| 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 | #include "ssh.h" |
| 10 | |
| 11 | unsigned short bnZero[1] = { 0 }; |
| 12 | unsigned short bnOne[2] = { 1, 1 }; |
| 13 | |
| 14 | Bignum Zero = bnZero, One = bnOne; |
| 15 | |
| 16 | Bignum newbn(int length) { |
| 17 | Bignum b = malloc((length+1)*sizeof(unsigned short)); |
| 18 | if (!b) |
| 19 | abort(); /* FIXME */ |
| 20 | memset(b, 0, (length+1)*sizeof(*b)); |
| 21 | b[0] = length; |
| 22 | return b; |
| 23 | } |
| 24 | |
| 25 | Bignum copybn(Bignum orig) { |
| 26 | Bignum b = malloc((orig[0]+1)*sizeof(unsigned short)); |
| 27 | if (!b) |
| 28 | abort(); /* FIXME */ |
| 29 | memcpy(b, orig, (orig[0]+1)*sizeof(*b)); |
| 30 | return b; |
| 31 | } |
| 32 | |
| 33 | void freebn(Bignum b) { |
| 34 | /* |
| 35 | * Burn the evidence, just in case. |
| 36 | */ |
| 37 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
| 38 | free(b); |
| 39 | } |
| 40 | |
| 41 | /* |
| 42 | * Compute c = a * b. |
| 43 | * Input is in the first len words of a and b. |
| 44 | * Result is returned in the first 2*len words of c. |
| 45 | */ |
| 46 | static void bigmul(unsigned short *a, unsigned short *b, unsigned short *c, |
| 47 | int len) |
| 48 | { |
| 49 | int i, j; |
| 50 | unsigned long ai, t; |
| 51 | |
| 52 | for (j = len - 1; j >= 0; j--) |
| 53 | c[j+len] = 0; |
| 54 | |
| 55 | for (i = len - 1; i >= 0; i--) { |
| 56 | ai = a[i]; |
| 57 | t = 0; |
| 58 | for (j = len - 1; j >= 0; j--) { |
| 59 | t += ai * (unsigned long) b[j]; |
| 60 | t += (unsigned long) c[i+j+1]; |
| 61 | c[i+j+1] = (unsigned short)t; |
| 62 | t = t >> 16; |
| 63 | } |
| 64 | c[i] = (unsigned short)t; |
| 65 | } |
| 66 | } |
| 67 | |
| 68 | /* |
| 69 | * Compute a = a % m. |
| 70 | * Input in first len2 words of a and first len words of m. |
| 71 | * Output in first len2 words of a |
| 72 | * (of which first len2-len words will be zero). |
| 73 | * The MSW of m MUST have its high bit set. |
| 74 | */ |
| 75 | static void bigmod(unsigned short *a, unsigned short *m, |
| 76 | int len, int len2) |
| 77 | { |
| 78 | unsigned short m0, m1; |
| 79 | unsigned int h; |
| 80 | int i, k; |
| 81 | |
| 82 | /* Special case for len == 1 */ |
| 83 | if (len == 1) { |
| 84 | a[1] = (((long) a[0] << 16) + a[1]) % m[0]; |
| 85 | a[0] = 0; |
| 86 | return; |
| 87 | } |
| 88 | |
| 89 | m0 = m[0]; |
| 90 | m1 = m[1]; |
| 91 | |
| 92 | for (i = 0; i <= len2-len; i++) { |
| 93 | unsigned long t; |
| 94 | unsigned int q, r, c; |
| 95 | |
| 96 | if (i == 0) { |
| 97 | h = 0; |
| 98 | } else { |
| 99 | h = a[i-1]; |
| 100 | a[i-1] = 0; |
| 101 | } |
| 102 | |
| 103 | /* Find q = h:a[i] / m0 */ |
| 104 | t = ((unsigned long) h << 16) + a[i]; |
| 105 | q = t / m0; |
| 106 | r = t % m0; |
| 107 | |
| 108 | /* Refine our estimate of q by looking at |
| 109 | h:a[i]:a[i+1] / m0:m1 */ |
| 110 | t = (long) m1 * (long) q; |
| 111 | if (t > ((unsigned long) r << 16) + a[i+1]) { |
| 112 | q--; |
| 113 | t -= m1; |
| 114 | r = (r + m0) & 0xffff; /* overflow? */ |
