| 1 | /* |
| 2 | * Bignum routines for RSA and DH and stuff. |
| 3 | */ |
| 4 | |
| 5 | #include <stdio.h> |
| 6 | #include <assert.h> |
| 7 | #include <stdlib.h> |
| 8 | #include <string.h> |
| 9 | |
| 10 | #include "misc.h" |
| 11 | |
| 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) |
| 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)) |
| 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) |
| 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) |
| 35 | #endif |
| 36 | |
| 37 | #define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8) |
| 38 | |
| 39 | #define BIGNUM_INTERNAL |
| 40 | typedef BignumInt *Bignum; |
| 41 | |
| 42 | #include "ssh.h" |
| 43 | |
| 44 | BignumInt bnZero[1] = { 0 }; |
| 45 | BignumInt bnOne[2] = { 1, 1 }; |
| 46 | |
| 47 | /* |
| 48 | * The Bignum format is an array of `BignumInt'. The first |
| 49 | * element of the array counts the remaining elements. The |
| 50 | * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_ |
| 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 | |
| 61 | Bignum Zero = bnZero, One = bnOne; |
| 62 | |
| 63 | static Bignum newbn(int length) |
| 64 | { |
| 65 | Bignum b = snewn(length + 1, BignumInt); |
| 66 | if (!b) |
| 67 | abort(); /* FIXME */ |
| 68 | memset(b, 0, (length + 1) * sizeof(*b)); |
| 69 | b[0] = length; |
| 70 | return b; |
| 71 | } |
| 72 | |
| 73 | void bn_restore_invariant(Bignum b) |
| 74 | { |
| 75 | while (b[0] > 1 && b[b[0]] == 0) |
| 76 | b[0]--; |
| 77 | } |
| 78 | |
| 79 | Bignum copybn(Bignum orig) |
| 80 | { |
| 81 | Bignum b = snewn(orig[0] + 1, BignumInt); |
| 82 | if (!b) |
| 83 | abort(); /* FIXME */ |
| 84 | memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); |
| 85 | return b; |
| 86 | } |
| 87 | |
| 88 | void freebn(Bignum b) |
| 89 | { |
| 90 | /* |
| 91 | * Burn the evidence, just in case. |
| 92 | */ |
| 93 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
| 94 | sfree(b); |
| 95 | } |
| 96 | |
| 97 | Bignum bn_power_2(int n) |
| 98 | { |
| 99 | Bignum ret = newbn(n / BIGNUM_INT_BITS + 1); |
| 100 | bignum_set_bit(ret, n, 1); |
| 101 | return ret; |
| 102 | } |
| 103 | |
| 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 | */ |
| 109 | static void internal_mul(BignumInt *a, BignumInt *b, |
| 110 | BignumInt *c, int len) |
| 111 | { |
| 112 | int i, j; |
| 113 | BignumDblInt t; |
| 114 | |
| 115 | for (j = 0; j < 2 * len; j++) |
| 116 | c[j] = 0; |
| 117 | |
| 118 | for (i = len - 1; i >= 0; i--) { |
| 119 | t = 0; |
| 120 | for (j = len - 1; j >= 0; j--) { |
| 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; |
| 125 | } |
| 126 | c[i] = (BignumInt) t; |
| 127 | } |
| 128 | } |
| 129 | |
| 130 | static void internal_add_shifted(BignumInt *number, |
| 131 | unsigned n, int shift) |
| 132 | { |
| 133 | int word = 1 + (shift / BIGNUM_INT_BITS); |
| 134 | int bshift = shift % BIGNUM_INT_BITS; |
| 135 | BignumDblInt addend; |
| 136 | |
| 137 | addend = (BignumDblInt)n << bshift; |
| 138 | |
| 139 | while (addend) { |
| 140 | addend += number[word]; |
| 141 | number[word] = (BignumInt) addend & BIGNUM_INT_MASK; |
| 142 | addend >>= BIGNUM_INT_BITS; |
