e5574168 |
1 | /* |
2 | * Bignum routines for RSA and DH and stuff. |
3 | */ |
4 | |
5 | #include <stdio.h> |
ed953b91 |
6 | #include <assert.h> |
e5574168 |
7 | #include <stdlib.h> |
8 | #include <string.h> |
9 | |
5c72ca61 |
10 | #include "misc.h" |
98ba26b9 |
11 | |
a3412f52 |
12 | #if defined __GNUC__ && defined __i386__ |
13 | typedef unsigned long BignumInt; |
14 | typedef unsigned long long BignumDblInt; |
15 | #define BIGNUM_INT_MASK 0xFFFFFFFFUL |
16 | #define BIGNUM_TOP_BIT 0x80000000UL |
17 | #define BIGNUM_INT_BITS 32 |
18 | #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) |
a47e8bba |
19 | #define DIVMOD_WORD(q, r, hi, lo, w) \ |
20 | __asm__("div %2" : \ |
21 | "=d" (r), "=a" (q) : \ |
22 | "r" (w), "d" (hi), "a" (lo)) |
a3412f52 |
23 | #else |
24 | typedef unsigned short BignumInt; |
25 | typedef unsigned long BignumDblInt; |
26 | #define BIGNUM_INT_MASK 0xFFFFU |
27 | #define BIGNUM_TOP_BIT 0x8000U |
28 | #define BIGNUM_INT_BITS 16 |
29 | #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) |
a47e8bba |
30 | #define DIVMOD_WORD(q, r, hi, lo, w) do { \ |
31 | BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \ |
32 | q = n / w; \ |
33 | r = n % w; \ |
34 | } while (0) |
a3412f52 |
35 | #endif |
36 | |
37 | #define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8) |
38 | |
3709bfe9 |
39 | #define BIGNUM_INTERNAL |
a3412f52 |
40 | typedef BignumInt *Bignum; |
3709bfe9 |
41 | |
e5574168 |
42 | #include "ssh.h" |
43 | |
a3412f52 |
44 | BignumInt bnZero[1] = { 0 }; |
45 | BignumInt bnOne[2] = { 1, 1 }; |
e5574168 |
46 | |
7d6ee6ff |
47 | /* |
a3412f52 |
48 | * The Bignum format is an array of `BignumInt'. The first |
7d6ee6ff |
49 | * element of the array counts the remaining elements. The |
a3412f52 |
50 | * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_ |
7d6ee6ff |
51 | * significant digit first. (So it's trivial to extract the bit |
52 | * with value 2^n for any n.) |
53 | * |
54 | * All Bignums in this module are positive. Negative numbers must |
55 | * be dealt with outside it. |
56 | * |
57 | * INVARIANT: the most significant word of any Bignum must be |
58 | * nonzero. |
59 | */ |
60 | |
7cca0d81 |
61 | Bignum Zero = bnZero, One = bnOne; |
e5574168 |
62 | |
32874aea |
63 | static Bignum newbn(int length) |
64 | { |
a3412f52 |
65 | Bignum b = snewn(length + 1, BignumInt); |
e5574168 |
66 | if (!b) |
67 | abort(); /* FIXME */ |
32874aea |
68 | memset(b, 0, (length + 1) * sizeof(*b)); |
e5574168 |
69 | b[0] = length; |
70 | return b; |
71 | } |
72 | |
32874aea |
73 | void bn_restore_invariant(Bignum b) |
74 | { |
75 | while (b[0] > 1 && b[b[0]] == 0) |
76 | b[0]--; |
3709bfe9 |
77 | } |
78 | |
32874aea |
79 | Bignum copybn(Bignum orig) |
80 | { |
a3412f52 |
81 | Bignum b = snewn(orig[0] + 1, BignumInt); |
7cca0d81 |
82 | if (!b) |
83 | abort(); /* FIXME */ |
32874aea |
84 | memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); |
7cca0d81 |
85 | return b; |
86 | } |
87 | |
32874aea |
88 | void freebn(Bignum b) |
89 | { |
e5574168 |
90 | /* |
91 | * Burn the evidence, just in case. |
92 | */ |
93 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
dcbde236 |
94 | sfree(b); |
e5574168 |
95 | } |
96 | |
32874aea |
97 | Bignum bn_power_2(int n) |
98 | { |
a3412f52 |
99 | Bignum ret = newbn(n / BIGNUM_INT_BITS + 1); |
3709bfe9 |
100 | bignum_set_bit(ret, n, 1); |
101 | return ret; |
102 | } |
103 | |
e5574168 |
104 | /* |
105 | * Compute c = a * b. |
106 | * Input is in the first len words of a and b. |
107 | * Result is returned in the first 2*len words of c. |
108 | */ |
a3412f52 |
109 | static void internal_mul(BignumInt *a, BignumInt *b, |
110 | BignumInt *c, int len) |
e5574168 |
111 | { |
112 | int i, j; |
a3412f52 |
113 | BignumDblInt t; |
e5574168 |
114 | |
32874aea |
115 | for (j = 0; j < 2 * len; j++) |
9400cf6f |
116 | c[j] = 0; |
e5574168 |
117 | |
118 | for (i = len - 1; i >= 0; i--) { |
e5574168 |
119 | t = 0; |
120 | for (j = len - 1; j >= 0; j--) { |
a3412f52 |
121 | t += MUL_WORD(a[i], (BignumDblInt) b[j]); |
122 | t += (BignumDblInt) c[i + j + 1]; |
123 | c[i + j + 1] = (BignumInt) t; |
124 | t = t >> BIGNUM_INT_BITS; |
e5574168 |
125 | } |
a3412f52 |
126 | c[i] = (BignumInt) t; |
e5574168 |
127 | } |
128 | } |
129 | |
a3412f52 |
130 | static void internal_add_shifted(BignumInt *number, |
32874aea |
131 | unsigned n, int shift) |
132 | { |
a3412f52 |
133 | int word = 1 + (shift / BIGNUM_INT_BITS); |
