168 |
248 | } |
249 | |
250 | /* Allocate n of size mlen, copy base to n */ |
a3412f52 |
251 | n = snewn(mlen, BignumInt); |
e5574168 |
252 | i = mlen - base[0]; |
32874aea |
253 | for (j = 0; j < i; j++) |
254 | n[j] = 0; |
255 | for (j = 0; j < base[0]; j++) |
256 | n[i + j] = base[base[0] - j]; |
e5574168 |
257 | |
258 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
a3412f52 |
259 | a = snewn(2 * mlen, BignumInt); |
260 | b = snewn(2 * mlen, BignumInt); |
32874aea |
261 | for (i = 0; i < 2 * mlen; i++) |
262 | a[i] = 0; |
263 | a[2 * mlen - 1] = 1; |
e5574168 |
264 | |
265 | /* Skip leading zero bits of exp. */ |
32874aea |
266 | i = 0; |
a3412f52 |
267 | j = BIGNUM_INT_BITS-1; |
e5574168 |
268 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
269 | j--; |
32874aea |
270 | if (j < 0) { |
271 | i++; |
a3412f52 |
272 | j = BIGNUM_INT_BITS-1; |
32874aea |
273 | } |
e5574168 |
274 | } |
275 | |
276 | /* Main computation */ |
277 | while (i < exp[0]) { |
278 | while (j >= 0) { |
9400cf6f |
279 | internal_mul(a + mlen, a + mlen, b, mlen); |
32874aea |
280 | internal_mod(b, mlen * 2, m, mlen, NULL, 0); |
e5574168 |
281 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
9400cf6f |
282 | internal_mul(b + mlen, n, a, mlen); |
32874aea |
283 | internal_mod(a, mlen * 2, m, mlen, NULL, 0); |
e5574168 |
284 | } else { |
a3412f52 |
285 | BignumInt *t; |
32874aea |
286 | t = a; |
287 | a = b; |
288 | b = t; |
e5574168 |
289 | } |
290 | j--; |
291 | } |
32874aea |
292 | i++; |
a3412f52 |
293 | j = BIGNUM_INT_BITS-1; |
e5574168 |
294 | } |
295 | |
296 | /* Fixup result in case the modulus was shifted */ |
297 | if (mshift) { |
32874aea |
298 | for (i = mlen - 1; i < 2 * mlen - 1; i++) |
a3412f52 |
299 | a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
300 | a[2 * mlen - 1] = a[2 * mlen - 1] << mshift; |
301 | internal_mod(a, mlen * 2, m, mlen, NULL, 0); |
302 | for (i = 2 * mlen - 1; i >= mlen; i--) |
a3412f52 |
303 | a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); |
e5574168 |
304 | } |
305 | |
306 | /* Copy result to buffer */ |
59600f67 |
307 | result = newbn(mod[0]); |
e5574168 |
308 | for (i = 0; i < mlen; i++) |
32874aea |
309 | result[result[0] - i] = a[i + mlen]; |
310 | while (result[0] > 1 && result[result[0]] == 0) |
311 | result[0]--; |
e5574168 |
312 | |
313 | /* Free temporary arrays */ |
32874aea |
314 | for (i = 0; i < 2 * mlen; i++) |
315 | a[i] = 0; |
316 | sfree(a); |
317 | for (i = 0; i < 2 * mlen; i++) |
318 | b[i] = 0; |
319 | sfree(b); |
320 | for (i = 0; i < mlen; i++) |
321 | m[i] = 0; |
322 | sfree(m); |
323 | for (i = 0; i < mlen; i++) |
324 | n[i] = 0; |
325 | sfree(n); |
59600f67 |
326 | |
327 | return result; |
e5574168 |
328 | } |
7cca0d81 |
329 | |
330 | /* |
331 | * Compute (p * q) % mod. |
332 | * The most significant word of mod MUST be non-zero. |
333 | * We assume that the result array is the same size as the mod array. |
334 | */ |
59600f67 |
335 | Bignum modmul(Bignum p, Bignum q, Bignum mod) |
7cca0d81 |
336 | { |
a3412f52 |
337 | BignumInt *a, *n, *m, *o; |
7cca0d81 |
338 | int mshift; |
80b10571 |
339 | int pqlen, mlen, rlen, i, j; |
59600f67 |
