| 1 | /* |
| 2 | * RSA implementation just sufficient for ssh client-side |
| 3 | * initialisation step |
| 4 | * Modified by Joris, Jun 1999. |
| 5 | */ |
| 6 | |
| 7 | #define JORIS_RSA |
| 8 | |
| 9 | /*#include <windows.h> |
| 10 | #define RSADEBUG |
| 11 | #define DLVL 2 |
| 12 | #include "stel.h"*/ |
| 13 | |
| 14 | #include <stdio.h> |
| 15 | #include <stdlib.h> |
| 16 | #include <string.h> |
| 17 | |
| 18 | #include "ssh.h" |
| 19 | |
| 20 | typedef unsigned short *Bignum; |
| 21 | |
| 22 | static unsigned short Zero[1] = { 0 }; |
| 23 | |
| 24 | #if defined TESTMODE || defined RSADEBUG |
| 25 | #ifndef DLVL |
| 26 | #define DLVL 10000 |
| 27 | #endif |
| 28 | #define debug(x) bndebug(#x,x) |
| 29 | static int level = 0; |
| 30 | static void bndebug(char *name, Bignum b) { |
| 31 | int i; |
| 32 | int w = 50-level-strlen(name)-5*b[0]; |
| 33 | if (level >= DLVL) |
| 34 | return; |
| 35 | if (w < 0) w = 0; |
| 36 | dprintf("%*s%s%*s", level, "", name, w, ""); |
| 37 | for (i=b[0]; i>0; i--) |
| 38 | dprintf(" %04x", b[i]); |
| 39 | dprintf("\n"); |
| 40 | } |
| 41 | #define dmsg(x) do {if(level<DLVL){dprintf("%*s",level,"");printf x;}} while(0) |
| 42 | #define enter(x) do { dmsg(x); level += 4; } while(0) |
| 43 | #define leave(x) do { level -= 4; dmsg(x); } while(0) |
| 44 | #else |
| 45 | #define debug(x) |
| 46 | #define dmsg(x) |
| 47 | #define enter(x) |
| 48 | #define leave(x) |
| 49 | #endif |
| 50 | |
| 51 | static Bignum newbn(int length) { |
| 52 | Bignum b = malloc((length+1)*sizeof(unsigned short)); |
| 53 | if (!b) |
| 54 | abort(); /* FIXME */ |
| 55 | b[0] = length; |
| 56 | return b; |
| 57 | } |
| 58 | |
| 59 | static void freebn(Bignum b) { |
| 60 | free(b); |
| 61 | } |
| 62 | |
| 63 | #ifdef JORIS_RSA |
| 64 | |
| 65 | /* |
| 66 | * Compute c = a * b. |
| 67 | * Input is in the first len words of a and b. |
| 68 | * Result is returned in the first 2*len words of c. |
| 69 | */ |
| 70 | static void bigmul(unsigned short *a, unsigned short *b, unsigned short *c, |
| 71 | int len) |
| 72 | { |
| 73 | int i, j; |
| 74 | unsigned long ai, t; |
| 75 | |
| 76 | for (j = len - 1; j >= 0; j--) |
| 77 | c[j+len] = 0; |
| 78 | |
| 79 | for (i = len - 1; i >= 0; i--) { |
| 80 | ai = a[i]; |
| 81 | t = 0; |
| 82 | for (j = len - 1; j >= 0; j--) { |
| 83 | t += ai * (unsigned long) b[j]; |
| 84 | t += (unsigned long) c[i+j+1]; |
| 85 | c[i+j+1] = t; |
| 86 | t = t >> 16; |
| 87 | } |
| 88 | c[i] = t; |
| 89 | } |
| 90 | } |
| 91 | |
| 92 | |
| 93 | /* |
| 94 | * Compute a = a % m. |
| 95 | * Input in first 2*len words of a and first len words of m. |
| 96 | * Output in first 2*len words of a (of which first len words will be zero). |
| 97 | * The MSW of m MUST have its high bit set. |
| 98 | */ |
| 99 | static void bigmod(unsigned short *a, unsigned short *m, int len) |