134 | int bshift = shift % BIGNUM_INT_BITS; |
135 | BignumDblInt addend; |
9400cf6f |
136 | |
3014da2b |
137 | addend = (BignumDblInt)n << bshift; |
9400cf6f |
138 | |
139 | while (addend) { |
32874aea |
140 | addend += number[word]; |
a3412f52 |
141 | number[word] = (BignumInt) addend & BIGNUM_INT_MASK; |
142 | addend >>= BIGNUM_INT_BITS; |
32874aea |
143 | word++; |
9400cf6f |
144 | } |
145 | } |
146 | |
e5574168 |
147 | /* |
148 | * Compute a = a % m. |
9400cf6f |
149 | * Input in first alen words of a and first mlen words of m. |
150 | * Output in first alen words of a |
151 | * (of which first alen-mlen words will be zero). |
e5574168 |
152 | * The MSW of m MUST have its high bit set. |
9400cf6f |
153 | * Quotient is accumulated in the `quotient' array, which is a Bignum |
154 | * rather than the internal bigendian format. Quotient parts are shifted |
155 | * left by `qshift' before adding into quot. |
e5574168 |
156 | */ |
a3412f52 |
157 | static void internal_mod(BignumInt *a, int alen, |
158 | BignumInt *m, int mlen, |
159 | BignumInt *quot, int qshift) |
e5574168 |
160 | { |
a3412f52 |
161 | BignumInt m0, m1; |
e5574168 |
162 | unsigned int h; |
163 | int i, k; |
164 | |
e5574168 |
165 | m0 = m[0]; |
9400cf6f |
166 | if (mlen > 1) |
32874aea |
167 | m1 = m[1]; |
9400cf6f |
168 | else |
32874aea |
169 | m1 = 0; |
e5574168 |
170 | |
32874aea |
171 | for (i = 0; i <= alen - mlen; i++) { |
a3412f52 |
172 | BignumDblInt t; |
9400cf6f |
173 | unsigned int q, r, c, ai1; |
e5574168 |
174 | |
175 | if (i == 0) { |
176 | h = 0; |
177 | } else { |
32874aea |
178 | h = a[i - 1]; |
179 | a[i - 1] = 0; |
e5574168 |
180 | } |
181 | |
32874aea |
182 | if (i == alen - 1) |
183 | ai1 = 0; |
184 | else |
185 | ai1 = a[i + 1]; |
9400cf6f |
186 | |
e5574168 |
187 | /* Find q = h:a[i] / m0 */ |
62ef3d44 |
188 | if (h >= m0) { |
189 | /* |
190 | * Special case. |
191 | * |
192 | * To illustrate it, suppose a BignumInt is 8 bits, and |
193 | * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then |
194 | * our initial division will be 0xA123 / 0xA1, which |
195 | * will give a quotient of 0x100 and a divide overflow. |
196 | * However, the invariants in this division algorithm |
197 | * are not violated, since the full number A1:23:... is |
198 | * _less_ than the quotient prefix A1:B2:... and so the |
199 | * following correction loop would have sorted it out. |
200 | * |
201 | * In this situation we set q to be the largest |
202 | * quotient we _can_ stomach (0xFF, of course). |
203 | */ |
204 | q = BIGNUM_INT_MASK; |
205 | } else { |
206 | DIVMOD_WORD(q, r, h, a[i], m0); |
207 | |
208 | /* Refine our estimate of q by looking at |
209 | h:a[i]:a[i+1] / m0:m1 */ |
210 | t = MUL_WORD(m1, q); |
211 | if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) { |
212 | q--; |
213 | t -= m1; |
214 | r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */ |
215 | if (r >= (BignumDblInt) m0 && |
216 | t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--; |
217 | } |
e5574168 |
218 | } |
219 | |
9400cf6f |
220 | /* Subtract q * m from a[i...] */ |
e5574168 |
221 | c = 0; |
9400cf6f |
222 | for (k = mlen - 1; k >= 0; k--) { |
a47e8bba |
223 | t = MUL_WORD(q, m[k]); |
e5574168 |
224 | t += c; |
a3412f52 |
225 | c = t >> BIGNUM_INT_BITS; |
226 | if ((BignumInt) t > a[i + k]) |
32874aea |
227 | c++; |
a3412f52 |
228 | a[i + k] -= (BignumInt) t; |
e5574168 |
229 | } |
230 | |
231 | /* Add back m in case of borrow */ |
232 | if (c != h) { |
233 | t = 0; |
9400cf6f |
234 | for (k = mlen - 1; k >= 0; k--) { |
e5574168 |
235 | t += m[k]; |
32874aea |
236 | t += a[i + k]; |
a3412f52 |
237 | a[i + k] = (BignumInt) t; |
238 | t = t >> BIGNUM_INT_BITS; |
e5574168 |
239 | } |
32874aea |
240 | q--; |
e5574168 |
241 | } |
32874aea |
242 | if (quot) |
a3412f52 |
243 | internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); |
e5574168 |
244 | } |
245 | } |
246 | |
247 | /* |
248 | * Compute (base ^ exp) % mod. |
e5574168 |
249 | */ |
ed953b91 |
250 | Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) |
e5574168 |
251 | { |
a3412f52 |
252 | BignumInt *a, *b, *n, *m; |
e5574168 |
253 | int mshift; |
254 | int mlen, i, j; |
ed953b91 |
255 | Bignum base, result; |
256 | |
257 | /* |
258 | * The most significant word of mod needs to be non-zero. It |
259 | * should already be, but let's make sure. |
260 | */ |
261 | assert(mod[mod[0]] != 0); |
262 | |
263 | /* |