340 | Bignum result; |
7cca0d81 |
341 | |
342 | /* Allocate m of size mlen, copy mod to m */ |
343 | /* We use big endian internally */ |
344 | mlen = mod[0]; |
a3412f52 |
345 | m = snewn(mlen, BignumInt); |
32874aea |
346 | for (j = 0; j < mlen; j++) |
347 | m[j] = mod[mod[0] - j]; |
7cca0d81 |
348 | |
349 | /* Shift m left to make msb bit set */ |
a3412f52 |
350 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
351 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
32874aea |
352 | break; |
7cca0d81 |
353 | if (mshift) { |
354 | for (i = 0; i < mlen - 1; i++) |
a3412f52 |
355 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
356 | m[mlen - 1] = m[mlen - 1] << mshift; |
7cca0d81 |
357 | } |
358 | |
359 | pqlen = (p[0] > q[0] ? p[0] : q[0]); |
360 | |
361 | /* Allocate n of size pqlen, copy p to n */ |
a3412f52 |
362 | n = snewn(pqlen, BignumInt); |
7cca0d81 |
363 | i = pqlen - p[0]; |
32874aea |
364 | for (j = 0; j < i; j++) |
365 | n[j] = 0; |
366 | for (j = 0; j < p[0]; j++) |
367 | n[i + j] = p[p[0] - j]; |
7cca0d81 |
368 | |
369 | /* Allocate o of size pqlen, copy q to o */ |
a3412f52 |
370 | o = snewn(pqlen, BignumInt); |
7cca0d81 |
371 | i = pqlen - q[0]; |
32874aea |
372 | for (j = 0; j < i; j++) |
373 | o[j] = 0; |
374 | for (j = 0; j < q[0]; j++) |
375 | o[i + j] = q[q[0] - j]; |
7cca0d81 |
376 | |
377 | /* Allocate a of size 2*pqlen for result */ |
a3412f52 |
378 | a = snewn(2 * pqlen, BignumInt); |
7cca0d81 |
379 | |
380 | /* Main computation */ |
9400cf6f |
381 | internal_mul(n, o, a, pqlen); |
32874aea |
382 | internal_mod(a, pqlen * 2, m, mlen, NULL, 0); |
7cca0d81 |
383 | |
384 | /* Fixup result in case the modulus was shifted */ |
385 | if (mshift) { |
32874aea |
386 | for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) |
a3412f52 |
387 | a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
388 | a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift; |
389 | internal_mod(a, pqlen * 2, m, mlen, NULL, 0); |
390 | for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--) |
a3412f52 |
391 | a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); |
7cca0d81 |
392 | } |
393 | |
394 | /* Copy result to buffer */ |
32874aea |
395 | rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2); |
80b10571 |
396 | result = newbn(rlen); |
397 | for (i = 0; i < rlen; i++) |
32874aea |
398 | result[result[0] - i] = a[i + 2 * pqlen - rlen]; |
399 | while (result[0] > 1 && result[result[0]] == 0) |
400 | result[0]--; |
7cca0d81 |
401 | |
402 | /* Free temporary arrays */ |
32874aea |
403 | for (i = 0; i < 2 * pqlen; i++) |
404 | a[i] = 0; |
405 | sfree(a); |
406 | for (i = 0; i < mlen; i++) |
407 | m[i] = 0; |
408 | sfree(m); |
409 | for (i = 0; i < pqlen; i++) |
410 | n[i] = 0; |
411 | sfree(n); |
412 | for (i = 0; i < pqlen; i++) |
413 | o[i] = 0; |
414 | sfree(o); |
59600f67 |
415 | |
416 | return result; |
7cca0d81 |
417 | } |
418 | |
419 | /* |
9400cf6f |
420 | * Compute p % mod. |
421 | * The most significant word of mod MUST be non-zero. |
422 | * We assume that the result array is the same size as the mod array. |
5c72ca61 |
423 | * We optionally write out a quotient if `quotient' is non-NULL. |
