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Chapter: Cryptography and Network Security

Digital Signature Algorithm(DSA)

1. DSA Key Generation 2. DSA Signature Creation 3. DSA Signature Verification



o   US Govt approved signature scheme


o   designed by NIST & NSA in early 90's


o   published as FIPS-186 in 1991


o   revised in 1993, 1996 & then 2000


o   uses the SHA hash algorithm


o   DSS is the standard, DSA is the algorithm


o   FIPS 186-2 (2000) includes alternative RSA & elliptic curve signature variants




o   creates a 320 bit signature


o   with 512-1024 bit security


o   smaller and faster than RSA


o   a digital signature scheme only


o   security depends on difficulty of computing discrete logarithms


o   variant of ElGamal & Schnorr schemes



1. DSA Key Generation


o   have shared global public key values (p,q,g):


o   choose q, a 160 bit


o   choose a large prime p = 2L

o     where L= 512 to 1024 bits and is a multiple of 64 and q is a prime factor of (p-1)


o   choose g = h(p-1)/q

o     where h<p-1, h(pp-11)//q (mod p) > 1


o   users choose private & compute public key:

o     choose x<q


o     compute y = gx (mod p)


2. DSA Signature Creation


o   to sign a message M the sender:

o     generates a random signature key k, k<q


o     nb. k must be random, be destroyed after use, and never be reused


o   then computes signature pair:


§  r = (gk(mod p))(mod q)


§  s = (k-1.H(M)+ x.r)(mod q)


o   sends signature (r,s) with message M


3. DSA Signature Verification


o   having received M & signature (r,s)


o   to verify a signature, recipient computes:


§  w = s-1(mod q)


§  u1= (H(M).w)(mod q) u2= (r.w)(mod q)


§  v = (gu1.yu2(mod p)) (mod q)


o   if v=r then signature is verified

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