264 | * Make sure the base is smaller than the modulus, by reducing |
265 | * it modulo the modulus if not. |
266 | */ |
267 | base = bigmod(base_in, mod); |
e5574168 |
268 | |
269 | /* Allocate m of size mlen, copy mod to m */ |
270 | /* We use big endian internally */ |
271 | mlen = mod[0]; |
a3412f52 |
272 | m = snewn(mlen, BignumInt); |
32874aea |
273 | for (j = 0; j < mlen; j++) |
274 | m[j] = mod[mod[0] - j]; |
e5574168 |
275 | |
276 | /* Shift m left to make msb bit set */ |
a3412f52 |
277 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
278 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
32874aea |
279 | break; |
e5574168 |
280 | if (mshift) { |
281 | for (i = 0; i < mlen - 1; i++) |
a3412f52 |
282 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
283 | m[mlen - 1] = m[mlen - 1] << mshift; |
e5574168 |
284 | } |
285 | |
286 | /* Allocate n of size mlen, copy base to n */ |
a3412f52 |
287 | n = snewn(mlen, BignumInt); |
e5574168 |
288 | i = mlen - base[0]; |
32874aea |
289 | for (j = 0; j < i; j++) |
290 | n[j] = 0; |
291 | for (j = 0; j < base[0]; j++) |
292 | n[i + j] = base[base[0] - j]; |
e5574168 |
293 | |
294 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
a3412f52 |
295 | a = snewn(2 * mlen, BignumInt); |
296 | b = snewn(2 * mlen, BignumInt); |
32874aea |
297 | for (i = 0; i < 2 * mlen; i++) |
298 | a[i] = 0; |
299 | a[2 * mlen - 1] = 1; |
e5574168 |
300 | |
301 | /* Skip leading zero bits of exp. */ |
32874aea |
302 | i = 0; |
a3412f52 |
303 | j = BIGNUM_INT_BITS-1; |
e5574168 |
304 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
305 | j--; |
32874aea |
306 | if (j < 0) { |
307 | i++; |
a3412f52 |
308 | j = BIGNUM_INT_BITS-1; |
32874aea |
309 | } |
e5574168 |
310 | } |
311 | |
312 | /* Main computation */ |
313 | while (i < exp[0]) { |
314 | while (j >= 0) { |
9400cf6f |
315 | internal_mul(a + mlen, a + mlen, b, mlen); |
32874aea |
316 | internal_mod(b, mlen * 2, m, mlen, NULL, 0); |
e5574168 |
317 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
9400cf6f |
318 | internal_mul(b + mlen, n, a, mlen); |
32874aea |
319 | internal_mod(a, mlen * 2, m, mlen, NULL, 0); |
e5574168 |
320 | } else { |
a3412f52 |
321 | BignumInt *t; |
32874aea |
322 | t = a; |
323 | a = b; |
324 | b = t; |
e5574168 |
325 | } |
326 | j--; |
327 | } |
32874aea |
328 | i++; |
a3412f52 |
329 | j = BIGNUM_INT_BITS-1; |
e5574168 |
330 | } |
331 | |
332 | /* Fixup result in case the modulus was shifted */ |
333 | if (mshift) { |
32874aea |
334 | for (i = mlen - 1; i < 2 * mlen - 1; i++) |
a3412f52 |
335 | a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
336 | a[2 * mlen - 1] = a[2 * mlen - 1] << mshift; |
337 | internal_mod(a, mlen * 2, m, mlen, NULL, 0); |
338 | for (i = 2 * mlen - 1; i >= mlen; i--) |
a3412f52 |
339 | a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); |
e5574168 |
340 | } |
341 | |
342 | /* Copy result to buffer */ |
59600f67 |
343 | result = newbn(mod[0]); |
e5574168 |
344 | for (i = 0; i < mlen; i++) |
32874aea |
345 | result[result[0] - i] = a[i + mlen]; |
346 | while (result[0] > 1 && result[result[0]] == 0) |
347 | result[0]--; |
e5574168 |
348 | |
349 | /* Free temporary arrays */ |
32874aea |
350 | for (i = 0; i < 2 * mlen; i++) |
351 | a[i] = 0; |
352 | sfree(a); |
353 | for (i = 0; i < 2 * mlen; i++) |
354 | b[i] = 0; |
355 | sfree(b); |
356 | for (i = 0; i < mlen; i++) |
357 | m[i] = 0; |
358 | sfree(m); |
359 | for (i = 0; i < mlen; i++) |
360 | n[i] = 0; |
361 | sfree(n); |
59600f67 |
362 | |
ed953b91 |
363 | freebn(base); |
364 | |
59600f67 |
365 | return result; |
e5574168 |
366 | } |
7cca0d81 |
367 | |
368 | /* |
369 | * Compute (p * q) % mod. |
370 | * The most significant word of mod MUST be non-zero. |
371 | * We assume that the result array is the same size as the mod array. |
372 | */ |
59600f67 |
373 | Bignum modmul(Bignum p, Bignum q, Bignum mod) |
7cca0d81 |
374 | { |
a3412f52 |
375 | BignumInt *a, *n, *m, *o; |
7cca0d81 |
376 | int mshift; |
80b10571 |
377 | int pqlen, mlen, rlen, i, j; |
59600f67 |
378 | Bignum result; |
7cca0d81 |
379 | |
380 | /* Allocate m of size mlen, copy mod to m */ |
381 | /* We use big endian internally */ |
382 | mlen = mod[0]; |
a3412f52 |
383 | m = snewn(mlen, BignumInt); |
32874aea |
384 | for (j = 0; j < mlen; j++) |
385 | m[j] = mod[mod[0] - j]; |
7cca0d81 |
386 | |
387 | /* Shift m left to make msb bit set */ |
a3412f52 |
388 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
