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 123
