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