| 100 | { |
| 101 | unsigned short m0, m1; |
| 102 | unsigned int h; |
| 103 | int i, k; |
| 104 | |
| 105 | /* Special case for len == 1 */ |
| 106 | if (len == 1) { |
| 107 | a[1] = (((long) a[0] << 16) + a[1]) % m[0]; |
| 108 | a[0] = 0; |
| 109 | return; |
| 110 | } |
| 111 | |
| 112 | m0 = m[0]; |
| 113 | m1 = m[1]; |
| 114 | |
| 115 | for (i = 0; i <= len; i++) { |
| 116 | unsigned long t; |
| 117 | unsigned int q, r, c; |
| 118 | |
| 119 | if (i == 0) { |
| 120 | h = 0; |
| 121 | } else { |
| 122 | h = a[i-1]; |
| 123 | a[i-1] = 0; |
| 124 | } |
| 125 | |
| 126 | /* Find q = h:a[i] / m0 */ |
| 127 | t = ((unsigned long) h << 16) + a[i]; |
| 128 | q = t / m0; |
| 129 | r = t % m0; |
| 130 | |
| 131 | /* Refine our estimate of q by looking at |
| 132 | h:a[i]:a[i+1] / m0:m1 */ |
| 133 | t = (long) m1 * (long) q; |
| 134 | if (t > ((unsigned long) r << 16) + a[i+1]) { |
| 135 | q--; |
| 136 | t -= m1; |
| 137 | r = (r + m0) & 0xffff; /* overflow? */ |
| 138 | if (r >= m0 && t > ((unsigned long) r << 16) + a[i+1]) |
| 139 | q--; |
| 140 | } |
| 141 | |
| 142 | /* Substract q * m from a[i...] */ |
| 143 | c = 0; |
| 144 | for (k = len - 1; k >= 0; k--) { |
| 145 | t = (long) q * (long) m[k]; |
| 146 | t += c; |
| 147 | c = t >> 16; |
| 148 | if ((unsigned short) t > a[i+k]) c++; |
| 149 | a[i+k] -= (unsigned short) t; |
| 150 | } |
| 151 | |
| 152 | /* Add back m in case of borrow */ |
| 153 | if (c != h) { |
| 154 | t = 0; |
| 155 | for (k = len - 1; k >= 0; k--) { |
| 156 | t += m[k]; |
| 157 | t += a[i+k]; |
| 158 | a[i+k] = t; |
| 159 | t = t >> 16; |
| 160 | } |
| 161 | } |
| 162 | } |
| 163 | } |
| 164 | |
| 165 | |
| 166 | /* |
| 167 | * Compute (base ^ exp) % mod. |
| 168 | * The base MUST be smaller than the modulus. |
| 169 | * The most significant word of mod MUST be non-zero. |
| 170 | * We assume that the result array is the same size as the mod array. |
| 171 | */ |
| 172 | static void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) |
| 173 | { |
| 174 | unsigned short *a, *b, *n, *m; |
| 175 | int mshift; |
| 176 | int mlen, i, j; |
| 177 | |
| 178 | /* Allocate m of size mlen, copy mod to m */ |
| 179 | /* We use big endian internally */ |
| 180 | mlen = mod[0]; |
| 181 | m = malloc(mlen * sizeof(unsigned short)); |
| 182 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
| 183 | |
| 184 | /* Shift m left to make msb bit set */ |
| 185 | for (mshift = 0; mshift < 15; mshift++) |
| 186 | if ((m[0] << mshift) & 0x8000) break; |
| 187 | if (mshift) { |
| 188 | for (i = 0; i < mlen - 1; i++) |
| 189 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
| 190 | m[mlen-1] = m[mlen-1] << mshift; |
| 191 | } |
| 192 | |
| 193 | /* Allocate n of size mlen, copy base to n */ |
| 194 | n = malloc(mlen * sizeof(unsigned short)); |
| 195 | i = mlen - base[0]; |