389 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
32874aea |
390 | break; |
7cca0d81 |
391 | if (mshift) { |
392 | for (i = 0; i < mlen - 1; i++) |
a3412f52 |
393 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
394 | m[mlen - 1] = m[mlen - 1] << mshift; |
7cca0d81 |
395 | } |
396 | |
397 | pqlen = (p[0] > q[0] ? p[0] : q[0]); |
398 | |
399 | /* Allocate n of size pqlen, copy p to n */ |
a3412f52 |
400 | n = snewn(pqlen, BignumInt); |
7cca0d81 |
401 | i = pqlen - p[0]; |
32874aea |
402 | for (j = 0; j < i; j++) |
403 | n[j] = 0; |
404 | for (j = 0; j < p[0]; j++) |
405 | n[i + j] = p[p[0] - j]; |
7cca0d81 |
406 | |
407 | /* Allocate o of size pqlen, copy q to o */ |
a3412f52 |
408 | o = snewn(pqlen, BignumInt); |
7cca0d81 |
409 | i = pqlen - q[0]; |
32874aea |
410 | for (j = 0; j < i; j++) |
411 | o[j] = 0; |
412 | for (j = 0; j < q[0]; j++) |
413 | o[i + j] = q[q[0] - j]; |
7cca0d81 |
414 | |
415 | /* Allocate a of size 2*pqlen for result */ |
a3412f52 |
416 | a = snewn(2 * pqlen, BignumInt); |
7cca0d81 |
417 | |
418 | /* Main computation */ |
9400cf6f |
419 | internal_mul(n, o, a, pqlen); |
32874aea |
420 | internal_mod(a, pqlen * 2, m, mlen, NULL, 0); |
7cca0d81 |
421 | |
422 | /* Fixup result in case the modulus was shifted */ |
423 | if (mshift) { |
32874aea |
424 | for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) |
a3412f52 |
425 | a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
426 | a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift; |
427 | internal_mod(a, pqlen * 2, m, mlen, NULL, 0); |
428 | for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--) |
a3412f52 |
429 | a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); |
7cca0d81 |
430 | } |
431 | |
432 | /* Copy result to buffer */ |
32874aea |
433 | rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2); |
80b10571 |
434 | result = newbn(rlen); |
435 | for (i = 0; i < rlen; i++) |
32874aea |
436 | result[result[0] - i] = a[i + 2 * pqlen - rlen]; |
437 | while (result[0] > 1 && result[result[0]] == 0) |
438 | result[0]--; |
7cca0d81 |
439 | |
440 | /* Free temporary arrays */ |
32874aea |
441 | for (i = 0; i < 2 * pqlen; i++) |
442 | a[i] = 0; |
443 | sfree(a); |
444 | for (i = 0; i < mlen; i++) |
445 | m[i] = 0; |
446 | sfree(m); |
447 | for (i = 0; i < pqlen; i++) |
448 | n[i] = 0; |
449 | sfree(n); |
450 | for (i = 0; i < pqlen; i++) |
451 | o[i] = 0; |
452 | sfree(o); |
59600f67 |
453 | |
454 | return result; |
7cca0d81 |
455 | } |
456 | |
457 | /* |
9400cf6f |
458 | * Compute p % mod. |
459 | * The most significant word of mod MUST be non-zero. |
460 | * We assume that the result array is the same size as the mod array. |
5c72ca61 |
461 | * We optionally write out a quotient if `quotient' is non-NULL. |
462 | * We can avoid writing out the result if `result' is NULL. |
9400cf6f |
463 | */ |
f28753ab |
464 | static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) |
9400cf6f |
465 | { |
a3412f52 |
466 | BignumInt *n, *m; |
9400cf6f |
467 | int mshift; |
468 | int plen, mlen, i, j; |
469 | |
470 | /* Allocate m of size mlen, copy mod to m */ |
471 | /* We use big endian internally */ |
472 | mlen = mod[0]; |
a3412f52 |
473 | m = snewn(mlen, BignumInt); |
32874aea |
474 | for (j = 0; j < mlen; j++) |
475 | m[j] = mod[mod[0] - j]; |
9400cf6f |
476 | |
477 | /* Shift m left to make msb bit set */ |
a3412f52 |
478 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
479 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
32874aea |
480 | break; |
9400cf6f |
481 | if (mshift) { |
482 | for (i = 0; i < mlen - 1; i++) |
a3412f52 |
483 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
484 | m[mlen - 1] = m[mlen - 1] << mshift; |
9400cf6f |
485 | } |
486 | |
487 | plen = p[0]; |
488 | /* Ensure plen > mlen */ |
32874aea |
489 | if (plen <= mlen) |
490 | plen = mlen + 1; |
9400cf6f |
491 | |
492 | /* Allocate n of size plen, copy p to n */ |
a3412f52 |
493 | n = snewn(plen, BignumInt); |
32874aea |
494 | for (j = 0; j < plen; j++) |
495 | n[j] = 0; |
496 | for (j = 1; j <= p[0]; j++) |
497 | n[plen - j] = p[j]; |
9400cf6f |
498 | |
499 | /* Main computation */ |
500 | internal_mod(n, plen, m, mlen, quotient, mshift); |
501 | |
502 | /* Fixup result in case the modulus was shifted */ |
503 | if (mshift) { |
504 | for (i = plen - mlen - 1; i < plen - 1; i++) |
a3412f52 |
505 | n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