424 | * We can avoid writing out the result if `result' is NULL. |
9400cf6f |
425 | */ |
f28753ab |
426 | static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) |
9400cf6f |
427 | { |
a3412f52 |
428 | BignumInt *n, *m; |
9400cf6f |
429 | int mshift; |
430 | int plen, mlen, i, j; |
431 | |
432 | /* Allocate m of size mlen, copy mod to m */ |
433 | /* We use big endian internally */ |
434 | mlen = mod[0]; |
a3412f52 |
435 | m = snewn(mlen, BignumInt); |
32874aea |
436 | for (j = 0; j < mlen; j++) |
437 | m[j] = mod[mod[0] - j]; |
9400cf6f |
438 | |
439 | /* Shift m left to make msb bit set */ |
a3412f52 |
440 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
441 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
32874aea |
442 | break; |
9400cf6f |
443 | if (mshift) { |
444 | for (i = 0; i < mlen - 1; i++) |
a3412f52 |
445 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
446 | m[mlen - 1] = m[mlen - 1] << mshift; |
9400cf6f |
447 | } |
448 | |
449 | plen = p[0]; |
450 | /* Ensure plen > mlen */ |
32874aea |
451 | if (plen <= mlen) |
452 | plen = mlen + 1; |
9400cf6f |
453 | |
454 | /* Allocate n of size plen, copy p to n */ |
a3412f52 |
455 | n = snewn(plen, BignumInt); |
32874aea |
456 | for (j = 0; j < plen; j++) |
457 | n[j] = 0; |
458 | for (j = 1; j <= p[0]; j++) |
459 | n[plen - j] = p[j]; |
9400cf6f |
460 | |
461 | /* Main computation */ |
462 | internal_mod(n, plen, m, mlen, quotient, mshift); |
463 | |
464 | /* Fixup result in case the modulus was shifted */ |
465 | if (mshift) { |
466 | for (i = plen - mlen - 1; i < plen - 1; i++) |
a3412f52 |
467 | n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
468 | n[plen - 1] = n[plen - 1] << mshift; |
9400cf6f |
469 | internal_mod(n, plen, m, mlen, quotient, 0); |
470 | for (i = plen - 1; i >= plen - mlen; i--) |
a3412f52 |
471 | n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift)); |
9400cf6f |
472 | } |
473 | |
474 | /* Copy result to buffer */ |
5c72ca61 |
475 | if (result) { |
476 | for (i = 1; i <= result[0]; i++) { |
477 | int j = plen - i; |
478 | result[i] = j >= 0 ? n[j] : 0; |
479 | } |
9400cf6f |
480 | } |
481 | |
482 | /* Free temporary arrays */ |
32874aea |
483 | for (i = 0; i < mlen; i++) |
484 | m[i] = 0; |
485 | sfree(m); |
486 | for (i = 0; i < plen; i++) |
487 | n[i] = 0; |
488 | sfree(n); |
9400cf6f |
489 | } |
490 | |
491 | /* |
7cca0d81 |
492 | * Decrement a number. |
493 | */ |
32874aea |
494 | void decbn(Bignum bn) |
495 | { |
7cca0d81 |
496 | int i = 1; |
497 | while (i < bn[0] && bn[i] == 0) |
a3412f52 |
498 | bn[i++] = BIGNUM_INT_MASK; |
7cca0d81 |
499 | bn[i]--; |
500 | } |
501 | |
27cd7fc2 |
502 | Bignum bignum_from_bytes(const unsigned char *data, int nbytes) |
32874aea |
503 | { |
3709bfe9 |
504 | Bignum result; |
505 | int w, i; |
506 | |
a3412f52 |
507 | w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */ |
3709bfe9 |
508 | |
509 | result = newbn(w); |
32874aea |
510 | for (i = 1; i <= w; i++) |
511 | result[i] = 0; |
512 | for (i = nbytes; i--;) { |
513 | unsigned char byte = *data++; |
a3412f52 |
514 | result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS); |