| 196 | for (j = 0; j < i; j++) n[j] = 0; |
| 197 | for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; |
| 198 | |
| 199 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
| 200 | a = malloc(2 * mlen * sizeof(unsigned short)); |
| 201 | b = malloc(2 * mlen * sizeof(unsigned short)); |
| 202 | for (i = 0; i < 2*mlen; i++) a[i] = 0; |
| 203 | a[2*mlen-1] = 1; |
| 204 | |
| 205 | /* Skip leading zero bits of exp. */ |
| 206 | i = 0; j = 15; |
| 207 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
| 208 | j--; |
| 209 | if (j < 0) { i++; j = 15; } |
| 210 | } |
| 211 | |
| 212 | /* Main computation */ |
| 213 | while (i < exp[0]) { |
| 214 | while (j >= 0) { |
| 215 | bigmul(a + mlen, a + mlen, b, mlen); |
| 216 | bigmod(b, m, mlen); |
| 217 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
| 218 | bigmul(b + mlen, n, a, mlen); |
| 219 | bigmod(a, m, mlen); |
| 220 | } else { |
| 221 | unsigned short *t; |
| 222 | t = a; a = b; b = t; |
| 223 | } |
| 224 | j--; |
| 225 | } |
| 226 | i++; j = 15; |
| 227 | } |
| 228 | |
| 229 | /* Fixup result in case the modulus was shifted */ |
| 230 | if (mshift) { |
| 231 | for (i = mlen - 1; i < 2*mlen - 1; i++) |
| 232 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
| 233 | a[2*mlen-1] = a[2*mlen-1] << mshift; |
| 234 | bigmod(a, m, mlen); |
| 235 | for (i = 2*mlen - 1; i >= mlen; i--) |
| 236 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
| 237 | } |
| 238 | |
| 239 | /* Copy result to buffer */ |
| 240 | for (i = 0; i < mlen; i++) |
| 241 | result[result[0] - i] = a[i+mlen]; |
| 242 | |
| 243 | /* Free temporary arrays */ |
| 244 | for (i = 0; i < 2*mlen; i++) a[i] = 0; free(a); |
| 245 | for (i = 0; i < 2*mlen; i++) b[i] = 0; free(b); |
| 246 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
| 247 | for (i = 0; i < mlen; i++) n[i] = 0; free(n); |
| 248 | } |
| 249 | |
| 250 | #else |
| 251 | |
| 252 | static int msb(Bignum r) { |
| 253 | int i; |
| 254 | int j; |
| 255 | unsigned short n; |
| 256 | |
| 257 | for (i=r[0]; i>0; i--) |
| 258 | if (r[i]) |
| 259 | break; |
| 260 | |
| 261 | j = (i-1)*16; |
| 262 | n = r[i]; |
| 263 | if (n & 0xFF00) j += 8, n >>= 8; |
| 264 | if (n & 0x00F0) j += 4, n >>= 4; |
| 265 | if (n & 0x000C) j += 2, n >>= 2; |
| 266 | if (n & 0x0002) j += 1, n >>= 1; |
| 267 | |
| 268 | return j; |
| 269 | } |
| 270 | |
| 271 | static void add(Bignum r1, Bignum r2, Bignum result) { |
| 272 | int i; |
| 273 | long stuff = 0; |
| 274 | |
| 275 | enter((">add\n")); |
| 276 | debug(r1); |
| 277 | debug(r2); |
| 278 | |
| 279 | for (i = 1 ;; i++) { |
| 280 | if (i <= r1[0]) |
| 281 | stuff += r1[i]; |
| 282 | if (i <= r2[0]) |
| 283 | stuff += r2[i]; |
| 284 | if (i <= result[0]) |
| 285 | result[i] = stuff & 0xFFFFU; |
| 286 | if (i > r1[0] && i > r2[0] && i >= result[0]) |
| 287 | break; |
