Change No. 1

                                                  1996 December 30

                                                  186


FIPS PUB 186, Digital Signature Standard
(DSS). 




                Department of
Commerce
                    National Institute of
Standards and Technology
                    Computer Systems
Laboratory
                    Gaithersburg, MD 
20899



The following change is made to Appendix 3.2
Algorithm for Precomputing one or more k and r Values:

Change
"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:"

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

Copies of FIPS 180-1 and 186 are available from:

                 National Technical
Information Service (NTIS)
                 ATTN:  Sales Office, Sills
Building
                 5285 Port Royal Road
                 Springfield, VA  22161
  
                 Phone - (703) 487-4650
  
                 Office Hours - 7:45 a.m. to
5:00 p.m.

Attachment
  --------


  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 160­bit 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
160­bit 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
160­bit 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 180­1, 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

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