Harald Welte | 0e3e88e | 2011-01-01 15:25:50 +0100 | [diff] [blame] | 1 | /* An implementation of the GSM A3A8 algorithm. (Specifically, COMP128.) |
| 2 | */ |
| 3 | |
| 4 | /* Copyright 1998, Marc Briceno, Ian Goldberg, and David Wagner. |
| 5 | * All rights reserved. |
| 6 | * |
| 7 | * Redistribution and use in source and binary forms, with or without |
| 8 | * modification, are permitted provided that the following conditions are met: |
| 9 | * |
| 10 | * * Redistributions of source code must retain the above copyright notice, |
| 11 | * this list of conditions and the following disclaimer. |
| 12 | * |
| 13 | * * Redistributions in binary form must reproduce the above copyright notice, |
| 14 | * this list of conditions and the following disclaimer in the documentation |
| 15 | * and/or other materials provided with the distribution. |
| 16 | * |
| 17 | * * Neither the name of the authors nor the names of the contributors |
| 18 | * may be used to endorse or promote products derived from this software |
| 19 | * without specific prior written permission. |
| 20 | * |
| 21 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| 22 | * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 23 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 24 | * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE |
| 25 | * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| 26 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| 27 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| 28 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| 29 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 30 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| 31 | * POSSIBILITY OF SUCH DAMAGE. |
| 32 | */ |
| 33 | |
| 34 | /* |
| 35 | * Coded in C merely because C is a much more precise, concise form of |
| 36 | * expression for these purposes. See Judge Patel if you have any problems |
| 37 | * with this... |
| 38 | * Of course, it's only authentication, so it should be exportable for the |
| 39 | * usual boring reasons. |
| 40 | */ |
| 41 | |
| 42 | typedef unsigned char Byte; |
| 43 | |
| 44 | #include <stdio.h> |
| 45 | /* #define TEST */ |
| 46 | |
| 47 | /* |
| 48 | * rand[0..15]: the challenge from the base station |
| 49 | * key[0..15]: the SIM's A3/A8 long-term key Ki |
| 50 | * simoutput[0..11]: what you'd get back if you fed rand and key to a real |
| 51 | * SIM. |
| 52 | * |
| 53 | * The GSM spec states that simoutput[0..3] is SRES, |
| 54 | * and simoutput[4..11] is Kc (the A5 session key). |
| 55 | * (See GSM 11.11, Section 8.16. See also the leaked document |
| 56 | * referenced below.) |
| 57 | * Note that Kc is bits 74..127 of the COMP128 output, followed by 10 |
| 58 | * zeros. |
| 59 | * In other words, A5 is keyed with only 54 bits of entropy. This |
| 60 | * represents a deliberate weakening of the key used for voice privacy |
| 61 | * by a factor of over 1000. |
| 62 | * |
| 63 | * Verified with a Pacific Bell Schlumberger SIM. Your mileage may vary. |
| 64 | * |
| 65 | * Marc Briceno <marc@scard.org>, Ian Goldberg <iang@cs.berkeley.edu>, |
| 66 | * and David Wagner <daw@cs.berkeley.edu> |
| 67 | */ |
| 68 | |