| 143 | word++; |
| 144 | } |
| 145 | } |
| 146 | |
| 147 | /* |
| 148 | * Compute a = a % m. |
| 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). |
| 152 | * The MSW of m MUST have its high bit set. |
| 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. |
| 156 | */ |
| 157 | static void internal_mod(BignumInt *a, int alen, |
| 158 | BignumInt *m, int mlen, |
| 159 | BignumInt *quot, int qshift) |
| 160 | { |
| 161 | BignumInt m0, m1; |
| 162 | unsigned int h; |
| 163 | int i, k; |
| 164 | |
| 165 | m0 = m[0]; |
| 166 | if (mlen > 1) |
| 167 | m1 = m[1]; |
| 168 | else |
| 169 | m1 = 0; |
| 170 | |
| 171 | for (i = 0; i <= alen - mlen; i++) { |
| 172 | BignumDblInt t; |
| 173 | unsigned int q, r, c, ai1; |
| 174 | |
| 175 | if (i == 0) { |
| 176 | h = 0; |
| 177 | } else { |
| 178 | h = a[i - 1]; |
| 179 | a[i - 1] = 0; |
| 180 | } |
| 181 | |
| 182 | if (i == alen - 1) |
| 183 | ai1 = 0; |
| 184 | else |
| 185 | ai1 = a[i + 1]; |
| 186 | |
| 187 | /* Find q = h:a[i] / m0 */ |
| 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 | } |
| 218 | } |
| 219 | |
| 220 | /* Subtract q * m from a[i...] */ |
| 221 | c = 0; |
| 222 | for (k = mlen - 1; k >= 0; k--) { |
| 223 | t = MUL_WORD(q, m[k]); |
| 224 | t += c; |
| 225 | c = t >> BIGNUM_INT_BITS; |
| 226 | if ((BignumInt) t > a[i + k]) |
| 227 | c++; |
| 228 | a[i + k] -= (BignumInt) t; |
| 229 | } |
| 230 | |
| 231 | /* Add back m in case of borrow */ |
| 232 | if (c != h) { |
| 233 | t = 0; |
| 234 | for (k = mlen - 1; k >= 0; k--) { |
| 235 | t += m[k]; |
| 236 | t += a[i + k]; |
| 237 | a[i + k] = (BignumInt) t; |
| 238 | t = t >> BIGNUM_INT_BITS; |
| 239 | } |
| 240 | q--; |
| 241 | } |
| 242 | if (quot) |
| 243 | internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); |
| 244 | } |
| 245 | } |
| 246 | |
| 247 | /* |
| 248 | * Compute (base ^ exp) % mod. |
| 249 | */ |
| 250 | Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) |
| 251 | { |
| 252 | BignumInt *a, *b, *n, *m; |
| 253 | int mshift; |
| 254 | int mlen, i, j; |
| 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); |
| 268 | |
| 269 | /* Allocate m of size mlen, copy mod to m */ |
| 270 | /* We use big endian internally */ |
| 271 | mlen = mod[0]; |
| 272 | m = snewn(mlen, BignumInt); |
| 273 | for (j = 0; j < mlen; j++) |
| 274 | m[j] = mod[mod[0] - j]; |
| 275 | |
| 276 | /* Shift m left to make msb bit set */ |
| 277 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
| 278 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
| 279 | break; |
| 280 | if (mshift) { |
| 281 | for (i = 0; i < mlen - 1; i++) |
| 282 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
| 283 | m[mlen - 1] = m[mlen - 1] << mshift; |
| 284 | } |
| 285 | |
| 286 | /* Allocate n of size mlen, copy base to n */ |
| 287 | n = snewn(mlen, BignumInt); |
| 288 | i = mlen - base[0]; |
| 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]; |
| 293 | |
| 294 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
| 295 | a = snewn(2 * mlen, BignumInt); |
| 296 | b = snewn(2 * mlen, BignumInt); |
| 297 | for (i = 0; i < 2 * mlen; i++) |
| 298 | a[i] = 0; |
