| 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 | static unsigned short Zero[1] = { 0 }; |
| 12 | |
| 13 | #if defined TESTMODE || defined RSADEBUG |
| 14 | #ifndef DLVL |
| 15 | #define DLVL 10000 |
| 16 | #endif |
| 17 | #define debug(x) bndebug(#x,x) |
| 18 | static int level = 0; |
| 19 | static void bndebug(char *name, Bignum b) { |
| 20 | int i; |
| 21 | int w = 50-level-strlen(name)-5*b[0]; |
| 22 | if (level >= DLVL) |
| 23 | return; |
| 24 | if (w < 0) w = 0; |
| 25 | dprintf("%*s%s%*s", level, "", name, w, ""); |
| 26 | for (i=b[0]; i>0; i--) |
| 27 | dprintf(" %04x", b[i]); |
| 28 | dprintf("\n"); |
| 29 | } |
| 30 | #define dmsg(x) do {if(level<DLVL){dprintf("%*s",level,"");printf x;}} while(0) |
| 31 | #define enter(x) do { dmsg(x); level += 4; } while(0) |
| 32 | #define leave(x) do { level -= 4; dmsg(x); } while(0) |
| 33 | #else |
| 34 | #define debug(x) |
| 35 | #define dmsg(x) |
| 36 | #define enter(x) |
| 37 | #define leave(x) |
| 38 | #endif |
| 39 | |
| 40 | Bignum newbn(int length) { |
| 41 | Bignum b = malloc((length+1)*sizeof(unsigned short)); |
| 42 | if (!b) |
| 43 | abort(); /* FIXME */ |
| 44 | memset(b, 0, (length+1)*sizeof(*b)); |
| 45 | b[0] = length; |
| 46 | return b; |
| 47 | } |
| 48 | |
| 49 | void freebn(Bignum b) { |
| 50 | /* |
| 51 | * Burn the evidence, just in case. |
| 52 | */ |
| 53 | memset(b, 0, sizeof(b[0]) * (b[0] + 1)); |
| 54 | free(b); |
| 55 | } |
| 56 | |
| 57 | /* |
| 58 | * Compute c = a * b. |
| 59 | * Input is in the first len words of a and b. |
| 60 | * Result is returned in the first 2*len words of c. |
| 61 | */ |
| 62 | static void bigmul(unsigned short *a, unsigned short *b, unsigned short *c, |
| 63 | int len) |
| 64 | { |
| 65 | int i, j; |
| 66 | unsigned long ai, t; |
| 67 | |
| 68 | for (j = len - 1; j >= 0; j--) |
| 69 | c[j+len] = 0; |
| 70 | |
| 71 | for (i = len - 1; i >= 0; i--) { |
| 72 | ai = a[i]; |
| 73 | t = 0; |
| 74 | for (j = len - 1; j >= 0; j--) { |
| 75 | t += ai * (unsigned long) b[j]; |
| 76 | t += (unsigned long) c[i+j+1]; |
| 77 | c[i+j+1] = (unsigned short)t; |
| 78 | t = t >> 16; |
| 79 | } |
| 80 | c[i] = (unsigned short)t; |
| 81 | } |
| 82 | } |
| 83 | |
| 84 | /* |
| 85 | * Compute a = a % m. |
| 86 | * Input in first 2*len words of a and first len words of m. |
| 87 | * Output in first 2*len words of a (of which first len words will be zero). |
| 88 | * The MSW of m MUST have its high bit set. |
| 89 | */ |
| 90 | static void bigmod(unsigned short *a, unsigned short *m, int len) |
| 91 | { |
| 92 | unsigned short m0, m1; |
| 93 | unsigned int h; |
| 94 | int i, k; |
| 95 | |
| 96 | /* Special case for len == 1 */ |
| 97 | if (len == 1) { |
| 98 | a[1] = (((long) a[0] << 16) + a[1]) % m[0]; |
| 99 | a[0] = 0; |
| 100 | return; |
| 101 | } |
| 102 | |
| 103 | m0 = m[0]; |
| 104 | m1 = m[1]; |
| 105 | |
| 106 | for (i = 0; i <= len; i++) { |
| 107 | unsigned long t; |
| 108 | unsigned int q, r, c; |
| 109 | |
| 110 | if (i == 0) { |
| 111 | h = 0; |
| 112 | } else { |
| 113 | h = a[i-1]; |
| 114 | a[i-1] = 0; |
| 115 | } |
| 116 | |
| 117 | /* Find q = h:a[i] / m0 */ |
| 118 | t = ((unsigned long) h << 16) + a[i]; |
| 119 | q = t / m0; |
| 120 | r = t % m0; |
| 121 | |
| 122 | /* Refine our estimate of q by looking at |
| 123 | h:a[i]:a[i+1] / m0:m1 */ |
| 124 | t = (long) m1 * (long) q; |
| 125 | if (t > ((unsigned long) r << 16) + a[i+1]) { |
| 126 | q--; |
| 127 | t -= m1; |
| 128 | r = (r + m0) & 0xffff; /* overflow? */ |
| 129 | if (r >= (unsigned long)m0 && |
| 130 | t > ((unsigned long) r << 16) + a[i+1]) |
| 131 | q--; |
| 132 | } |
| 133 | |