32874aea |
506 | n[plen - 1] = n[plen - 1] << mshift; |
9400cf6f |
507 | internal_mod(n, plen, m, mlen, quotient, 0); |
508 | for (i = plen - 1; i >= plen - mlen; i--) |
a3412f52 |
509 | n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift)); |
9400cf6f |
510 | } |
511 | |
512 | /* Copy result to buffer */ |
5c72ca61 |
513 | if (result) { |
514 | for (i = 1; i <= result[0]; i++) { |
515 | int j = plen - i; |
516 | result[i] = j >= 0 ? n[j] : 0; |
517 | } |
9400cf6f |
518 | } |
519 | |
520 | /* Free temporary arrays */ |
32874aea |
521 | for (i = 0; i < mlen; i++) |
522 | m[i] = 0; |
523 | sfree(m); |
524 | for (i = 0; i < plen; i++) |
525 | n[i] = 0; |
526 | sfree(n); |
9400cf6f |
527 | } |
528 | |
529 | /* |
7cca0d81 |
530 | * Decrement a number. |
531 | */ |
32874aea |
532 | void decbn(Bignum bn) |
533 | { |
7cca0d81 |
534 | int i = 1; |
535 | while (i < bn[0] && bn[i] == 0) |
a3412f52 |
536 | bn[i++] = BIGNUM_INT_MASK; |
7cca0d81 |
537 | bn[i]--; |
538 | } |
539 | |
27cd7fc2 |
540 | Bignum bignum_from_bytes(const unsigned char *data, int nbytes) |
32874aea |
541 | { |
3709bfe9 |
542 | Bignum result; |
543 | int w, i; |
544 | |
a3412f52 |
545 | w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */ |
3709bfe9 |
546 | |
547 | result = newbn(w); |
32874aea |
548 | for (i = 1; i <= w; i++) |
549 | result[i] = 0; |
550 | for (i = nbytes; i--;) { |
551 | unsigned char byte = *data++; |
a3412f52 |
552 | result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS); |
3709bfe9 |
553 | } |
554 | |
32874aea |
555 | while (result[0] > 1 && result[result[0]] == 0) |
556 | result[0]--; |
3709bfe9 |
557 | return result; |
558 | } |
559 | |
7cca0d81 |
560 | /* |
2e85c969 |
561 | * Read an SSH-1-format bignum from a data buffer. Return the number |
0016d70b |
562 | * of bytes consumed, or -1 if there wasn't enough data. |
7cca0d81 |
563 | */ |
0016d70b |
564 | int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result) |
32874aea |
565 | { |
27cd7fc2 |
566 | const unsigned char *p = data; |
7cca0d81 |
567 | int i; |
568 | int w, b; |
569 | |
0016d70b |
570 | if (len < 2) |
571 | return -1; |
572 | |
7cca0d81 |
573 | w = 0; |
32874aea |
574 | for (i = 0; i < 2; i++) |
575 | w = (w << 8) + *p++; |
576 | b = (w + 7) / 8; /* bits -> bytes */ |
7cca0d81 |
577 | |
0016d70b |
578 | if (len < b+2) |
579 | return -1; |
580 | |
32874aea |
581 | if (!result) /* just return length */ |
582 | return b + 2; |
a52f067e |
583 | |
3709bfe9 |
584 | *result = bignum_from_bytes(p, b); |
7cca0d81 |
585 | |
3709bfe9 |
586 | return p + b - data; |
7cca0d81 |
587 | } |
5c58ad2d |
588 | |
589 | /* |
2e85c969 |
590 | * Return the bit count of a bignum, for SSH-1 encoding. |
5c58ad2d |
591 | */ |
32874aea |
592 | int bignum_bitcount(Bignum bn) |
593 | { |
a3412f52 |
594 | int bitcount = bn[0] * BIGNUM_INT_BITS - 1; |
32874aea |
595 | while (bitcount >= 0 |
a3412f52 |
596 | && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--; |
5c58ad2d |
597 | return bitcount + 1; |
598 | } |
599 | |
600 | /* |
2e85c969 |
601 | * Return the byte length of a bignum when SSH-1 encoded. |
5c58ad2d |
602 | */ |
32874aea |
603 | int ssh1_bignum_length(Bignum bn) |
604 | { |
605 | return 2 + (bignum_bitcount(bn) + 7) / 8; |
ddecd643 |
606 | } |
607 | |
608 | /* |
2e85c969 |
609 | * Return the byte length of a bignum when SSH-2 encoded. |
ddecd643 |
610 | */ |
32874aea |
611 | int ssh2_bignum_length(Bignum bn) |
612 | { |
613 | return 4 + (bignum_bitcount(bn) + 8) / 8; |
5c58ad2d |
614 | } |
615 | |
616 | /* |
617 | * Return a byte from a bignum; 0 is least significant, etc. |
618 | */ |
32874aea |
619 | int bignum_byte(Bignum bn, int i) |
620 | { |
a3412f52 |
621 | if (i >= BIGNUM_INT_BYTES * bn[0]) |
32874aea |
622 | return 0; /* beyond the end */ |
5c58ad2d |
623 | else |
a3412f52 |
624 | return (bn[i / BIGNUM_INT_BYTES + 1] >> |
625 | ((i % BIGNUM_INT_BYTES)*8)) & 0xFF; |
5c58ad2d |
626 | } |
627 | |
628 | /* |
9400cf6f |
629 | * Return a bit from a bignum; 0 is least significant, etc. |
630 | */ |
32874aea |
631 | int bignum_bit(Bignum bn, int i) |
632 | { |
a3412f52 |
633 | if (i >= BIGNUM_INT_BITS * bn[0]) |
32874aea |
634 | return 0; /* beyond the end */ |
9400cf6f |
635 | else |
a3412f52 |
636 | return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1; |
9400cf6f |
637 | } |
638 | |
639 | /* |
640 | * Set a bit in a bignum; 0 is least significant, etc. |
641 | */ |
32874aea |