| 288 | stuff >>= 16; |
| 289 | } |
| 290 | |
| 291 | debug(result); |
| 292 | leave(("<add\n")); |
| 293 | } |
| 294 | |
| 295 | static void sub(Bignum r1, Bignum r2, Bignum result) { |
| 296 | int i; |
| 297 | long stuff = 0; |
| 298 | |
| 299 | enter((">sub\n")); |
| 300 | debug(r1); |
| 301 | debug(r2); |
| 302 | |
| 303 | for (i = 1 ;; i++) { |
| 304 | if (i <= r1[0]) |
| 305 | stuff += r1[i]; |
| 306 | if (i <= r2[0]) |
| 307 | stuff -= r2[i]; |
| 308 | if (i <= result[0]) |
| 309 | result[i] = stuff & 0xFFFFU; |
| 310 | if (i > r1[0] && i > r2[0] && i >= result[0]) |
| 311 | break; |
| 312 | stuff = stuff<0 ? -1 : 0; |
| 313 | } |
| 314 | |
| 315 | debug(result); |
| 316 | leave(("<sub\n")); |
| 317 | } |
| 318 | |
| 319 | static int ge(Bignum r1, Bignum r2) { |
| 320 | int i; |
| 321 | |
| 322 | enter((">ge\n")); |
| 323 | debug(r1); |
| 324 | debug(r2); |
| 325 | |
| 326 | if (r1[0] < r2[0]) |
| 327 | i = r2[0]; |
| 328 | else |
| 329 | i = r1[0]; |
| 330 | |
| 331 | while (i > 0) { |
| 332 | unsigned short n1 = (i > r1[0] ? 0 : r1[i]); |
| 333 | unsigned short n2 = (i > r2[0] ? 0 : r2[i]); |
| 334 | |
| 335 | if (n1 > n2) { |
| 336 | dmsg(("greater\n")); |
| 337 | leave(("<ge\n")); |
| 338 | return 1; /* r1 > r2 */ |
| 339 | } else if (n1 < n2) { |
| 340 | dmsg(("less\n")); |
| 341 | leave(("<ge\n")); |
| 342 | return 0; /* r1 < r2 */ |
| 343 | } |
| 344 | |
| 345 | i--; |
| 346 | } |
| 347 | |
| 348 | dmsg(("equal\n")); |
| 349 | leave(("<ge\n")); |
| 350 | return 1; /* r1 = r2 */ |
| 351 | } |
| 352 | |
| 353 | static void modmult(Bignum r1, Bignum r2, Bignum modulus, Bignum result) { |
| 354 | Bignum temp = newbn(modulus[0]+1); |
| 355 | Bignum tmp2 = newbn(modulus[0]+1); |
| 356 | int i; |
| 357 | int bit, bits, digit, smallbit; |
| 358 | |
| 359 | enter((">modmult\n")); |
| 360 | debug(r1); |
| 361 | debug(r2); |
| 362 | debug(modulus); |
| 363 | |
| 364 | for (i=1; i<=result[0]; i++) |
| 365 | result[i] = 0; /* result := 0 */ |
| 366 | for (i=1; i<=temp[0]; i++) |
| 367 | temp[i] = (i > r2[0] ? 0 : r2[i]); /* temp := r2 */ |
| 368 | |
| 369 | bits = 1+msb(r1); |
| 370 | |
| 371 | for (bit = 0; bit < bits; bit++) { |
| 372 | digit = 1 + bit / 16; |
| 373 | smallbit = bit % 16; |
| 374 | |
| 375 | debug(temp); |
| 376 | if (digit <= r1[0] && (r1[digit] & (1<<smallbit))) { |
| 377 | dmsg(("bit %d\n", bit)); |
| 378 | add(temp, result, tmp2); |
| 379 | if (ge(tmp2, modulus)) |
| 380 | sub(tmp2, modulus, result); |
| 381 | else |
| 382 | add(tmp2, Zero, result); |
| 383 | debug(result); |
| 384 | } |
| 385 | |
| 386 | add(temp, temp, tmp2); |
| 387 | if (ge(tmp2, modulus)) |
| 388 | sub(tmp2, modulus, temp); |
| 389 | else |
| 390 | add(tmp2, Zero, temp); |
| 391 | } |
| 392 | |
| 393 | freebn(temp); |
| 394 | freebn(tmp2); |
| 395 | |
| 396 | debug(result); |