| 69 | void A3A8(/* in */ Byte rand[16], /* in */ Byte key[16], |
| 70 | /* out */ Byte simoutput[12]); |
| 71 | |
| 72 | /* The compression tables. */ |
| 73 | static const Byte table_0[512] = { |
| 74 | 102,177,186,162, 2,156,112, 75, 55, 25, 8, 12,251,193,246,188, |
| 75 | 109,213,151, 53, 42, 79,191,115,233,242,164,223,209,148,108,161, |
| 76 | 252, 37,244, 47, 64,211, 6,237,185,160,139,113, 76,138, 59, 70, |
| 77 | 67, 26, 13,157, 63,179,221, 30,214, 36,166, 69,152,124,207,116, |
| 78 | 247,194, 41, 84, 71, 1, 49, 14, 95, 35,169, 21, 96, 78,215,225, |
| 79 | 182,243, 28, 92,201,118, 4, 74,248,128, 17, 11,146,132,245, 48, |
| 80 | 149, 90,120, 39, 87,230,106,232,175, 19,126,190,202,141,137,176, |
| 81 | 250, 27,101, 40,219,227, 58, 20, 51,178, 98,216,140, 22, 32,121, |
| 82 | 61,103,203, 72, 29,110, 85,212,180,204,150,183, 15, 66,172,196, |
| 83 | 56,197,158, 0,100, 45,153, 7,144,222,163,167, 60,135,210,231, |
| 84 | 174,165, 38,249,224, 34,220,229,217,208,241, 68,206,189,125,255, |
| 85 | 239, 54,168, 89,123,122, 73,145,117,234,143, 99,129,200,192, 82, |
| 86 | 104,170,136,235, 93, 81,205,173,236, 94,105, 52, 46,228,198, 5, |
| 87 | 57,254, 97,155,142,133,199,171,187, 50, 65,181,127,107,147,226, |
| 88 | 184,218,131, 33, 77, 86, 31, 44, 88, 62,238, 18, 24, 43,154, 23, |
| 89 | 80,159,134,111, 9,114, 3, 91, 16,130, 83, 10,195,240,253,119, |
| 90 | 177,102,162,186,156, 2, 75,112, 25, 55, 12, 8,193,251,188,246, |
| 91 | 213,109, 53,151, 79, 42,115,191,242,233,223,164,148,209,161,108, |
| 92 | 37,252, 47,244,211, 64,237, 6,160,185,113,139,138, 76, 70, 59, |
| 93 | 26, 67,157, 13,179, 63, 30,221, 36,214, 69,166,124,152,116,207, |
| 94 | 194,247, 84, 41, 1, 71, 14, 49, 35, 95, 21,169, 78, 96,225,215, |
| 95 | 243,182, 92, 28,118,201, 74, 4,128,248, 11, 17,132,146, 48,245, |
| 96 | 90,149, 39,120,230, 87,232,106, 19,175,190,126,141,202,176,137, |
| 97 | 27,250, 40,101,227,219, 20, 58,178, 51,216, 98, 22,140,121, 32, |
| 98 | 103, 61, 72,203,110, 29,212, 85,204,180,183,150, 66, 15,196,172, |
| 99 | 197, 56, 0,158, 45,100, 7,153,222,144,167,163,135, 60,231,210, |
| 100 | 165,174,249, 38, 34,224,229,220,208,217, 68,241,189,206,255,125, |
| 101 | 54,239, 89,168,122,123,145, 73,234,117, 99,143,200,129, 82,192, |
| 102 | 170,104,235,136, 81, 93,173,205, 94,236, 52,105,228, 46, 5,198, |
| 103 | 254, 57,155, 97,133,142,171,199, 50,187,181, 65,107,127,226,147, |
| 104 | 218,184, 33,131, 86, 77, 44, 31, 62, 88, 18,238, 43, 24, 23,154, |
| 105 | 159, 80,111,134,114, 9, 91, 3,130, 16, 10, 83,240,195,119,253 |
| 106 | }, table_1[256] = { |
| 107 | 19, 11, 80,114, 43, 1, 69, 94, 39, 18,127,117, 97, 3, 85, 43, |
| 108 | 27,124, 70, 83, 47, 71, 63, 10, 47, 89, 79, 4, 14, 59, 11, 5, |
| 109 | 35,107,103, 68, 21, 86, 36, 91, 85,126, 32, 50,109, 94,120, 6, |
| 110 | 53, 79, 28, 45, 99, 95, 41, 34, 88, 68, 93, 55,110,125,105, 20, |
| 111 | 90, 80, 76, 96, 23, 60, 89, 64,121, 56, 14, 74,101, 8, 19, 78, |
| 112 | 76, 66,104, 46,111, 50, 32, 3, 39, 0, 58, 25, 92, 22, 18, 51, |
| 113 | 57, 65,119,116, 22,109, 7, 86, 59, 93, 62,110, 78, 99, 77, 67, |
| 114 | 12,113, 87, 98,102, 5, 88, 33, 38, 56, 23, 8, 75, 45, 13, 75, |
| 115 | 95, 63, 28, 49,123,120, 20,112, 44, 30, 15, 98,106, 2,103, 29, |
