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 | |
7cca0d81 |
11 | unsigned short bnZero[1] = { 0 }; |
12 | unsigned short bnOne[2] = { 1, 1 }; |
e5574168 |
13 | |
7cca0d81 |
14 | Bignum Zero = bnZero, One = bnOne; |
e5574168 |
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 | |
7cca0d81 |
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 | |
e5574168 |
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. |
7cca0d81 |
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). |
e5574168 |
73 | * The MSW of m MUST have its high bit set. |
74 | */ |
7cca0d81 |
75 | static void bigmod(unsigned short *a, unsigned short *m, |
76 | int len, int len2) |
e5574168 |
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 | |
7cca0d81 |
92 | for (i = 0; i <= len2-len; i++) { |
e5574168 |
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); |
7cca0d81 |
193 | bigmod(b, m, mlen, mlen*2); |
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194 | if ((exp[exp[0] - i] & (1 << j)) != 0) { |
195 | bigmul(b + mlen, n, a, mlen); |
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196 | bigmod(a, m, mlen, mlen*2); |
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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; |
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211 | bigmod(a, m, mlen, mlen*2); |
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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 | } |
7cca0d81 |
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 | |
a52f067e |
322 | if (!result) /* just return length */ |
323 | return b + 2; |
324 | |
7cca0d81 |
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 | } |
5c58ad2d |
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 | } |