DSA
Electronic digital signature for text files. Needed for Labs on Information Theory, 4 labs. Implemented on the basis of the SHA-1 hash function, according to the DSS standard.
Theory
The Digital Signature Algorithm (DSA) is a digital information technology that has been developed for the digital signatures and the discrete logarithm problem.
Signing
- Generate a random per-message value k where 1<k<q;
- Calculate r = (g**k mod p) mod q;
- Calculate s = k**-1(Hash(m)+x*r) mod q;
- In the unlikely case that r=0 or s=0, start again with a different random k;
- The signature is (r,s).
Verifying
- Reject the signature if 0<r<q or 0<s<q is not satisfied;
- Calculate w=s**-1 mod q;
- Calculate u_1 = Hash(m) * w mod q;
- Calculate u_2 = r * w mod q;
- Calculate v = (g** u_1 * y** u_2 mod p) mod q;
- The signature is valid if and only if v = r.
Literature