| The origional FIPE 180 used SHA-0 (FIPS 180) for its appendix 5 |
| examples. This is an updated version that uses SHA-1 (FIPS 180-1) |
| supplied to me by Wei Dai |
| -- |
| APPENDIX 5. EXAMPLE OF THE DSA |
| |
| |
| This appendix is for informational purposes only and is not required to meet |
| the standard. |
| |
| Let L = 512 (size of p). The values in this example are expressed in |
| hexadecimal notation. The p and q given here were generated by the prime |
| generation standard described in appendix 2 using the 160-bit SEED: |
| |
| d5014e4b 60ef2ba8 b6211b40 62ba3224 e0427dd3 |
| |
| With this SEED, the algorithm found p and q when the counter was at 105. |
| |
| x was generated by the algorithm described in appendix 3, section 3.1, using |
| the SHA to construct G (as in appendix 3, section 3.3) and a 160-bit XSEED: |
| |
| XSEED = |
| |
| bd029bbe 7f51960b cf9edb2b 61f06f0f eb5a38b6 |
| |
| t = |
| 67452301 EFCDAB89 98BADCFE 10325476 C3D2E1F0 |
| |
| x = G(t,XSEED) mod q |
| |
| k was generated by the algorithm described in appendix 3, section 3.2, using |
| the SHA to construct G (as in appendix 3, section 3.3) and a 160-bit KSEED: |
| |
| KSEED = |
| |
| 687a66d9 0648f993 867e121f 4ddf9ddb 01205584 |
| |
| t = |
| EFCDAB89 98BADCFE 10325476 C3D2E1F0 67452301 |
| |
| k = G(t,KSEED) mod q |
| |
| Finally: |
| |
| h = 2 |
| |
| p = |
| 8df2a494 492276aa 3d25759b b06869cb eac0d83a fb8d0cf7 |
| cbb8324f 0d7882e5 d0762fc5 b7210eaf c2e9adac 32ab7aac |
| 49693dfb f83724c2 ec0736ee 31c80291 |
| |
| |
| q = |
| c773218c 737ec8ee 993b4f2d ed30f48e dace915f |
| |
| |
| g = |
| 626d0278 39ea0a13 413163a5 5b4cb500 299d5522 956cefcb |
| 3bff10f3 99ce2c2e 71cb9de5 fa24babf 58e5b795 21925c9c |
| c42e9f6f 464b088c c572af53 e6d78802 |
| |
| |
| x = |
| 2070b322 3dba372f de1c0ffc 7b2e3b49 8b260614 |
| |
| |
| k = |
| 358dad57 1462710f 50e254cf 1a376b2b deaadfbf |
| |
| |
| kinv = |
| |
| 0d516729 8202e49b 4116ac10 4fc3f415 ae52f917 |
| |
| M = ASCII form of "abc" (See FIPS PUB 180-1, Appendix A) |
| |
| SHA(M) = |
| |
| a9993e36 4706816a ba3e2571 7850c26c 9cd0d89d |
| |
| |
| y = |
| |
| 19131871 d75b1612 a819f29d 78d1b0d7 346f7aa7 7bb62a85 |
| 9bfd6c56 75da9d21 2d3a36ef 1672ef66 0b8c7c25 5cc0ec74 |
| 858fba33 f44c0669 9630a76b 030ee333 |
| |
| |
| r = |
| 8bac1ab6 6410435c b7181f95 b16ab97c 92b341c0 |
| |
| s = |
| 41e2345f 1f56df24 58f426d1 55b4ba2d b6dcd8c8 |
| |
| |
| w = |
| 9df4ece5 826be95f ed406d41 b43edc0b 1c18841b |
| |
| |
| u1 = |
| bf655bd0 46f0b35e c791b004 804afcbb 8ef7d69d |
| |
| |
| u2 = |
| 821a9263 12e97ade abcc8d08 2b527897 8a2df4b0 |
| |
| |
| gu1 mod p = |
| |
| 51b1bf86 7888e5f3 af6fb476 9dd016bc fe667a65 aafc2753 |
| 9063bd3d 2b138b4c e02cc0c0 2ec62bb6 7306c63e 4db95bbf |
| 6f96662a 1987a21b e4ec1071 010b6069 |
| |
| |
| yu2 mod p = |
| |
| 8b510071 2957e950 50d6b8fd 376a668e 4b0d633c 1e46e665 |
| 5c611a72 e2b28483 be52c74d 4b30de61 a668966e dc307a67 |
| c19441f4 22bf3c34 08aeba1f 0a4dbec7 |
| |
| v = |
| 8bac1ab6 6410435c b7181f95 b16ab97c 92b341c0 |