| 299 | a[2 * mlen - 1] = 1; |
| 300 | |
| 301 | /* Skip leading zero bits of exp. */ |
| 302 | i = 0; |
| 303 | j = BIGNUM_INT_BITS-1; |
| 304 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
| 305 | j--; |
| 306 | if (j < 0) { |
| 307 | i++; |
| 308 | j = BIGNUM_INT_BITS-1; |
| 309 | } |
| 310 | } |
| 311 | |
| 312 | /* Main computation */ |
| 313 | while (i < exp[0]) { |
| 314 | while (j >= 0) { |
| 315 | internal_mul(a + mlen, a + mlen, b, mlen); |
| 316 | internal_mod(b, mlen * 2, m, mlen, NULL, 0); |
| 317 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
| 318 | internal_mul(b + mlen, n, a, mlen); |
| 319 | internal_mod(a, mlen * 2, m, mlen, NULL, 0); |
| 320 | } else { |
| 321 | BignumInt *t; |
| 322 | t = a; |
| 323 | a = b; |
| 324 | b = t; |
| 325 | } |
| 326 | j--; |
| 327 | } |
| 328 | i++; |
| 329 | j = BIGNUM_INT_BITS-1; |
| 330 | } |
| 331 | |
| 332 | /* Fixup result in case the modulus was shifted */ |
| 333 | if (mshift) { |
| 334 | for (i = mlen - 1; i < 2 * mlen - 1; i++) |
| 335 | a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
| 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--) |
| 339 | a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); |
| 340 | } |
| 341 | |
| 342 | /* Copy result to buffer */ |
| 343 | result = newbn(mod[0]); |
| 344 | for (i = 0; i < mlen; i++) |
| 345 | result[result[0] - i] = a[i + mlen]; |
| 346 | while (result[0] > 1 && result[result[0]] == 0) |
| 347 | result[0]--; |
| 348 | |
| 349 | /* Free temporary arrays */ |
| 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); |
| 362 | |
| 363 | freebn(base); |
| 364 | |
| 365 | return result; |
| 366 | } |
| 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 | */ |
| 373 | Bignum modmul(Bignum p, Bignum q, Bignum mod) |
| 374 | { |
| 375 | BignumInt *a, *n, *m, *o; |
| 376 | int mshift; |
| 377 | int pqlen, mlen, rlen, i, j; |
| 378 | Bignum result; |
| 379 | |
| 380 | /* Allocate m of size mlen, copy mod to m */ |
| 381 | /* We use big endian internally */ |
| 382 | mlen = mod[0]; |
| 383 | m = snewn(mlen, BignumInt); |
| 384 | for (j = 0; j < mlen; j++) |
| 385 | m[j] = mod[mod[0] - j]; |
| 386 | |
| 387 | /* Shift m left to make msb bit set */ |
| 388 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
| 389 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
| 390 | break; |
| 391 | if (mshift) { |
| 392 | for (i = 0; i < mlen - 1; i++) |
| 393 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
| 394 | m[mlen - 1] = m[mlen - 1] << mshift; |
| 395 | } |
| 396 | |
| 397 | pqlen = (p[0] > q[0] ? p[0] : q[0]); |
| 398 | |
| 399 | /* Allocate n of size pqlen, copy p to n */ |
| 400 | n = snewn(pqlen, BignumInt); |
| 401 | i = pqlen - p[0]; |
| 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]; |
| 406 | |
| 407 | /* Allocate o of size pqlen, copy q to o */ |
| 408 | o = snewn(pqlen, BignumInt); |
| 409 | i = pqlen - q[0]; |
| 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]; |
| 414 | |
| 415 | /* Allocate a of size 2*pqlen for result */ |
| 416 | a = snewn(2 * pqlen, BignumInt); |
| 417 | |
| 418 | /* Main computation */ |