642 | void bignum_set_bit(Bignum bn, int bitnum, int value) |
643 | { |
a3412f52 |
644 | if (bitnum >= BIGNUM_INT_BITS * bn[0]) |
32874aea |
645 | abort(); /* beyond the end */ |
9400cf6f |
646 | else { |
a3412f52 |
647 | int v = bitnum / BIGNUM_INT_BITS + 1; |
648 | int mask = 1 << (bitnum % BIGNUM_INT_BITS); |
32874aea |
649 | if (value) |
650 | bn[v] |= mask; |
651 | else |
652 | bn[v] &= ~mask; |
9400cf6f |
653 | } |
654 | } |
655 | |
656 | /* |
2e85c969 |
657 | * Write a SSH-1-format bignum into a buffer. It is assumed the |
5c58ad2d |
658 | * buffer is big enough. Returns the number of bytes used. |
659 | */ |
32874aea |
660 | int ssh1_write_bignum(void *data, Bignum bn) |
661 | { |
5c58ad2d |
662 | unsigned char *p = data; |
663 | int len = ssh1_bignum_length(bn); |
664 | int i; |
ddecd643 |
665 | int bitc = bignum_bitcount(bn); |
5c58ad2d |
666 | |
667 | *p++ = (bitc >> 8) & 0xFF; |
32874aea |
668 | *p++ = (bitc) & 0xFF; |
669 | for (i = len - 2; i--;) |
670 | *p++ = bignum_byte(bn, i); |
5c58ad2d |
671 | return len; |
672 | } |
9400cf6f |
673 | |
674 | /* |
675 | * Compare two bignums. Returns like strcmp. |
676 | */ |
32874aea |
677 | int bignum_cmp(Bignum a, Bignum b) |
678 | { |
9400cf6f |
679 | int amax = a[0], bmax = b[0]; |
680 | int i = (amax > bmax ? amax : bmax); |
681 | while (i) { |
a3412f52 |
682 | BignumInt aval = (i > amax ? 0 : a[i]); |
683 | BignumInt bval = (i > bmax ? 0 : b[i]); |
32874aea |
684 | if (aval < bval) |
685 | return -1; |
686 | if (aval > bval) |
687 | return +1; |
688 | i--; |
9400cf6f |
689 | } |
690 | return 0; |
691 | } |
692 | |
693 | /* |
694 | * Right-shift one bignum to form another. |
695 | */ |
32874aea |
696 | Bignum bignum_rshift(Bignum a, int shift) |
697 | { |
9400cf6f |
698 | Bignum ret; |
699 | int i, shiftw, shiftb, shiftbb, bits; |
a3412f52 |
700 | BignumInt ai, ai1; |
9400cf6f |
701 | |
ddecd643 |
702 | bits = bignum_bitcount(a) - shift; |
a3412f52 |
703 | ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS); |
9400cf6f |
704 | |
705 | if (ret) { |
a3412f52 |
706 | shiftw = shift / BIGNUM_INT_BITS; |
707 | shiftb = shift % BIGNUM_INT_BITS; |
708 | shiftbb = BIGNUM_INT_BITS - shiftb; |
32874aea |
709 | |
710 | ai1 = a[shiftw + 1]; |
711 | for (i = 1; i <= ret[0]; i++) { |
712 | ai = ai1; |
713 | ai1 = (i + shiftw + 1 <= a[0] ? a[i + shiftw + 1] : 0); |
a3412f52 |
714 | ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK; |
32874aea |
715 | } |
9400cf6f |
716 | } |
717 | |
718 | return ret; |
719 | } |
720 | |
721 | /* |
722 | * Non-modular multiplication and addition. |
723 | */ |
32874aea |
724 | Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) |
725 | { |
9400cf6f |
726 | int alen = a[0], blen = b[0]; |
727 | int mlen = (alen > blen ? alen : blen); |
728 | int rlen, i, maxspot; |
a3412f52 |
729 | BignumInt *workspace; |
9400cf6f |
730 | Bignum ret; |
731 | |
732 | /* mlen space for a, mlen space for b, 2*mlen for result */ |
a3412f52 |
733 | workspace = snewn(mlen * 4, BignumInt); |
9400cf6f |
734 | for (i = 0; i < mlen; i++) { |
32874aea |
735 | workspace[0 * mlen + i] = (mlen - i <= a[0] ? a[mlen - i] : 0); |
736 | workspace[1 * mlen + i] = (mlen - i <= b[0] ? b[mlen - i] : 0); |
9400cf6f |
737 | } |
738 | |
32874aea |
739 | internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, |
740 | workspace + 2 * mlen, mlen); |
9400cf6f |
741 | |
742 | /* now just copy the result back */ |
743 | rlen = alen + blen + 1; |
744 | if (addend && rlen <= addend[0]) |
32874aea |
745 | rlen = addend[0] + 1; |
9400cf6f |
746 | ret = newbn(rlen); |
747 | maxspot = 0; |
748 | for (i = 1; i <= ret[0]; i++) { |
32874aea |
749 | ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); |
750 | if (ret[i] != 0) |
751 | maxspot = i; |
9400cf6f |
752 | } |
753 | ret[0] = maxspot; |
754 | |
755 | /* now add in the addend, if any */ |
756 | if (addend) { |
a3412f52 |
757 | BignumDblInt carry = 0; |
32874aea |
758 | for (i = 1; i <= rlen; i++) { |
759 | carry += (i <= ret[0] ? ret[i] : 0); |
760 | carry += (i <= addend[0] ? addend[i] : 0); |
a3412f52 |
761 | ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; |
762 | carry >>= BIGNUM_INT_BITS; |
32874aea |
763 | if (ret[i] != 0 && i > maxspot) |
764 | maxspot = i; |
765 | } |
9400cf6f |
766 | } |
767 | ret[0] = maxspot; |
768 | |
c523f55f |
769 | sfree(workspace); |
9400cf6f |
770 | return ret; |
771 | } |
772 | |
773 | /* |
774 | * Non-modular multiplication. |
