e5574168 |
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 | } |