3709bfe9 |
515 | } |
516 | |
32874aea |
517 | while (result[0] > 1 && result[result[0]] == 0) |
518 | result[0]--; |
3709bfe9 |
519 | return result; |
520 | } |
521 | |
7cca0d81 |
522 | /* |
523 | * Read an ssh1-format bignum from a data buffer. Return the number |
524 | * of bytes consumed. |
525 | */ |
27cd7fc2 |
526 | int ssh1_read_bignum(const unsigned char *data, Bignum * result) |
32874aea |
527 | { |
27cd7fc2 |
528 | const unsigned char *p = data; |
7cca0d81 |
529 | int i; |
530 | int w, b; |
531 | |
532 | w = 0; |
32874aea |
533 | for (i = 0; i < 2; i++) |
534 | w = (w << 8) + *p++; |
535 | b = (w + 7) / 8; /* bits -> bytes */ |
7cca0d81 |
536 | |
32874aea |
537 | if (!result) /* just return length */ |
538 | return b + 2; |
a52f067e |
539 | |
3709bfe9 |
540 | *result = bignum_from_bytes(p, b); |
7cca0d81 |
541 | |
3709bfe9 |
542 | return p + b - data; |
7cca0d81 |
543 | } |
5c58ad2d |
544 | |
545 | /* |
546 | * Return the bit count of a bignum, for ssh1 encoding. |
547 | */ |
32874aea |
548 | int bignum_bitcount(Bignum bn) |
549 | { |
a3412f52 |
550 | int bitcount = bn[0] * BIGNUM_INT_BITS - 1; |
32874aea |
551 | while (bitcount >= 0 |
a3412f52 |
552 | && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--; |
5c58ad2d |
553 | return bitcount + 1; |
554 | } |
555 | |
556 | /* |
557 | * Return the byte length of a bignum when ssh1 encoded. |
558 | */ |
32874aea |
559 | int ssh1_bignum_length(Bignum bn) |
560 | { |
561 | return 2 + (bignum_bitcount(bn) + 7) / 8; |
ddecd643 |
562 | } |
563 | |
564 | /* |
565 | * Return the byte length of a bignum when ssh2 encoded. |
566 | */ |
32874aea |
567 | int ssh2_bignum_length(Bignum bn) |
568 | { |
569 | return 4 + (bignum_bitcount(bn) + 8) / 8; |
5c58ad2d |
570 | } |
571 | |
572 | /* |
573 | * Return a byte from a bignum; 0 is least significant, etc. |
574 | */ |
32874aea |
575 | int bignum_byte(Bignum bn, int i) |
576 | { |
a3412f52 |
577 | if (i >= BIGNUM_INT_BYTES * bn[0]) |
32874aea |
578 | return 0; /* beyond the end */ |
5c58ad2d |
579 | else |
a3412f52 |
580 | return (bn[i / BIGNUM_INT_BYTES + 1] >> |
581 | ((i % BIGNUM_INT_BYTES)*8)) & 0xFF; |
5c58ad2d |
582 | } |
583 | |
584 | /* |
9400cf6f |
585 | * Return a bit from a bignum; 0 is least significant, etc. |
586 | */ |
32874aea |
587 | int bignum_bit(Bignum bn, int i) |
588 | { |
a3412f52 |
589 | if (i >= BIGNUM_INT_BITS * bn[0]) |
32874aea |
590 | return 0; /* beyond the end */ |
9400cf6f |
591 | else |
a3412f52 |
592 | return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1; |
9400cf6f |
593 | } |
594 | |
595 | /* |
596 | * Set a bit in a bignum; 0 is least significant, etc. |
597 | */ |
32874aea |
598 | void bignum_set_bit(Bignum bn, int bitnum, int value) |
599 | { |
a3412f52 |
600 | if (bitnum >= BIGNUM_INT_BITS * bn[0]) |
32874aea |
601 | abort(); /* beyond the end */ |
9400cf6f |
602 | else { |
a3412f52 |
603 | int v = bitnum / BIGNUM_INT_BITS + 1; |
604 | int mask = 1 << (bitnum % BIGNUM_INT_BITS); |
32874aea |
605 | if (value) |
606 | bn[v] |= mask; |
607 | else |
608 | bn[v] &= ~mask; |
9400cf6f |
609 | } |
610 | } |
611 | |
612 | /* |
5c58ad2d |