| 397 | leave(("<modmult\n")); |
| 398 | } |
| 399 | |
| 400 | static void modpow(Bignum r1, Bignum r2, Bignum modulus, Bignum result) { |
| 401 | Bignum temp = newbn(modulus[0]+1); |
| 402 | Bignum tmp2 = newbn(modulus[0]+1); |
| 403 | int i; |
| 404 | int bit, bits, digit, smallbit; |
| 405 | |
| 406 | enter((">modpow\n")); |
| 407 | debug(r1); |
| 408 | debug(r2); |
| 409 | debug(modulus); |
| 410 | |
| 411 | for (i=1; i<=result[0]; i++) |
| 412 | result[i] = (i==1); /* result := 1 */ |
| 413 | for (i=1; i<=temp[0]; i++) |
| 414 | temp[i] = (i > r1[0] ? 0 : r1[i]); /* temp := r1 */ |
| 415 | |
| 416 | bits = 1+msb(r2); |
| 417 | |
| 418 | for (bit = 0; bit < bits; bit++) { |
| 419 | digit = 1 + bit / 16; |
| 420 | smallbit = bit % 16; |
| 421 | |
| 422 | debug(temp); |
| 423 | if (digit <= r2[0] && (r2[digit] & (1<<smallbit))) { |
| 424 | dmsg(("bit %d\n", bit)); |
| 425 | modmult(temp, result, modulus, tmp2); |
| 426 | add(tmp2, Zero, result); |
| 427 | debug(result); |
| 428 | } |
| 429 | |
| 430 | modmult(temp, temp, modulus, tmp2); |
| 431 | add(tmp2, Zero, temp); |
| 432 | } |
| 433 | |
| 434 | freebn(temp); |
| 435 | freebn(tmp2); |
| 436 | |
| 437 | debug(result); |
| 438 | leave(("<modpow\n")); |
| 439 | } |
| 440 | |
| 441 | #endif |
| 442 | |
| 443 | int makekey(unsigned char *data, struct RSAKey *result, |
| 444 | unsigned char **keystr) { |
| 445 | unsigned char *p = data; |
| 446 | Bignum bn[2]; |
| 447 | int i, j; |
| 448 | int w, b; |
| 449 | |
| 450 | result->bits = 0; |
| 451 | for (i=0; i<4; i++) |
| 452 | result->bits = (result->bits << 8) + *p++; |
| 453 | |
| 454 | for (j=0; j<2; j++) { |
| 455 | |
| 456 | w = 0; |
| 457 | for (i=0; i<2; i++) |
| 458 | w = (w << 8) + *p++; |
| 459 | |
| 460 | result->bytes = b = (w+7)/8; /* bits -> bytes */ |
| 461 | w = (w+15)/16; /* bits -> words */ |
| 462 | |
| 463 | bn[j] = newbn(w); |
| 464 | |
| 465 | if (keystr) *keystr = p; /* point at key string, second time */ |
| 466 | |
| 467 | for (i=1; i<=w; i++) |
| 468 | bn[j][i] = 0; |
| 469 | for (i=0; i<b; i++) { |
| 470 | unsigned char byte = *p++; |
| 471 | if ((b-i) & 1) |
| 472 | bn[j][w-i/2] |= byte; |
| 473 | else |
| 474 | bn[j][w-i/2] |= byte<<8; |
| 475 | } |
| 476 | |
| 477 | debug(bn[j]); |
| 478 | |
| 479 | } |
| 480 | |
| 481 | result->exponent = bn[0]; |
| 482 | result->modulus = bn[1]; |
| 483 | |
| 484 | return p - data; |
| 485 | } |
| 486 | |
| 487 | void rsaencrypt(unsigned char *data, int length, struct RSAKey *key) { |
| 488 | Bignum b1, b2; |
| 489 | int w, i; |
| 490 | unsigned char *p; |
| 491 | |
| 492 | debug(key->exponent); |
| 493 | |
| 494 | memmove(data+key->bytes-length, data, length); |
| 495 | data[0] = 0; |
| 496 | data[1] = 2; |
| 497 | |
| 498 | for (i = 2; i < key->bytes-length-1; i++) { |
| 499 | do { |
| 500 | data[i] = random_byte(); |