775 | */ |
32874aea |
776 | Bignum bigmul(Bignum a, Bignum b) |
777 | { |
9400cf6f |
778 | return bigmuladd(a, b, NULL); |
779 | } |
780 | |
781 | /* |
3709bfe9 |
782 | * Create a bignum which is the bitmask covering another one. That |
783 | * is, the smallest integer which is >= N and is also one less than |
784 | * a power of two. |
785 | */ |
32874aea |
786 | Bignum bignum_bitmask(Bignum n) |
787 | { |
3709bfe9 |
788 | Bignum ret = copybn(n); |
789 | int i; |
a3412f52 |
790 | BignumInt j; |
3709bfe9 |
791 | |
792 | i = ret[0]; |
793 | while (n[i] == 0 && i > 0) |
32874aea |
794 | i--; |
3709bfe9 |
795 | if (i <= 0) |
32874aea |
796 | return ret; /* input was zero */ |
3709bfe9 |
797 | j = 1; |
798 | while (j < n[i]) |
32874aea |
799 | j = 2 * j + 1; |
3709bfe9 |
800 | ret[i] = j; |
801 | while (--i > 0) |
a3412f52 |
802 | ret[i] = BIGNUM_INT_MASK; |
3709bfe9 |
803 | return ret; |
804 | } |
805 | |
806 | /* |
5c72ca61 |
807 | * Convert a (max 32-bit) long into a bignum. |
9400cf6f |
808 | */ |
a3412f52 |
809 | Bignum bignum_from_long(unsigned long nn) |
32874aea |
810 | { |
9400cf6f |
811 | Bignum ret; |
a3412f52 |
812 | BignumDblInt n = nn; |
9400cf6f |
813 | |
5c72ca61 |
814 | ret = newbn(3); |
a3412f52 |
815 | ret[1] = (BignumInt)(n & BIGNUM_INT_MASK); |
816 | ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK); |
5c72ca61 |
817 | ret[3] = 0; |
818 | ret[0] = (ret[2] ? 2 : 1); |
32874aea |
819 | return ret; |
9400cf6f |
820 | } |
821 | |
822 | /* |
823 | * Add a long to a bignum. |
824 | */ |
a3412f52 |
825 | Bignum bignum_add_long(Bignum number, unsigned long addendx) |
32874aea |
826 | { |
827 | Bignum ret = newbn(number[0] + 1); |
9400cf6f |
828 | int i, maxspot = 0; |
a3412f52 |
829 | BignumDblInt carry = 0, addend = addendx; |
9400cf6f |
830 | |
831 | for (i = 1; i <= ret[0]; i++) { |
a3412f52 |
832 | carry += addend & BIGNUM_INT_MASK; |
32874aea |
833 | carry += (i <= number[0] ? number[i] : 0); |
a3412f52 |
834 | addend >>= BIGNUM_INT_BITS; |
835 | ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; |
836 | carry >>= BIGNUM_INT_BITS; |
32874aea |
837 | if (ret[i] != 0) |
838 | maxspot = i; |
9400cf6f |
839 | } |
840 | ret[0] = maxspot; |
841 | return ret; |
842 | } |
843 | |
844 | /* |
845 | * Compute the residue of a bignum, modulo a (max 16-bit) short. |
846 | */ |
32874aea |
847 | unsigned short bignum_mod_short(Bignum number, unsigned short modulus) |
848 | { |
a3412f52 |
849 | BignumDblInt mod, r; |
9400cf6f |
850 | int i; |
851 | |
852 | r = 0; |
853 | mod = modulus; |
854 | for (i = number[0]; i > 0; i--) |
736cc6d1 |
855 | r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod; |
6e522441 |
856 | return (unsigned short) r; |
9400cf6f |
857 | } |
858 | |
a3412f52 |
859 | #ifdef DEBUG |
32874aea |
860 | void diagbn(char *prefix, Bignum md) |
861 | { |
9400cf6f |
862 | int i, nibbles, morenibbles; |
863 | static const char hex[] = "0123456789ABCDEF"; |
864 | |
5c72ca61 |
865 | debug(("%s0x", prefix ? prefix : "")); |
9400cf6f |
866 | |
32874aea |
867 | nibbles = (3 + bignum_bitcount(md)) / 4; |
868 | if (nibbles < 1) |
869 | nibbles = 1; |
870 | morenibbles = 4 * md[0] - nibbles; |
871 | for (i = 0; i < morenibbles; i++) |
5c72ca61 |
872 | debug(("-")); |
32874aea |
873 | for (i = nibbles; i--;) |
5c72ca61 |
874 | debug(("%c", |
875 | hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF])); |
9400cf6f |
876 | |
32874aea |
877 | if (prefix) |
5c72ca61 |
878 | debug(("\n")); |
879 | } |
f28753ab |
880 | #endif |
5c72ca61 |
881 | |
882 | /* |
883 | * Simple division. |
884 | */ |
885 | Bignum bigdiv(Bignum a, Bignum b) |
886 | { |
887 | Bignum q = newbn(a[0]); |
888 | bigdivmod(a, b, NULL, q); |
889 | return q; |
890 | } |
891 | |
892 | /* |
893 | * Simple remainder. |
894 | */ |
895 | Bignum bigmod(Bignum a, Bignum b) |
896 | { |
897 | Bignum r = newbn(b[0]); |
898 | bigdivmod(a, b, r, NULL); |
899 | return r; |
9400cf6f |
900 | } |
901 | |
902 | /* |
903 | * Greatest common divisor. |
904 | */ |
32874aea |
905 | Bignum biggcd(Bignum av, Bignum bv) |
906 | { |
9400cf6f |
907 | Bignum a = copybn(av); |
908 | Bignum b = copybn(bv); |
909 | |
9400cf6f |
910 | while (bignum_cmp(b, Zero) != 0) { |
32874aea |
911 | Bignum t = newbn(b[0]); |
5c72ca61 |
912 | bigdivmod(a, b, t, NULL); |
32874aea |
913 | while (t[0] > 1 && t[t[0]] == 0) |
914 | t[0]--; |
915 | freebn(a); |
916 | a = b; |
917 | b = t; |
9400cf6f |
918 | } |
919 | |