613 | * Write a ssh1-format bignum into a buffer. It is assumed the |
614 | * buffer is big enough. Returns the number of bytes used. |
615 | */ |
32874aea |
616 | int ssh1_write_bignum(void *data, Bignum bn) |
617 | { |
5c58ad2d |
618 | unsigned char *p = data; |
619 | int len = ssh1_bignum_length(bn); |
620 | int i; |
ddecd643 |
621 | int bitc = bignum_bitcount(bn); |
5c58ad2d |
622 | |
623 | *p++ = (bitc >> 8) & 0xFF; |
32874aea |
624 | *p++ = (bitc) & 0xFF; |
625 | for (i = len - 2; i--;) |
626 | *p++ = bignum_byte(bn, i); |
5c58ad2d |
627 | return len; |
628 | } |
9400cf6f |
629 | |
630 | /* |
631 | * Compare two bignums. Returns like strcmp. |
632 | */ |
32874aea |
633 | int bignum_cmp(Bignum a, Bignum b) |
634 | { |
9400cf6f |
635 | int amax = a[0], bmax = b[0]; |
636 | int i = (amax > bmax ? amax : bmax); |
637 | while (i) { |
a3412f52 |
638 | BignumInt aval = (i > amax ? 0 : a[i]); |
639 | BignumInt bval = (i > bmax ? 0 : b[i]); |
32874aea |
640 | if (aval < bval) |
641 | return -1; |
642 | if (aval > bval) |
643 | return +1; |
644 | i--; |
9400cf6f |
645 | } |
646 | return 0; |
647 | } |
648 | |
649 | /* |
650 | * Right-shift one bignum to form another. |
651 | */ |
32874aea |
652 | Bignum bignum_rshift(Bignum a, int shift) |
653 | { |
9400cf6f |
654 | Bignum ret; |
655 | int i, shiftw, shiftb, shiftbb, bits; |
a3412f52 |
656 | BignumInt ai, ai1; |
9400cf6f |
657 | |
ddecd643 |
658 | bits = bignum_bitcount(a) - shift; |
a3412f52 |
659 | ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS); |
9400cf6f |
660 | |
661 | if (ret) { |
a3412f52 |
662 | shiftw = shift / BIGNUM_INT_BITS; |
663 | shiftb = shift % BIGNUM_INT_BITS; |
664 | shiftbb = BIGNUM_INT_BITS - shiftb; |
32874aea |
665 | |
666 | ai1 = a[shiftw + 1]; |
667 | for (i = 1; i <= ret[0]; i++) { |
668 | ai = ai1; |
669 | ai1 = (i + shiftw + 1 <= a[0] ? a[i + shiftw + 1] : 0); |
a3412f52 |
670 | ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK; |
32874aea |
671 | } |
9400cf6f |
672 | } |
673 | |
674 | return ret; |
675 | } |
676 | |
677 | /* |
678 | * Non-modular multiplication and addition. |
679 | */ |
32874aea |
680 | Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) |
681 | { |
9400cf6f |
682 | int alen = a[0], blen = b[0]; |
683 | int mlen = (alen > blen ? alen : blen); |
684 | int rlen, i, maxspot; |
a3412f52 |
685 | BignumInt *workspace; |
9400cf6f |
686 | Bignum ret; |
687 | |
688 | /* mlen space for a, mlen space for b, 2*mlen for result */ |
a3412f52 |
689 | workspace = snewn(mlen * 4, BignumInt); |
9400cf6f |
690 | for (i = 0; i < mlen; i++) { |
32874aea |
691 | workspace[0 * mlen + i] = (mlen - i <= a[0] ? a[mlen - i] : 0); |
692 | workspace[1 * mlen + i] = (mlen - i <= b[0] ? b[mlen - i] : 0); |
9400cf6f |
693 | } |
694 | |
32874aea |
695 | internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, |
696 | workspace + 2 * mlen, mlen); |
9400cf6f |
697 | |
698 | /* now just copy the result back */ |
699 | rlen = alen + blen + 1; |
700 | if (addend && rlen <= addend[0]) |
32874aea |
701 | rlen = addend[0] + 1; |
9400cf6f |
702 | ret = newbn(rlen); |
703 | maxspot = 0; |
704 | for (i = 1; i <= ret[0]; i++) { |
32874aea |