| 116 | 82,107, 42,124, 24, 30, 41, 16,108,100,117, 40, 73, 40, 7,114, |
| 117 | 82,115, 36,112, 12,102,100, 84, 92, 48, 72, 97, 9, 54, 55, 74, |
| 118 | 113,123, 17, 26, 53, 58, 4, 9, 69,122, 21,118, 42, 60, 27, 73, |
| 119 | 118,125, 34, 15, 65,115, 84, 64, 62, 81, 70, 1, 24,111,121, 83, |
| 120 | 104, 81, 49,127, 48,105, 31, 10, 6, 91, 87, 37, 16, 54,116,126, |
| 121 | 31, 38, 13, 0, 72,106, 77, 61, 26, 67, 46, 29, 96, 37, 61, 52, |
| 122 | 101, 17, 44,108, 71, 52, 66, 57, 33, 51, 25, 90, 2,119,122, 35 |
| 123 | }, table_2[128] = { |
| 124 | 52, 50, 44, 6, 21, 49, 41, 59, 39, 51, 25, 32, 51, 47, 52, 43, |
| 125 | 37, 4, 40, 34, 61, 12, 28, 4, 58, 23, 8, 15, 12, 22, 9, 18, |
| 126 | 55, 10, 33, 35, 50, 1, 43, 3, 57, 13, 62, 14, 7, 42, 44, 59, |
| 127 | 62, 57, 27, 6, 8, 31, 26, 54, 41, 22, 45, 20, 39, 3, 16, 56, |
| 128 | 48, 2, 21, 28, 36, 42, 60, 33, 34, 18, 0, 11, 24, 10, 17, 61, |
| 129 | 29, 14, 45, 26, 55, 46, 11, 17, 54, 46, 9, 24, 30, 60, 32, 0, |
| 130 | 20, 38, 2, 30, 58, 35, 1, 16, 56, 40, 23, 48, 13, 19, 19, 27, |
| 131 | 31, 53, 47, 38, 63, 15, 49, 5, 37, 53, 25, 36, 63, 29, 5, 7 |
| 132 | }, table_3[64] = { |
| 133 | 1, 5, 29, 6, 25, 1, 18, 23, 17, 19, 0, 9, 24, 25, 6, 31, |
| 134 | 28, 20, 24, 30, 4, 27, 3, 13, 15, 16, 14, 18, 4, 3, 8, 9, |
| 135 | 20, 0, 12, 26, 21, 8, 28, 2, 29, 2, 15, 7, 11, 22, 14, 10, |
| 136 | 17, 21, 12, 30, 26, 27, 16, 31, 11, 7, 13, 23, 10, 5, 22, 19 |
| 137 | }, table_4[32] = { |
| 138 | 15, 12, 10, 4, 1, 14, 11, 7, 5, 0, 14, 7, 1, 2, 13, 8, |
| 139 | 10, 3, 4, 9, 6, 0, 3, 2, 5, 6, 8, 9, 11, 13, 15, 12 |
| 140 | }, *table[5] = { table_0, table_1, table_2, table_3, table_4 }; |
| 141 | |
| 142 | /* |
| 143 | * This code derived from a leaked document from the GSM standards. |
| 144 | * Some missing pieces were filled in by reverse-engineering a working SIM. |
| 145 | * We have verified that this is the correct COMP128 algorithm. |
| 146 | * |
| 147 | * The first page of the document identifies it as |
| 148 | * _Technical Information: GSM System Security Study_. |
| 149 | * 10-1617-01, 10th June 1988. |
| 150 | * The bottom of the title page is marked |
| 151 | * Racal Research Ltd. |
| 152 | * Worton Drive, Worton Grange Industrial Estate, |
| 153 | * Reading, Berks. RG2 0SB, England. |
| 154 | * Telephone: Reading (0734) 868601 Telex: 847152 |
| 155 | * The relevant bits are in Part I, Section 20 (pages 66--67). Enjoy! |
| 156 | * |
| 157 | * Note: There are three typos in the spec (discovered by |
| 158 | * reverse-engineering). |
| 159 | * First, "z = (2 * x[n] + x[n]) mod 2^(9-j)" should clearly read |
| 160 | * "z = (2 * x[m] + x[n]) mod 2^(9-j)". |
| 161 | * Second, the "k" loop in the "Form bits from bytes" section is severely |
| 162 | * botched: the k index should run only from 0 to 3, and clearly the range |
| 163 | * on "the (8-k)th bit of byte j" is also off (should be 0..7, not 1..8, |
| 164 | * to be consistent with the subsequent section). |
| 165 | * Third, SRES is taken from the first 8 nibbles of x[], not the last 8 as |
| 166 | * claimed in the document. (And the document doesn't specify how Kc is |
| 167 | * derived, but that was also easily discovered with reverse engineering.) |