| 115 | if (r >= (unsigned long)m0 && |
| 116 | t > ((unsigned long) r << 16) + a[i+1]) |
| 117 | q--; |
| 118 | } |
| 119 | |
| 120 | /* Substract q * m from a[i...] */ |
| 121 | c = 0; |
| 122 | for (k = len - 1; k >= 0; k--) { |
| 123 | t = (long) q * (long) m[k]; |
| 124 | t += c; |
| 125 | c = t >> 16; |
| 126 | if ((unsigned short) t > a[i+k]) c++; |
| 127 | a[i+k] -= (unsigned short) t; |
| 128 | } |
| 129 | |
| 130 | /* Add back m in case of borrow */ |
| 131 | if (c != h) { |
| 132 | t = 0; |
| 133 | for (k = len - 1; k >= 0; k--) { |
| 134 | t += m[k]; |
| 135 | t += a[i+k]; |
| 136 | a[i+k] = (unsigned short)t; |
| 137 | t = t >> 16; |
| 138 | } |
| 139 | } |
| 140 | } |
| 141 | } |
| 142 | |
| 143 | /* |
| 144 | * Compute (base ^ exp) % mod. |
| 145 | * The base MUST be smaller than the modulus. |
| 146 | * The most significant word of mod MUST be non-zero. |
| 147 | * We assume that the result array is the same size as the mod array. |
| 148 | */ |
| 149 | void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) |
| 150 | { |
| 151 | unsigned short *a, *b, *n, *m; |
| 152 | int mshift; |
| 153 | int mlen, i, j; |
| 154 | |
| 155 | /* Allocate m of size mlen, copy mod to m */ |
| 156 | /* We use big endian internally */ |
| 157 | mlen = mod[0]; |
| 158 | m = malloc(mlen * sizeof(unsigned short)); |
| 159 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
| 160 | |
| 161 | /* Shift m left to make msb bit set */ |
| 162 | for (mshift = 0; mshift < 15; mshift++) |
| 163 | if ((m[0] << mshift) & 0x8000) break; |
| 164 | if (mshift) { |
| 165 | for (i = 0; i < mlen - 1; i++) |
| 166 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
| 167 | m[mlen-1] = m[mlen-1] << mshift; |
| 168 | } |
| 169 | |
| 170 | /* Allocate n of size mlen, copy base to n */ |
| 171 | n = malloc(mlen * sizeof(unsigned short)); |
| 172 | i = mlen - base[0]; |
| 173 | for (j = 0; j < i; j++) n[j] = 0; |
| 174 | for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; |
| 175 | |
| 176 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
| 177 | a = malloc(2 * mlen * sizeof(unsigned short)); |
| 178 | b = malloc(2 * mlen * sizeof(unsigned short)); |
| 179 | for (i = 0; i < 2*mlen; i++) a[i] = 0; |
| 180 | a[2*mlen-1] = 1; |
| 181 | |
| 182 | /* Skip leading zero bits of exp. */ |
| 183 | i = 0; j = 15; |
| 184 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
| 185 | j--; |
| 186 | if (j < 0) { i++; j = 15; } |
| 187 | } |
| 188 | |
| 189 | /* Main computation */ |
| 190 | while (i < exp[0]) { |
| 191 | while (j >= 0) { |
| 192 | bigmul(a + mlen, a + mlen, b, mlen); |
| 193 | bigmod(b, m, mlen, mlen*2); |
| 194 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
| 195 | bigmul(b + mlen, n, a, mlen); |
| 196 | bigmod(a, m, mlen, mlen*2); |
| 197 | } else { |
| 198 | unsigned short *t; |
| 199 | t = a; a = b; b = t; |
| 200 | } |
| 201 | j--; |
| 202 | } |
| 203 | i++; j = 15; |
| 204 | } |
| 205 | |
| 206 | /* Fixup result in case the modulus was shifted */ |