705 | ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); |
706 | if (ret[i] != 0) |
707 | maxspot = i; |
9400cf6f |
708 | } |
709 | ret[0] = maxspot; |
710 | |
711 | /* now add in the addend, if any */ |
712 | if (addend) { |
a3412f52 |
713 | BignumDblInt carry = 0; |
32874aea |
714 | for (i = 1; i <= rlen; i++) { |
715 | carry += (i <= ret[0] ? ret[i] : 0); |
716 | carry += (i <= addend[0] ? addend[i] : 0); |
a3412f52 |
717 | ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; |
718 | carry >>= BIGNUM_INT_BITS; |
32874aea |
719 | if (ret[i] != 0 && i > maxspot) |
720 | maxspot = i; |
721 | } |
9400cf6f |
722 | } |
723 | ret[0] = maxspot; |
724 | |
725 | return ret; |
726 | } |
727 | |
728 | /* |
729 | * Non-modular multiplication. |
730 | */ |
32874aea |
731 | Bignum bigmul(Bignum a, Bignum b) |
732 | { |
9400cf6f |
733 | return bigmuladd(a, b, NULL); |
734 | } |
735 | |
736 | /* |
3709bfe9 |
737 | * Create a bignum which is the bitmask covering another one. That |
738 | * is, the smallest integer which is >= N and is also one less than |
739 | * a power of two. |
740 | */ |
32874aea |
741 | Bignum bignum_bitmask(Bignum n) |
742 | { |
3709bfe9 |
743 | Bignum ret = copybn(n); |
744 | int i; |
a3412f52 |
745 | BignumInt j; |
3709bfe9 |
746 | |
747 | i = ret[0]; |
748 | while (n[i] == 0 && i > 0) |
32874aea |
749 | i--; |
3709bfe9 |
750 | if (i <= 0) |
32874aea |
751 | return ret; /* input was zero */ |
3709bfe9 |
752 | j = 1; |
753 | while (j < n[i]) |
32874aea |
754 | j = 2 * j + 1; |
3709bfe9 |
755 | ret[i] = j; |
756 | while (--i > 0) |
a3412f52 |
757 | ret[i] = BIGNUM_INT_MASK; |
3709bfe9 |
758 | return ret; |
759 | } |
760 | |
761 | /* |
5c72ca61 |
762 | * Convert a (max 32-bit) long into a bignum. |
9400cf6f |
763 | */ |
a3412f52 |
764 | Bignum bignum_from_long(unsigned long nn) |
32874aea |
765 | { |
9400cf6f |
766 | Bignum ret; |
a3412f52 |
767 | BignumDblInt n = nn; |
9400cf6f |
768 | |
5c72ca61 |
769 | ret = newbn(3); |
a3412f52 |
770 | ret[1] = (BignumInt)(n & BIGNUM_INT_MASK); |
771 | ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK); |
5c72ca61 |
772 | ret[3] = 0; |
773 | ret[0] = (ret[2] ? 2 : 1); |
32874aea |
774 | return ret; |
9400cf6f |
775 | } |
776 | |
777 | /* |
778 | * Add a long to a bignum. |
779 | */ |
a3412f52 |
780 | Bignum bignum_add_long(Bignum number, unsigned long addendx) |
32874aea |
781 | { |
782 | Bignum ret = newbn(number[0] + 1); |
9400cf6f |
783 | int i, maxspot = 0; |
a3412f52 |
784 | BignumDblInt carry = 0, addend = addendx; |
9400cf6f |
785 | |
786 | for (i = 1; i <= ret[0]; i++) { |
a3412f52 |
787 | carry += addend & BIGNUM_INT_MASK; |
32874aea |
788 | carry += (i <= number[0] ? number[i] : 0); |
a3412f52 |
789 | addend >>= BIGNUM_INT_BITS; |
790 | ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; |
791 | carry >>= BIGNUM_INT_BITS; |
32874aea |
792 | if (ret[i] != 0) |
793 | maxspot = i; |
9400cf6f |
794 | } |
795 | ret[0] = maxspot; |
796 | return ret; |
797 | } |
798 | |
799 | /* |
800 | * Compute the residue of a bignum, modulo a (max 16-bit) short. |
801 | */ |
32874aea |
802 | unsigned short bignum_mod_short(Bignum number, unsigned short modulus) |