920 | freebn(b); |
921 | return a; |
922 | } |
923 | |
924 | /* |
925 | * Modular inverse, using Euclid's extended algorithm. |
926 | */ |
32874aea |
927 | Bignum modinv(Bignum number, Bignum modulus) |
928 | { |
9400cf6f |
929 | Bignum a = copybn(modulus); |
930 | Bignum b = copybn(number); |
931 | Bignum xp = copybn(Zero); |
932 | Bignum x = copybn(One); |
933 | int sign = +1; |
934 | |
935 | while (bignum_cmp(b, One) != 0) { |
32874aea |
936 | Bignum t = newbn(b[0]); |
937 | Bignum q = newbn(a[0]); |
5c72ca61 |
938 | bigdivmod(a, b, t, q); |
32874aea |
939 | while (t[0] > 1 && t[t[0]] == 0) |
940 | t[0]--; |
941 | freebn(a); |
942 | a = b; |
943 | b = t; |
944 | t = xp; |
945 | xp = x; |
946 | x = bigmuladd(q, xp, t); |
947 | sign = -sign; |
948 | freebn(t); |
75374b2f |
949 | freebn(q); |
9400cf6f |
950 | } |
951 | |
952 | freebn(b); |
953 | freebn(a); |
954 | freebn(xp); |
955 | |
956 | /* now we know that sign * x == 1, and that x < modulus */ |
957 | if (sign < 0) { |
32874aea |
958 | /* set a new x to be modulus - x */ |
959 | Bignum newx = newbn(modulus[0]); |
a3412f52 |
960 | BignumInt carry = 0; |
32874aea |
961 | int maxspot = 1; |
962 | int i; |
963 | |
964 | for (i = 1; i <= newx[0]; i++) { |
a3412f52 |
965 | BignumInt aword = (i <= modulus[0] ? modulus[i] : 0); |
966 | BignumInt bword = (i <= x[0] ? x[i] : 0); |
32874aea |
967 | newx[i] = aword - bword - carry; |
968 | bword = ~bword; |
969 | carry = carry ? (newx[i] >= bword) : (newx[i] > bword); |
970 | if (newx[i] != 0) |
971 | maxspot = i; |
972 | } |
973 | newx[0] = maxspot; |
974 | freebn(x); |
975 | x = newx; |
9400cf6f |
976 | } |
977 | |
978 | /* and return. */ |
979 | return x; |
980 | } |
6e522441 |
981 | |
982 | /* |
983 | * Render a bignum into decimal. Return a malloced string holding |
984 | * the decimal representation. |
985 | */ |
32874aea |
986 | char *bignum_decimal(Bignum x) |
987 | { |
6e522441 |
988 | int ndigits, ndigit; |
989 | int i, iszero; |
a3412f52 |
990 | BignumDblInt carry; |
6e522441 |
991 | char *ret; |
a3412f52 |
992 | BignumInt *workspace; |
6e522441 |
993 | |
994 | /* |
995 | * First, estimate the number of digits. Since log(10)/log(2) |
996 | * is just greater than 93/28 (the joys of continued fraction |
997 | * approximations...) we know that for every 93 bits, we need |
998 | * at most 28 digits. This will tell us how much to malloc. |
999 | * |
1000 | * Formally: if x has i bits, that means x is strictly less |
1001 | * than 2^i. Since 2 is less than 10^(28/93), this is less than |
1002 | * 10^(28i/93). We need an integer power of ten, so we must |
1003 | * round up (rounding down might make it less than x again). |
1004 | * Therefore if we multiply the bit count by 28/93, rounding |
1005 | * up, we will have enough digits. |
1006 | */ |
ddecd643 |
1007 | i = bignum_bitcount(x); |
32874aea |
1008 | ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */ |
1009 | ndigits++; /* allow for trailing \0 */ |
3d88e64d |
1010 | ret = snewn(ndigits, char); |
6e522441 |
1011 | |
1012 | /* |
1013 | * Now allocate some workspace to hold the binary form as we |
1014 | * repeatedly divide it by ten. Initialise this to the |
1015 | * big-endian form of the number. |
1016 | */ |
a3412f52 |
1017 | workspace = snewn(x[0], BignumInt); |
6e522441 |
1018 | for (i = 0; i < x[0]; i++) |
32874aea |
1019 | workspace[i] = x[x[0] - i]; |
6e522441 |
1020 | |
1021 | /* |
1022 | * Next, write the decimal number starting with the last digit. |
1023 | * We use ordinary short division, dividing 10 into the |
1024 | * workspace. |
1025 | */ |
32874aea |
1026 | ndigit = ndigits - 1; |
6e522441 |
1027 | ret[ndigit] = '\0'; |
1028 | do { |
32874aea |
1029 | iszero = 1; |
1030 | carry = 0; |
1031 | for (i = 0; i < x[0]; i++) { |
a3412f52 |
1032 | carry = (carry << BIGNUM_INT_BITS) + workspace[i]; |
1033 | workspace[i] = (BignumInt) (carry / 10); |
32874aea |
1034 | if (workspace[i]) |
1035 | iszero = 0; |
1036 | carry %= 10; |
1037 | } |
1038 | ret[--ndigit] = (char) (carry + '0'); |
6e522441 |
1039 | } while (!iszero); |
1040 | |
1041 | /* |
1042 | * There's a chance we've fallen short of the start of the |
1043 | * string. Correct if so. |
1044 | */ |
1045 | if (ndigit > 0) |
32874aea |
1046 | memmove(ret, ret + ndigit, ndigits - ndigit); |
6e522441 |
1047 | |
1048 | /* |
1049 | * Done. |
1050 | */ |
c523f55f |
1051 | sfree(workspace); |
6e522441 |
1052 | return ret; |
1053 | } |