| 207 | if (mshift) { |
| 208 | for (i = mlen - 1; i < 2*mlen - 1; i++) |
| 209 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
| 210 | a[2*mlen-1] = a[2*mlen-1] << mshift; |
| 211 | bigmod(a, m, mlen, mlen*2); |
| 212 | for (i = 2*mlen - 1; i >= mlen; i--) |
| 213 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
| 214 | } |
| 215 | |
| 216 | /* Copy result to buffer */ |
| 217 | for (i = 0; i < mlen; i++) |
| 218 | result[result[0] - i] = a[i+mlen]; |
| 219 | |
| 220 | /* Free temporary arrays */ |
| 221 | for (i = 0; i < 2*mlen; i++) a[i] = 0; free(a); |
| 222 | for (i = 0; i < 2*mlen; i++) b[i] = 0; free(b); |
| 223 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
| 224 | for (i = 0; i < mlen; i++) n[i] = 0; free(n); |
| 225 | } |
| 226 | |
| 227 | /* |
| 228 | * Compute (p * q) % mod. |
| 229 | * The most significant word of mod MUST be non-zero. |
| 230 | * We assume that the result array is the same size as the mod array. |
| 231 | */ |
| 232 | void modmul(Bignum p, Bignum q, Bignum mod, Bignum result) |
| 233 | { |
| 234 | unsigned short *a, *n, *m, *o; |
| 235 | int mshift; |
| 236 | int pqlen, mlen, i, j; |
| 237 | |
| 238 | /* Allocate m of size mlen, copy mod to m */ |
| 239 | /* We use big endian internally */ |
| 240 | mlen = mod[0]; |
| 241 | m = malloc(mlen * sizeof(unsigned short)); |
| 242 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
| 243 | |
| 244 | /* Shift m left to make msb bit set */ |
| 245 | for (mshift = 0; mshift < 15; mshift++) |
| 246 | if ((m[0] << mshift) & 0x8000) break; |
| 247 | if (mshift) { |
| 248 | for (i = 0; i < mlen - 1; i++) |
| 249 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
| 250 | m[mlen-1] = m[mlen-1] << mshift; |
| 251 | } |
| 252 | |
| 253 | pqlen = (p[0] > q[0] ? p[0] : q[0]); |
| 254 | |
| 255 | /* Allocate n of size pqlen, copy p to n */ |
| 256 | n = malloc(pqlen * sizeof(unsigned short)); |
| 257 | i = pqlen - p[0]; |
| 258 | for (j = 0; j < i; j++) n[j] = 0; |
| 259 | for (j = 0; j < p[0]; j++) n[i+j] = p[p[0] - j]; |
| 260 | |
| 261 | /* Allocate o of size pqlen, copy q to o */ |
| 262 | o = malloc(pqlen * sizeof(unsigned short)); |
| 263 | i = pqlen - q[0]; |
| 264 | for (j = 0; j < i; j++) o[j] = 0; |
| 265 | for (j = 0; j < q[0]; j++) o[i+j] = q[q[0] - j]; |
| 266 | |
| 267 | /* Allocate a of size 2*pqlen for result */ |
| 268 | a = malloc(2 * pqlen * sizeof(unsigned short)); |
| 269 | |
| 270 | /* Main computation */ |
| 271 | bigmul(n, o, a, pqlen); |
| 272 | bigmod(a, m, mlen, 2*pqlen); |
| 273 | |
| 274 | /* Fixup result in case the modulus was shifted */ |
| 275 | if (mshift) { |
| 276 | for (i = 2*pqlen - mlen - 1; i < 2*pqlen - 1; i++) |
| 277 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
| 278 | a[2*pqlen-1] = a[2*pqlen-1] << mshift; |
| 279 | bigmod(a, m, mlen, pqlen*2); |
| 280 | for (i = 2*pqlen - 1; i >= 2*pqlen - mlen; i--) |
| 281 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
| 282 | } |
| 283 | |
| 284 | /* Copy result to buffer */ |