803 | { |
a3412f52 |
804 | BignumDblInt mod, r; |
9400cf6f |
805 | int i; |
806 | |
807 | r = 0; |
808 | mod = modulus; |
809 | for (i = number[0]; i > 0; i--) |
32874aea |
810 | r = (r * 65536 + number[i]) % mod; |
6e522441 |
811 | return (unsigned short) r; |
9400cf6f |
812 | } |
813 | |
a3412f52 |
814 | #ifdef DEBUG |
32874aea |
815 | void diagbn(char *prefix, Bignum md) |
816 | { |
9400cf6f |
817 | int i, nibbles, morenibbles; |
818 | static const char hex[] = "0123456789ABCDEF"; |
819 | |
5c72ca61 |
820 | debug(("%s0x", prefix ? prefix : "")); |
9400cf6f |
821 | |
32874aea |
822 | nibbles = (3 + bignum_bitcount(md)) / 4; |
823 | if (nibbles < 1) |
824 | nibbles = 1; |
825 | morenibbles = 4 * md[0] - nibbles; |
826 | for (i = 0; i < morenibbles; i++) |
5c72ca61 |
827 | debug(("-")); |
32874aea |
828 | for (i = nibbles; i--;) |
5c72ca61 |
829 | debug(("%c", |
830 | hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF])); |
9400cf6f |
831 | |
32874aea |
832 | if (prefix) |
5c72ca61 |
833 | debug(("\n")); |
834 | } |
f28753ab |
835 | #endif |
5c72ca61 |
836 | |
837 | /* |
838 | * Simple division. |
839 | */ |
840 | Bignum bigdiv(Bignum a, Bignum b) |
841 | { |
842 | Bignum q = newbn(a[0]); |
843 | bigdivmod(a, b, NULL, q); |
844 | return q; |
845 | } |
846 | |
847 | /* |
848 | * Simple remainder. |
849 | */ |
850 | Bignum bigmod(Bignum a, Bignum b) |
851 | { |
852 | Bignum r = newbn(b[0]); |
853 | bigdivmod(a, b, r, NULL); |
854 | return r; |
9400cf6f |
855 | } |
856 | |
857 | /* |
858 | * Greatest common divisor. |
859 | */ |
32874aea |
860 | Bignum biggcd(Bignum av, Bignum bv) |
861 | { |
9400cf6f |
862 | Bignum a = copybn(av); |
863 | Bignum b = copybn(bv); |
864 | |
9400cf6f |
865 | while (bignum_cmp(b, Zero) != 0) { |
32874aea |
866 | Bignum t = newbn(b[0]); |
5c72ca61 |
867 | bigdivmod(a, b, t, NULL); |
32874aea |
868 | while (t[0] > 1 && t[t[0]] == 0) |
869 | t[0]--; |
870 | freebn(a); |
871 | a = b; |
872 | b = t; |
9400cf6f |
873 | } |
874 | |
875 | freebn(b); |
876 | return a; |
877 | } |
878 | |
879 | /* |
880 | * Modular inverse, using Euclid's extended algorithm. |
881 | */ |
32874aea |
882 | Bignum modinv(Bignum number, Bignum modulus) |
883 | { |
9400cf6f |
884 | Bignum a = copybn(modulus); |
885 | Bignum b = copybn(number); |
886 | Bignum xp = copybn(Zero); |
887 | Bignum x = copybn(One); |
888 | int sign = +1; |
889 | |
890 | while (bignum_cmp(b, One) != 0) { |
32874aea |
891 | Bignum t = newbn(b[0]); |
892 | Bignum q = newbn(a[0]); |
5c72ca61 |
893 | bigdivmod(a, b, t, q); |
32874aea |
894 | while (t[0] > 1 && t[t[0]] == 0) |
895 | t[0]--; |
896 | freebn(a); |
897 | a = b; |
898 | b = t; |
899 | t = xp; |
900 | xp = x; |
901 | x = bigmuladd(q, xp, t); |
902 | sign = -sign; |
903 | freebn(t); |
9400cf6f |
904 | } |
905 | |
906 | freebn(b); |
907 | freebn(a); |
908 | freebn(xp); |
909 | |
910 | /* now we know that sign * x == 1, and that x < modulus */ |
911 | if (sign < 0) { |
32874aea |
912 | /* set a new x to be modulus - x */ |
913 | Bignum newx = newbn(modulus[0]); |
a3412f52 |
914 | BignumInt carry = 0; |
32874aea |
915 | int maxspot = 1; |
916 | int i; |
