| Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 1 | The origional FIPE 180 used SHA-0 (FIPS 180) for its appendix 5 |
| 2 | examples. This is an updated version that uses SHA-1 (FIPS 180-1) |
| 3 | supplied to me by Wei Dai |
| 4 | -- |
| 5 | APPENDIX 5. EXAMPLE OF THE DSA |
| 6 | |
| 7 | |
| 8 | This appendix is for informational purposes only and is not required to meet |
| 9 | the standard. |
| 10 | |
| 11 | Let L = 512 (size of p). The values in this example are expressed in |
| 12 | hexadecimal notation. The p and q given here were generated by the prime |
| 13 | generation standard described in appendix 2 using the 160-bit SEED: |
| 14 | |
| 15 | d5014e4b 60ef2ba8 b6211b40 62ba3224 e0427dd3 |
| 16 | |
| 17 | With this SEED, the algorithm found p and q when the counter was at 105. |
| 18 | |
| 19 | x was generated by the algorithm described in appendix 3, section 3.1, using |
| 20 | the SHA to construct G (as in appendix 3, section 3.3) and a 160-bit XSEED: |
| 21 | |
| 22 | XSEED = |
| 23 | |
| 24 | bd029bbe 7f51960b cf9edb2b 61f06f0f eb5a38b6 |
| 25 | |
| 26 | t = |
| 27 | 67452301 EFCDAB89 98BADCFE 10325476 C3D2E1F0 |
| 28 | |
| 29 | x = G(t,XSEED) mod q |
| 30 | |
| 31 | k was generated by the algorithm described in appendix 3, section 3.2, using |
| 32 | the SHA to construct G (as in appendix 3, section 3.3) and a 160-bit KSEED: |
| 33 | |
| 34 | KSEED = |
| 35 | |
| 36 | 687a66d9 0648f993 867e121f 4ddf9ddb 01205584 |
| 37 | |
| 38 | t = |
| 39 | EFCDAB89 98BADCFE 10325476 C3D2E1F0 67452301 |
| 40 | |
| 41 | k = G(t,KSEED) mod q |
| 42 | |
| 43 | Finally: |
| 44 | |
| 45 | h = 2 |
| 46 | |
| 47 | p = |
| 48 | 8df2a494 492276aa 3d25759b b06869cb eac0d83a fb8d0cf7 |
| 49 | cbb8324f 0d7882e5 d0762fc5 b7210eaf c2e9adac 32ab7aac |
| 50 | 49693dfb f83724c2 ec0736ee 31c80291 |
| 51 | |
| 52 | |
| 53 | q = |
| 54 | c773218c 737ec8ee 993b4f2d ed30f48e dace915f |
| 55 | |
| 56 | |
| 57 | g = |
| 58 | 626d0278 39ea0a13 413163a5 5b4cb500 299d5522 956cefcb |
| 59 | 3bff10f3 99ce2c2e 71cb9de5 fa24babf 58e5b795 21925c9c |
| 60 | c42e9f6f 464b088c c572af53 e6d78802 |
| 61 | |
| 62 | |
| 63 | x = |
| 64 | 2070b322 3dba372f de1c0ffc 7b2e3b49 8b260614 |
| 65 | |
| 66 | |
| 67 | k = |
| 68 | 358dad57 1462710f 50e254cf 1a376b2b deaadfbf |
| 69 | |
| 70 | |
| 71 | kinv = |
| 72 | |
| 73 | 0d516729 8202e49b 4116ac10 4fc3f415 ae52f917 |
| 74 | |
| 75 | M = ASCII form of "abc" (See FIPS PUB 180-1, Appendix A) |
| 76 | |
| 77 | SHA(M) = |
| 78 | |
| 79 | a9993e36 4706816a ba3e2571 7850c26c 9cd0d89d |
| 80 | |
| 81 | |
| 82 | y = |
| 83 | |
| 84 | 19131871 d75b1612 a819f29d 78d1b0d7 346f7aa7 7bb62a85 |
| 85 | 9bfd6c56 75da9d21 2d3a36ef 1672ef66 0b8c7c25 5cc0ec74 |
| 86 | 858fba33 f44c0669 9630a76b 030ee333 |
| 87 | |
| 88 | |
| 89 | r = |
| 90 | 8bac1ab6 6410435c b7181f95 b16ab97c 92b341c0 |
| 91 | |
| 92 | s = |
| 93 | 41e2345f 1f56df24 58f426d1 55b4ba2d b6dcd8c8 |
| 94 | |
| 95 | |
| 96 | w = |
| 97 | 9df4ece5 826be95f ed406d41 b43edc0b 1c18841b |
| 98 | |
| 99 | |
| 100 | u1 = |
| 101 | bf655bd0 46f0b35e c791b004 804afcbb 8ef7d69d |
| 102 | |
| 103 | |
| 104 | u2 = |
| 105 | 821a9263 12e97ade abcc8d08 2b527897 8a2df4b0 |
| 106 | |
| 107 | |
| 108 | gu1 mod p = |
| 109 | |
| 110 | 51b1bf86 7888e5f3 af6fb476 9dd016bc fe667a65 aafc2753 |
| 111 | 9063bd3d 2b138b4c e02cc0c0 2ec62bb6 7306c63e 4db95bbf |
| 112 | 6f96662a 1987a21b e4ec1071 010b6069 |
| 113 | |
| 114 | |
| 115 | yu2 mod p = |
| 116 | |
| 117 | 8b510071 2957e950 50d6b8fd 376a668e 4b0d633c 1e46e665 |
| 118 | 5c611a72 e2b28483 be52c74d 4b30de61 a668966e dc307a67 |
| 119 | c19441f4 22bf3c34 08aeba1f 0a4dbec7 |
| 120 | |
| 121 | v = |
| 122 | 8bac1ab6 6410435c b7181f95 b16ab97c 92b341c0 |