openssl/crypto/dsa/fips186a.txt

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