| 419 | internal_mul(n, o, a, pqlen); |
| 420 | internal_mod(a, pqlen * 2, m, mlen, NULL, 0); |
| 421 | |
| 422 | /* Fixup result in case the modulus was shifted */ |
| 423 | if (mshift) { |
| 424 | for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) |
| 425 | a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
| 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--) |
| 429 | a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); |
| 430 | } |
| 431 | |
| 432 | /* Copy result to buffer */ |
| 433 | rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2); |
| 434 | result = newbn(rlen); |
| 435 | for (i = 0; i < rlen; i++) |
| 436 | result[result[0] - i] = a[i + 2 * pqlen - rlen]; |
| 437 | while (result[0] > 1 && result[result[0]] == 0) |
| 438 | result[0]--; |
| 439 | |
| 440 | /* Free temporary arrays */ |
| 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); |
| 453 | |
| 454 | return result; |
| 455 | } |
| 456 | |
| 457 | /* |
| 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. |
| 461 | * We optionally write out a quotient if `quotient' is non-NULL. |
| 462 | * We can avoid writing out the result if `result' is NULL. |
| 463 | */ |
| 464 | static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) |
| 465 | { |
| 466 | BignumInt *n, *m; |
| 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]; |
| 473 | m = snewn(mlen, BignumInt); |
| 474 | for (j = 0; j < mlen; j++) |
| 475 | m[j] = mod[mod[0] - j]; |
| 476 | |
| 477 | /* Shift m left to make msb bit set */ |
| 478 | for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) |
| 479 | if ((m[0] << mshift) & BIGNUM_TOP_BIT) |
| 480 | break; |
| 481 | if (mshift) { |
| 482 | for (i = 0; i < mlen - 1; i++) |
| 483 | m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
| 484 | m[mlen - 1] = m[mlen - 1] << mshift; |
| 485 | } |
| 486 | |
| 487 | plen = p[0]; |
| 488 | /* Ensure plen > mlen */ |
| 489 | if (plen <= mlen) |
| 490 | plen = mlen + 1; |
| 491 | |
| 492 | /* Allocate n of size plen, copy p to n */ |
| 493 | n = snewn(plen, BignumInt); |
| 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]; |
| 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++) |
| 505 | n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift)); |
| 506 | n[plen - 1] = n[plen - 1] << mshift; |
| 507 | internal_mod(n, plen, m, mlen, quotient, 0); |
| 508 | for (i = plen - 1; i >= plen - mlen; i--) |
| 509 | n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift)); |
| 510 | } |
| 511 | |
| 512 | /* Copy result to buffer */ |
| 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 | } |
| 518 | } |
| 519 | |
| 520 | /* Free temporary arrays */ |
| 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); |
| 527 | } |
| 528 | |
| 529 | /* |
| 530 | * Decrement a number. |
| 531 | */ |
| 532 | void decbn(Bignum bn) |
| 533 | { |
| 534 | int i = 1; |
| 535 | while (i < bn[0] && bn[i] == 0) |
| 536 | bn[i++] = BIGNUM_INT_MASK; |
| 537 | bn[i]--; |
| 538 | } |
| 539 | |
| 540 | Bignum bignum_from_bytes(const unsigned char *data, int nbytes) |
| 541 | { |
| 542 | Bignum result; |
| 543 | int w, i; |
| 544 | |
