U.S. Department of Commerce
National Institute of Standards and Technology

FIPS Publication Change Notice

FIPS PUB 186, Digital Signature Standard (DSS)
Change No.: 1
Date of Change: 1996 December 30

Change Items:

1. The following change is made to Appendix 3.2 Algorithm for Precomputing one or more k and r Values:
   • Change from
     "This algorithm can be used to precompute k, k-1, and r for m messages at a time.
     Algorithm:"

   • To
     "This algorithm can be used to precompute k, k-1, and r for m messages at a time. Note that implementation of the DSA with precomputation may be covered by U.S. and foreign patents.
     
     Algorithm:"

2. The following change replaces Appendix 5, Example of the DSA. This example has been changed for use with FIPS 180-1, Secure Hash Standard (SHS):

   ---

   APPENDIX 5. EXAMPLE OF THE DSA

   (Revised for use with FIPS 180-1)

   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-1 to construct G (as in appendix 3, section 3.3) and a 160-bit XKEY:

   XKEY =

   	bd029bbe 7f51960b cf9edb2b 61f06f0f eb5a38b6

   t =

   	67452301 EFCDAB89 98BADCFE 10325476 C3D2E1F0

   x = G(t,XKEY) mod q

   k was generated by the algorithm described in appendix 3, section 3.2, using the SHA-1 to construct G (as in appendix 3, section 3.3) and a 160-bit KKEY:

   KKEY =

   	687a66d9 0648f993 867e121f 4ddf9ddb 01205584

   t =

   	EFCDAB89 98BADCFE 10325476 C3D2E1F0 67452301

   k = G(t,KKEY) 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

   k^-1 =

   	0d516729 8202e49b 4116ac10 4fc3f415 ae52f917

   M = ASCII form of "abc" (See FIPS PUB 180-1, Appendix A)

   (SHA-1)(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

   g^u1 mod p =

   	51b1bf86 7888e5f3 af6fb476 9dd016bc fe667a65 aafc2753
   	9063bd3d 2b138b4c e02cc0c0 2ec62bb6 7306c63e 4db95bbf
   	6f96662a 1987a21b e4ec1071 010b6069

   y^u2 mod p =

   	8b510071 2957e950 50d6b8fd 376a668e 4b0d633c 1e46e665
   	5c611a72 e2b28483 be52c74d 4b30de61 a668966e dc307a67 
   	c19441f4 22bf3c34 08aeba1f 0a4dbec7

   v =

   	8bac1ab6 6410435c b7181f95 b16ab97c 92b341c0