917 | |
918 | for (i = 1; i <= newx[0]; i++) { |
a3412f52 |
919 | BignumInt aword = (i <= modulus[0] ? modulus[i] : 0); |
920 | BignumInt bword = (i <= x[0] ? x[i] : 0); |
32874aea |
921 | newx[i] = aword - bword - carry; |
922 | bword = ~bword; |
923 | carry = carry ? (newx[i] >= bword) : (newx[i] > bword); |
924 | if (newx[i] != 0) |
925 | maxspot = i; |
926 | } |
927 | newx[0] = maxspot; |
928 | freebn(x); |
929 | x = newx; |
9400cf6f |
930 | } |
931 | |
932 | /* and return. */ |
933 | return x; |
934 | } |
6e522441 |
935 | |
936 | /* |
937 | * Render a bignum into decimal. Return a malloced string holding |
938 | * the decimal representation. |
939 | */ |
32874aea |
940 | char *bignum_decimal(Bignum x) |
941 | { |
6e522441 |
942 | int ndigits, ndigit; |
943 | int i, iszero; |
a3412f52 |
944 | BignumDblInt carry; |
6e522441 |
945 | char *ret; |
a3412f52 |
946 | BignumInt *workspace; |
6e522441 |
947 | |
948 | /* |
949 | * First, estimate the number of digits. Since log(10)/log(2) |
950 | * is just greater than 93/28 (the joys of continued fraction |
951 | * approximations...) we know that for every 93 bits, we need |
952 | * at most 28 digits. This will tell us how much to malloc. |
953 | * |
954 | * Formally: if x has i bits, that means x is strictly less |
955 | * than 2^i. Since 2 is less than 10^(28/93), this is less than |
956 | * 10^(28i/93). We need an integer power of ten, so we must |
957 | * round up (rounding down might make it less than x again). |
958 | * Therefore if we multiply the bit count by 28/93, rounding |
959 | * up, we will have enough digits. |
960 | */ |
ddecd643 |
961 | i = bignum_bitcount(x); |
32874aea |
962 | ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */ |
963 | ndigits++; /* allow for trailing \0 */ |
3d88e64d |
964 | ret = snewn(ndigits, char); |
6e522441 |
965 | |
966 | /* |
967 | * Now allocate some workspace to hold the binary form as we |
968 | * repeatedly divide it by ten. Initialise this to the |
969 | * big-endian form of the number. |
970 | */ |
a3412f52 |
971 | workspace = snewn(x[0], BignumInt); |
6e522441 |
972 | for (i = 0; i < x[0]; i++) |
32874aea |
973 | workspace[i] = x[x[0] - i]; |
6e522441 |
974 | |
975 | /* |
976 | * Next, write the decimal number starting with the last digit. |
977 | * We use ordinary short division, dividing 10 into the |
978 | * workspace. |
979 | */ |
32874aea |
980 | ndigit = ndigits - 1; |
6e522441 |
981 | ret[ndigit] = '\0'; |
982 | do { |
32874aea |
983 | iszero = 1; |
984 | carry = 0; |
985 | for (i = 0; i < x[0]; i++) { |
a3412f52 |
986 | carry = (carry << BIGNUM_INT_BITS) + workspace[i]; |
987 | workspace[i] = (BignumInt) (carry / 10); |
32874aea |
988 | if (workspace[i]) |
989 | iszero = 0; |
990 | carry %= 10; |
991 | } |
992 | ret[--ndigit] = (char) (carry + '0'); |
6e522441 |
993 | } while (!iszero); |
994 | |
995 | /* |
996 | * There's a chance we've fallen short of the start of the |
997 | * string. Correct if so. |
998 | */ |
999 | if (ndigit > 0) |
32874aea |
1000 | memmove(ret, ret + ndigit, ndigits - ndigit); |
6e522441 |
1001 | |
1002 | /* |
1003 | * Done. |
1004 | */ |
1005 | return ret; |
1006 | } |