| 545 | w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */ |
| 546 | |
| 547 | result = newbn(w); |
| 548 | for (i = 1; i <= w; i++) |
| 549 | result[i] = 0; |
| 550 | for (i = nbytes; i--;) { |
| 551 | unsigned char byte = *data++; |
| 552 | result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS); |
| 553 | } |
| 554 | |
| 555 | while (result[0] > 1 && result[result[0]] == 0) |
| 556 | result[0]--; |
| 557 | return result; |
| 558 | } |
| 559 | |
| 560 | /* |
| 561 | * Read an ssh1-format bignum from a data buffer. Return the number |
| 562 | * of bytes consumed, or -1 if there wasn't enough data. |
| 563 | */ |
| 564 | int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result) |
| 565 | { |
| 566 | const unsigned char *p = data; |
| 567 | int i; |
| 568 | int w, b; |
| 569 | |
| 570 | if (len < 2) |
| 571 | return -1; |
| 572 | |
| 573 | w = 0; |
| 574 | for (i = 0; i < 2; i++) |
| 575 | w = (w << 8) + *p++; |
| 576 | b = (w + 7) / 8; /* bits -> bytes */ |
| 577 | |
| 578 | if (len < b+2) |
| 579 | return -1; |
| 580 | |
| 581 | if (!result) /* just return length */ |
| 582 | return b + 2; |
| 583 | |
| 584 | *result = bignum_from_bytes(p, b); |
| 585 | |
| 586 | return p + b - data; |
| 587 | } |
| 588 | |
| 589 | /* |
| 590 | * Return the bit count of a bignum, for ssh1 encoding. |
| 591 | */ |
| 592 | int bignum_bitcount(Bignum bn) |
| 593 | { |
| 594 | int bitcount = bn[0] * BIGNUM_INT_BITS - 1; |
| 595 | while (bitcount >= 0 |
| 596 | && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--; |
| 597 | return bitcount + 1; |
| 598 | } |
| 599 | |
| 600 | /* |
| 601 | * Return the byte length of a bignum when ssh1 encoded. |
| 602 | */ |
| 603 | int ssh1_bignum_length(Bignum bn) |
| 604 | { |
| 605 | return 2 + (bignum_bitcount(bn) + 7) / 8; |
| 606 | } |
| 607 | |
| 608 | /* |
| 609 | * Return the byte length of a bignum when ssh2 encoded. |
| 610 | */ |
| 611 | int ssh2_bignum_length(Bignum bn) |
| 612 | { |
| 613 | return 4 + (bignum_bitcount(bn) + 8) / 8; |
| 614 | } |
| 615 | |
| 616 | /* |
| 617 | * Return a byte from a bignum; 0 is least significant, etc. |
| 618 | */ |
| 619 | int bignum_byte(Bignum bn, int i) |
| 620 | { |
| 621 | if (i >= BIGNUM_INT_BYTES * bn[0]) |
| 622 | return 0; /* beyond the end */ |
| 623 | else |
| 624 | return (bn[i / BIGNUM_INT_BYTES + 1] >> |
| 625 | ((i % BIGNUM_INT_BYTES)*8)) & 0xFF; |
| 626 | } |
| 627 | |
| 628 | /* |
| 629 | * Return a bit from a bignum; 0 is least significant, etc. |
| 630 | */ |
| 631 | int bignum_bit(Bignum bn, int i) |
| 632 | { |
| 633 | if (i >= BIGNUM_INT_BITS * bn[0]) |
| 634 | return 0; /* beyond the end */ |
| 635 | else |
| 636 | return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1; |
| 637 | } |
| 638 | |
| 639 | /* |
| 640 | * Set a bit in a bignum; 0 is least significant, etc. |
| 641 | */ |
| 642 | void bignum_set_bit(Bignum bn, int bitnum, int value) |
| 643 | { |
| 644 | if (bitnum >= BIGNUM_INT_BITS * bn[0]) |
| 645 | abort(); /* beyond the end */ |
| 646 | else { |
| 647 | int v = bitnum / BIGNUM_INT_BITS + 1; |
| 648 | int mask = 1 << (bitnum % BIGNUM_INT_BITS); |