| 501 | } while (data[i] == 0); |
| 502 | } |
| 503 | data[key->bytes-length-1] = 0; |
| 504 | |
| 505 | w = (key->bytes+1)/2; |
| 506 | |
| 507 | b1 = newbn(w); |
| 508 | b2 = newbn(w); |
| 509 | |
| 510 | p = data; |
| 511 | for (i=1; i<=w; i++) |
| 512 | b1[i] = 0; |
| 513 | for (i=0; i<key->bytes; i++) { |
| 514 | unsigned char byte = *p++; |
| 515 | if ((key->bytes-i) & 1) |
| 516 | b1[w-i/2] |= byte; |
| 517 | else |
| 518 | b1[w-i/2] |= byte<<8; |
| 519 | } |
| 520 | |
| 521 | debug(b1); |
| 522 | |
| 523 | modpow(b1, key->exponent, key->modulus, b2); |
| 524 | |
| 525 | debug(b2); |
| 526 | |
| 527 | p = data; |
| 528 | for (i=0; i<key->bytes; i++) { |
| 529 | unsigned char b; |
| 530 | if (i & 1) |
| 531 | b = b2[w-i/2] & 0xFF; |
| 532 | else |
| 533 | b = b2[w-i/2] >> 8; |
| 534 | *p++ = b; |
| 535 | } |
| 536 | |
| 537 | freebn(b1); |
| 538 | freebn(b2); |
| 539 | } |
| 540 | |
| 541 | int rsastr_len(struct RSAKey *key) { |
| 542 | Bignum md, ex; |
| 543 | |
| 544 | md = key->modulus; |
| 545 | ex = key->exponent; |
| 546 | return 4 * (ex[0]+md[0]) + 10; |
| 547 | } |
| 548 | |
| 549 | void rsastr_fmt(char *str, struct RSAKey *key) { |
| 550 | Bignum md, ex; |
| 551 | int len = 0, i; |
| 552 | |
| 553 | md = key->modulus; |
| 554 | ex = key->exponent; |
| 555 | |
| 556 | for (i=1; i<=ex[0]; i++) { |
| 557 | sprintf(str+len, "%04x", ex[i]); |
| 558 | len += strlen(str+len); |
| 559 | } |
| 560 | str[len++] = '/'; |
| 561 | for (i=1; i<=md[0]; i++) { |
| 562 | sprintf(str+len, "%04x", md[i]); |
| 563 | len += strlen(str+len); |
| 564 | } |
| 565 | str[len] = '\0'; |
| 566 | } |
| 567 | |
| 568 | #ifdef TESTMODE |
| 569 | |
| 570 | #ifndef NODDY |
| 571 | #define p1 10007 |
| 572 | #define p2 10069 |
| 573 | #define p3 10177 |
| 574 | #else |
| 575 | #define p1 3 |
| 576 | #define p2 7 |
| 577 | #define p3 13 |
| 578 | #endif |
| 579 | |
| 580 | unsigned short P1[2] = { 1, p1 }; |
| 581 | unsigned short P2[2] = { 1, p2 }; |
| 582 | unsigned short P3[2] = { 1, p3 }; |
| 583 | unsigned short bigmod[5] = { 4, 0, 0, 0, 32768U }; |
| 584 | unsigned short mod[5] = { 4, 0, 0, 0, 0 }; |
| 585 | unsigned short a[5] = { 4, 0, 0, 0, 0 }; |
| 586 | unsigned short b[5] = { 4, 0, 0, 0, 0 }; |
| 587 | unsigned short c[5] = { 4, 0, 0, 0, 0 }; |
| 588 | unsigned short One[2] = { 1, 1 }; |
| 589 | unsigned short Two[2] = { 1, 2 }; |
| 590 | |
| 591 | int main(void) { |
| 592 | modmult(P1, P2, bigmod, a); debug(a); |
| 593 | modmult(a, P3, bigmod, mod); debug(mod); |
| 594 | |
| 595 | sub(P1, One, a); debug(a); |
| 596 | sub(P2, One, b); debug(b); |
| 597 | modmult(a, b, bigmod, c); debug(c); |
| 598 | sub(P3, One, a); debug(a); |
| 599 | modmult(a, c, bigmod, b); debug(b); |
| 600 | |
| 601 | modpow(Two, b, mod, a); debug(a); |
| 602 | |
| 603 | return 0; |
| 604 | } |
| 605 | |
| 606 | #endif |