| 168 | * All of these typos have been corrected in the following code. |
| 169 | */ |
| 170 | |
| 171 | void A3A8(/* in */ Byte rand[16], /* in */ Byte key[16], |
| 172 | /* out */ Byte simoutput[12]) |
| 173 | { |
| 174 | Byte x[32], bit[128]; |
| 175 | int i, j, k, l, m, n, y, z, next_bit; |
| 176 | |
| 177 | /* ( Load RAND into last 16 bytes of input ) */ |
| 178 | for (i=16; i<32; i++) |
| 179 | x[i] = rand[i-16]; |
| 180 | |
| 181 | /* ( Loop eight times ) */ |
| 182 | for (i=1; i<9; i++) { |
| 183 | /* ( Load key into first 16 bytes of input ) */ |
| 184 | for (j=0; j<16; j++) |
| 185 | x[j] = key[j]; |
| 186 | /* ( Perform substitutions ) */ |
| 187 | for (j=0; j<5; j++) |
| 188 | for (k=0; k<(1<<j); k++) |
| 189 | for (l=0; l<(1<<(4-j)); l++) { |
| 190 | m = l + k*(1<<(5-j)); |
| 191 | n = m + (1<<(4-j)); |
| 192 | y = (x[m]+2*x[n]) % (1<<(9-j)); |
| 193 | z = (2*x[m]+x[n]) % (1<<(9-j)); |
| 194 | x[m] = table[j][y]; |
| 195 | x[n] = table[j][z]; |
| 196 | } |
| 197 | /* ( Form bits from bytes ) */ |
| 198 | for (j=0; j<32; j++) |
| 199 | for (k=0; k<4; k++) |
| 200 | bit[4*j+k] = (x[j]>>(3-k)) & 1; |
| 201 | /* ( Permutation but not on the last loop ) */ |
| 202 | if (i < 8) |
| 203 | for (j=0; j<16; j++) { |
| 204 | x[j+16] = 0; |
| 205 | for (k=0; k<8; k++) { |
| 206 | next_bit = ((8*j + k)*17) % 128; |
| 207 | x[j+16] |= bit[next_bit] << (7-k); |
| 208 | } |
| 209 | } |
| 210 | } |
| 211 | |
| 212 | /* |
| 213 | * ( At this stage the vector x[] consists of 32 nibbles. |
| 214 | * The first 8 of these are taken as the output SRES. ) |
| 215 | */ |
| 216 | |
| 217 | /* The remainder of the code is not given explicitly in the |
| 218 | * standard, but was derived by reverse-engineering. |
| 219 | */ |
| 220 | |
| 221 | for (i=0; i<4; i++) |
| 222 | simoutput[i] = (x[2*i]<<4) | x[2*i+1]; |
| 223 | for (i=0; i<6; i++) |
| 224 | simoutput[4+i] = (x[2*i+18]<<6) | (x[2*i+18+1]<<2) |
| 225 | | (x[2*i+18+2]>>2); |
| 226 | simoutput[4+6] = (x[2*6+18]<<6) | (x[2*6+18+1]<<2); |
| 227 | simoutput[4+7] = 0; |
| 228 | } |
| 229 | |
| 230 | |
| 231 | #ifdef TEST |
| 232 | int hextoint(char x) |
| 233 | { |
| 234 | x = toupper(x); |
| 235 | if (x >= 'A' && x <= 'F') |
| 236 | return x-'A'+10; |
| 237 | else if (x >= '0' && x <= '9') |
| 238 | return x-'0'; |
| 239 | fprintf(stderr, "bad input.\n"); |
| 240 | exit(1); |
| 241 | } |
| 242 | |
| 243 | int main(int argc, char **argv) |
| 244 | { |
| 245 | Byte key[16], rand[16], simoutput[12]; |
| 246 | int i; |
| 247 | |
| 248 | if (argc != 3 || strlen(argv[1]) != 34 || strlen(argv[2]) != 34 |
| 249 | || strncmp(argv[1], "0x", 2) != 0 |
| 250 | || strncmp(argv[2], "0x", 2) != 0) { |
| 251 | fprintf(stderr, "Usage: %s 0x<key> 0x<rand>\n", argv[0]); |
| 252 | exit(1); |
| 253 | } |
| 254 | |
| 255 | for (i=0; i<16; i++) |
| 256 | key[i] = (hextoint(argv[1][2*i+2])<<4) |
| 257 | | hextoint(argv[1][2*i+3]); |
| 258 | for (i=0; i<16; i++) |
| 259 | rand[i] = (hextoint(argv[2][2*i+2])<<4) |
| 260 | | hextoint(argv[2][2*i+3]); |
| 261 | A3A8(rand, key, simoutput); |
| 262 | printf("simoutput: "); |
| 263 | for (i=0; i<12; i++) |
| 264 | printf("%02X", simoutput[i]); |
| 265 | printf("\n"); |
| 266 | return 0; |
| 267 | } |
| 268 | #endif |
| 269 | |