| 649 | if (value) |
| 650 | bn[v] |= mask; |
| 651 | else |
| 652 | bn[v] &= ~mask; |
| 653 | } |
| 654 | } |
| 655 | |
| 656 | /* |
| 657 | * Write a ssh1-format bignum into a buffer. It is assumed the |
| 658 | * buffer is big enough. Returns the number of bytes used. |
| 659 | */ |
| 660 | int ssh1_write_bignum(void *data, Bignum bn) |
| 661 | { |
| 662 | unsigned char *p = data; |
| 663 | int len = ssh1_bignum_length(bn); |
| 664 | int i; |
| 665 | int bitc = bignum_bitcount(bn); |
| 666 | |
| 667 | *p++ = (bitc >> 8) & 0xFF; |
| 668 | *p++ = (bitc) & 0xFF; |
| 669 | for (i = len - 2; i--;) |
| 670 | *p++ = bignum_byte(bn, i); |
| 671 | return len; |
| 672 | } |
| 673 | |
| 674 | /* |
| 675 | * Compare two bignums. Returns like strcmp. |
| 676 | */ |
| 677 | int bignum_cmp(Bignum a, Bignum b) |
| 678 | { |
| 679 | int amax = a[0], bmax = b[0]; |
| 680 | int i = (amax > bmax ? amax : bmax); |
| 681 | while (i) { |
| 682 | BignumInt aval = (i > amax ? 0 : a[i]); |
| 683 | BignumInt bval = (i > bmax ? 0 : b[i]); |
| 684 | if (aval < bval) |
| 685 | return -1; |
| 686 | if (aval > bval) |
| 687 | return +1; |
| 688 | i--; |
| 689 | } |
| 690 | return 0; |
| 691 | } |
| 692 | |
| 693 | /* |
| 694 | * Right-shift one bignum to form another. |
| 695 | */ |
| 696 | Bignum bignum_rshift(Bignum a, int shift) |
| 697 | { |
| 698 | Bignum ret; |
| 699 | int i, shiftw, shiftb, shiftbb, bits; |
| 700 | BignumInt ai, ai1; |
| 701 | |
| 702 | bits = bignum_bitcount(a) - shift; |
| 703 | ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS); |
| 704 | |
| 705 | if (ret) { |
| 706 | shiftw = shift / BIGNUM_INT_BITS; |
| 707 | shiftb = shift % BIGNUM_INT_BITS; |
| 708 | shiftbb = BIGNUM_INT_BITS - shiftb; |
| 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); |
| 714 | ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK; |
| 715 | } |
| 716 | } |
| 717 | |
| 718 | return ret; |
| 719 | } |
| 720 | |
| 721 | /* |
| 722 | * Non-modular multiplication and addition. |
| 723 | */ |
| 724 | Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) |
| 725 | { |
| 726 | int alen = a[0], blen = b[0]; |
| 727 | int mlen = (alen > blen ? alen : blen); |
| 728 | int rlen, i, maxspot; |
| 729 | BignumInt *workspace; |
| 730 | Bignum ret; |
| 731 | |
| 732 | /* mlen space for a, mlen space for b, 2*mlen for result */ |
| 733 | workspace = snewn(mlen * 4, BignumInt); |
| 734 | for (i = 0; i < mlen; i++) { |
| 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); |
| 737 | } |
| 738 | |
| 739 | internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, |
| 740 | workspace + 2 * mlen, mlen); |
| 741 | |
| 742 | /* now just copy the result back */ |
| 743 | rlen = alen + blen + 1; |
| 744 | if (addend && rlen <= addend[0]) |
| 745 | rlen = addend[0] + 1; |
| 746 | ret = newbn(rlen); |
| 747 | maxspot = 0; |
| 748 | for (i = 1; i <= ret[0]; i++) { |
| 749 | ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); |
| 750 | if (ret[i] != 0) |
| 751 | maxspot = i; |
| 752 | } |
| 753 | ret[0] = maxspot; |
| 754 | |
| 755 | /* now add in the addend, if any */ |
| 756 | if (addend) { |