| 134 | /* Substract q * m from a[i...] */ |
| 135 | c = 0; |
| 136 | for (k = len - 1; k >= 0; k--) { |
| 137 | t = (long) q * (long) m[k]; |
| 138 | t += c; |
| 139 | c = t >> 16; |
| 140 | if ((unsigned short) t > a[i+k]) c++; |
| 141 | a[i+k] -= (unsigned short) t; |
| 142 | } |
| 143 | |
| 144 | /* Add back m in case of borrow */ |
| 145 | if (c != h) { |
| 146 | t = 0; |
| 147 | for (k = len - 1; k >= 0; k--) { |
| 148 | t += m[k]; |
| 149 | t += a[i+k]; |
| 150 | a[i+k] = (unsigned short)t; |
| 151 | t = t >> 16; |
| 152 | } |
| 153 | } |
| 154 | } |
| 155 | } |
| 156 | |
| 157 | /* |
| 158 | * Compute (base ^ exp) % mod. |
| 159 | * The base MUST be smaller than the modulus. |
| 160 | * The most significant word of mod MUST be non-zero. |
| 161 | * We assume that the result array is the same size as the mod array. |
| 162 | */ |
| 163 | void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) |
| 164 | { |
| 165 | unsigned short *a, *b, *n, *m; |
| 166 | int mshift; |
| 167 | int mlen, i, j; |
| 168 | |
| 169 | /* Allocate m of size mlen, copy mod to m */ |
| 170 | /* We use big endian internally */ |
| 171 | mlen = mod[0]; |
| 172 | m = malloc(mlen * sizeof(unsigned short)); |
| 173 | for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; |
| 174 | |
| 175 | /* Shift m left to make msb bit set */ |
| 176 | for (mshift = 0; mshift < 15; mshift++) |
| 177 | if ((m[0] << mshift) & 0x8000) break; |
| 178 | if (mshift) { |
| 179 | for (i = 0; i < mlen - 1; i++) |
| 180 | m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); |
| 181 | m[mlen-1] = m[mlen-1] << mshift; |
| 182 | } |
| 183 | |
| 184 | /* Allocate n of size mlen, copy base to n */ |
| 185 | n = malloc(mlen * sizeof(unsigned short)); |
| 186 | i = mlen - base[0]; |
| 187 | for (j = 0; j < i; j++) n[j] = 0; |
| 188 | for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; |
| 189 | |
| 190 | /* Allocate a and b of size 2*mlen. Set a = 1 */ |
| 191 | a = malloc(2 * mlen * sizeof(unsigned short)); |
| 192 | b = malloc(2 * mlen * sizeof(unsigned short)); |
| 193 | for (i = 0; i < 2*mlen; i++) a[i] = 0; |
| 194 | a[2*mlen-1] = 1; |
| 195 | |
| 196 | /* Skip leading zero bits of exp. */ |
| 197 | i = 0; j = 15; |
| 198 | while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { |
| 199 | j--; |
| 200 | if (j < 0) { i++; j = 15; } |
| 201 | } |
| 202 | |
| 203 | /* Main computation */ |
| 204 | while (i < exp[0]) { |
| 205 | while (j >= 0) { |
| 206 | bigmul(a + mlen, a + mlen, b, mlen); |
| 207 | bigmod(b, m, mlen); |
| 208 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
| 209 | bigmul(b + mlen, n, a, mlen); |
| 210 | bigmod(a, m, mlen); |
| 211 | } else { |
| 212 | unsigned short *t; |
| 213 | t = a; a = b; b = t; |
| 214 | } |
| 215 | j--; |
| 216 | } |
| 217 | i++; j = 15; |
| 218 | } |
| 219 | |
| 220 | /* Fixup result in case the modulus was shifted */ |
| 221 | if (mshift) { |
| 222 | for (i = mlen - 1; i < 2*mlen - 1; i++) |
| 223 | a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); |
| 224 | a[2*mlen-1] = a[2*mlen-1] << mshift; |
| 225 | bigmod(a, m, mlen); |
| 226 | for (i = 2*mlen - 1; i >= mlen; i--) |
| 227 | a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); |
| 228 | } |
| 229 | |
| 230 | /* Copy result to buffer */ |
| 231 | for (i = 0; i < mlen; i++) |
| 232 | result[result[0] - i] = a[i+mlen]; |
| 233 | |
| 234 | /* Free temporary arrays */ |
| 235 | for (i = 0; i < 2*mlen; i++) a[i] = 0; free(a); |
| 236 | for (i = 0; i < 2*mlen; i++) b[i] = 0; free(b); |
| 237 | for (i = 0; i < mlen; i++) m[i] = 0; free(m); |
| 238 | for (i = 0; i < mlen; i++) n[i] = 0; free(n); |
| 239 | } |