| 285 | for (i = 0; i < mlen; i++) |
| 286 | result[result[0] - i] = a[i+2*pqlen-mlen]; |
| 287 | |
| 288 | /* Free temporary arrays */ |
| 289 | for (i = 0; i < 2*pqlen; i++) a[i] = 0; free(a); |
| 290 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
| 291 | for (i = 0; i < pqlen; i++) n[i] = 0; free(n); |
| 292 | for (i = 0; i < pqlen; i++) o[i] = 0; free(o); |
| 293 | } |
| 294 | |
| 295 | /* |
| 296 | * Decrement a number. |
| 297 | */ |
| 298 | void decbn(Bignum bn) { |
| 299 | int i = 1; |
| 300 | while (i < bn[0] && bn[i] == 0) |
| 301 | bn[i++] = 0xFFFF; |
| 302 | bn[i]--; |
| 303 | } |
| 304 | |
| 305 | /* |
| 306 | * Read an ssh1-format bignum from a data buffer. Return the number |
| 307 | * of bytes consumed. |
| 308 | */ |
| 309 | int ssh1_read_bignum(unsigned char *data, Bignum *result) { |
| 310 | unsigned char *p = data; |
| 311 | Bignum bn; |
| 312 | int i; |
| 313 | int w, b; |
| 314 | |
| 315 | w = 0; |
| 316 | for (i=0; i<2; i++) |
| 317 | w = (w << 8) + *p++; |
| 318 | |
| 319 | b = (w+7)/8; /* bits -> bytes */ |
| 320 | w = (w+15)/16; /* bits -> words */ |
| 321 | |
| 322 | if (!result) /* just return length */ |
| 323 | return b + 2; |
| 324 | |
| 325 | bn = newbn(w); |
| 326 | |
| 327 | for (i=1; i<=w; i++) |
| 328 | bn[i] = 0; |
| 329 | for (i=b; i-- ;) { |
| 330 | unsigned char byte = *p++; |
| 331 | if (i & 1) |
| 332 | bn[1+i/2] |= byte<<8; |
| 333 | else |
| 334 | bn[1+i/2] |= byte; |
| 335 | } |
| 336 | |
| 337 | *result = bn; |
| 338 | |
| 339 | return p - data; |
| 340 | } |
| 341 | |
| 342 | /* |
| 343 | * Return the bit count of a bignum, for ssh1 encoding. |
| 344 | */ |
| 345 | int ssh1_bignum_bitcount(Bignum bn) { |
| 346 | int bitcount = bn[0] * 16 - 1; |
| 347 | |
| 348 | while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0) |
| 349 | bitcount--; |
| 350 | return bitcount + 1; |
| 351 | } |
| 352 | |
| 353 | /* |
| 354 | * Return the byte length of a bignum when ssh1 encoded. |
| 355 | */ |
| 356 | int ssh1_bignum_length(Bignum bn) { |
| 357 | return 2 + (ssh1_bignum_bitcount(bn)+7)/8; |
| 358 | } |
| 359 | |
| 360 | /* |
| 361 | * Return a byte from a bignum; 0 is least significant, etc. |
| 362 | */ |
| 363 | int bignum_byte(Bignum bn, int i) { |
| 364 | if (i >= 2*bn[0]) |
| 365 | return 0; /* beyond the end */ |
| 366 | else if (i & 1) |
| 367 | return (bn[i/2+1] >> 8) & 0xFF; |
| 368 | else |
| 369 | return (bn[i/2+1] ) & 0xFF; |
| 370 | } |
| 371 | |
| 372 | /* |
| 373 | * Write a ssh1-format bignum into a buffer. It is assumed the |
| 374 | * buffer is big enough. Returns the number of bytes used. |
| 375 | */ |
| 376 | int ssh1_write_bignum(void *data, Bignum bn) { |
| 377 | unsigned char *p = data; |
| 378 | int len = ssh1_bignum_length(bn); |
| 379 | int i; |
| 380 | int bitc = ssh1_bignum_bitcount(bn); |
| 381 | |
| 382 | *p++ = (bitc >> 8) & 0xFF; |
| 383 | *p++ = (bitc ) & 0xFF; |
| 384 | for (i = len-2; i-- ;) |
| 385 | *p++ = bignum_byte(bn, i); |
| 386 | return len; |
| 387 | } |