| 757 | BignumDblInt carry = 0; |
| 758 | for (i = 1; i <= rlen; i++) { |
| 759 | carry += (i <= ret[0] ? ret[i] : 0); |
| 760 | carry += (i <= addend[0] ? addend[i] : 0); |
| 761 | ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; |
| 762 | carry >>= BIGNUM_INT_BITS; |
| 763 | if (ret[i] != 0 && i > maxspot) |
| 764 | maxspot = i; |
| 765 | } |
| 766 | } |
| 767 | ret[0] = maxspot; |
| 768 | |
| 769 | sfree(workspace); |
| 770 | return ret; |
| 771 | } |
| 772 | |
| 773 | /* |
| 774 | * Non-modular multiplication. |
| 775 | */ |
| 776 | Bignum bigmul(Bignum a, Bignum b) |
| 777 | { |
| 778 | return bigmuladd(a, b, NULL); |
| 779 | } |
| 780 | |
| 781 | /* |
| 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 | */ |
| 786 | Bignum bignum_bitmask(Bignum n) |
| 787 | { |
| 788 | Bignum ret = copybn(n); |
| 789 | int i; |
| 790 | BignumInt j; |
| 791 | |
| 792 | i = ret[0]; |
| 793 | while (n[i] == 0 && i > 0) |
| 794 | i--; |
| 795 | if (i <= 0) |
| 796 | return ret; /* input was zero */ |
| 797 | j = 1; |
| 798 | while (j < n[i]) |
| 799 | j = 2 * j + 1; |
| 800 | ret[i] = j; |
| 801 | while (--i > 0) |
| 802 | ret[i] = BIGNUM_INT_MASK; |
| 803 | return ret; |
| 804 | } |
| 805 | |
| 806 | /* |
| 807 | * Convert a (max 32-bit) long into a bignum. |
| 808 | */ |
| 809 | Bignum bignum_from_long(unsigned long nn) |
| 810 | { |
| 811 | Bignum ret; |
| 812 | BignumDblInt n = nn; |
| 813 | |
| 814 | ret = newbn(3); |
| 815 | ret[1] = (BignumInt)(n & BIGNUM_INT_MASK); |
| 816 | ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK); |
| 817 | ret[3] = 0; |
| 818 | ret[0] = (ret[2] ? 2 : 1); |
| 819 | return ret; |
| 820 | } |
| 821 | |
| 822 | /* |
| 823 | * Add a long to a bignum. |
| 824 | */ |
| 825 | Bignum bignum_add_long(Bignum number, unsigned long addendx) |
| 826 | { |
| 827 | Bignum ret = newbn(number[0] + 1); |
| 828 | int i, maxspot = 0; |
| 829 | BignumDblInt carry = 0, addend = addendx; |
| 830 | |
| 831 | for (i = 1; i <= ret[0]; i++) { |
| 832 | carry += addend & BIGNUM_INT_MASK; |
| 833 | carry += (i <= number[0] ? number[i] : 0); |
| 834 | addend >>= BIGNUM_INT_BITS; |
| 835 | ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; |
| 836 | carry >>= BIGNUM_INT_BITS; |
| 837 | if (ret[i] != 0) |
| 838 | maxspot = i; |
| 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 | */ |
| 847 | unsigned short bignum_mod_short(Bignum number, unsigned short modulus) |
| 848 | { |
| 849 | BignumDblInt mod, r; |
| 850 | int i; |
| 851 | |
| 852 | r = 0; |
| 853 | mod = modulus; |
| 854 | for (i = number[0]; i > 0; i--) |
| 855 | r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod; |
| 856 | return (unsigned short) r; |
| 857 | } |
| 858 | |
| 859 | #ifdef DEBUG |
| 860 | void diagbn(char *prefix, Bignum md) |
| 861 | { |
| 862 | int i, nibbles, morenibbles; |
| 863 | static const char hex[] = "0123456789ABCDEF"; |
| 864 | |
| 865 | debug(("%s0x", prefix ? prefix : "")); |
| 866 | |
| 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++) |
| 872 | debug(("-")); |
| 873 | for (i = nibbles; i--;) |
| 874 | debug(("%c", |
| 875 | hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF])); |
| 876 | |
| 877 | if (prefix) |
| 878 | debug(("\n")); |
| 879 | } |
| 880 | #endif |
| 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; |
| 900 | } |
| 901 | |
| 902 | /* |
| 903 | * Greatest common divisor. |
| 904 | */ |
| 905 | Bignum biggcd(Bignum av, Bignum bv) |
| 906 | { |
| 907 | Bignum a = copybn(av); |
| 908 | Bignum b = copybn(bv); |
| 909 | |
| 910 | while (bignum_cmp(b, Zero) != 0) { |
| 911 | Bignum t = newbn(b[0]); |
| 912 | bigdivmod(a, b, t, NULL); |
| 913 | while (t[0] > 1 && t[t[0]] == 0) |
| 914 | t[0]--; |
| 915 | freebn(a); |
| 916 | a = b; |
| 917 | b = t; |
| 918 | } |
| 919 | |
| 920 | freebn(b); |
| 921 | return a; |
| 922 | } |
| 923 | |
| 924 | /* |
| 925 | * Modular inverse, using Euclid's extended algorithm. |
| 926 | */ |
| 927 | Bignum modinv(Bignum number, Bignum modulus) |
| 928 | { |
| 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) { |
| 936 | Bignum t = newbn(b[0]); |
| 937 | Bignum q = newbn(a[0]); |
| 938 | bigdivmod(a, b, t, q); |
| 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); |
| 949 | freebn(q); |
| 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) { |
| 958 | /* set a new x to be modulus - x */ |
| 959 | Bignum newx = newbn(modulus[0]); |
| 960 | BignumInt carry = 0; |
| 961 | int maxspot = 1; |
| 962 | int i; |
| 963 | |
| 964 | for (i = 1; i <= newx[0]; i++) { |
| 965 | BignumInt aword = (i <= modulus[0] ? modulus[i] : 0); |
| 966 | BignumInt bword = (i <= x[0] ? x[i] : 0); |
| 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; |
| 976 | } |
| 977 | |
| 978 | /* and return. */ |
| 979 | return x; |
| 980 | } |
| 981 | |
| 982 | /* |
| 983 | * Render a bignum into decimal. Return a malloced string holding |
| 984 | * the decimal representation. |
| 985 | */ |
| 986 | char *bignum_decimal(Bignum x) |
| 987 | { |
| 988 | int ndigits, ndigit; |
| 989 | int i, iszero; |
| 990 | BignumDblInt carry; |
| 991 | char *ret; |
| 992 | BignumInt *workspace; |
| 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 | */ |
| 1007 | i = bignum_bitcount(x); |
| 1008 | ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */ |
| 1009 | ndigits++; /* allow for trailing \0 */ |
| 1010 | ret = snewn(ndigits, char); |
| 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 | */ |
| 1017 | workspace = snewn(x[0], BignumInt); |
| 1018 | for (i = 0; i < x[0]; i++) |
| 1019 | workspace[i] = x[x[0] - i]; |
| 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 | */ |
| 1026 | ndigit = ndigits - 1; |
| 1027 | ret[ndigit] = '\0'; |
| 1028 | do { |
| 1029 | iszero = 1; |
| 1030 | carry = 0; |
| 1031 | for (i = 0; i < x[0]; i++) { |
| 1032 | carry = (carry << BIGNUM_INT_BITS) + workspace[i]; |
| 1033 | workspace[i] = (BignumInt) (carry / 10); |
| 1034 | if (workspace[i]) |
| 1035 | iszero = 0; |
| 1036 | carry %= 10; |
| 1037 | } |
| 1038 | ret[--ndigit] = (char) (carry + '0'); |
| 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) |
| 1046 | memmove(ret, ret + ndigit, ndigits - ndigit); |
| 1047 | |
| 1048 | /* |
| 1049 | * Done. |
| 1050 | */ |
| 1051 | sfree(workspace); |
| 1052 | return ret; |
| 1053 | } |