Digital Signature Algorithm (DSA) Kenan Gençol presented in the course BIL617 Cryptology instructed by Asst.Prof.Dr. Nuray AT Department of Computer Engineering, Anadolu University 19,April,2010

Agenda Digital Signature: The Big Picture Digital Signature: The Big Picture Digital Signature Process Digital Signature Process Digital Signature Standard (DSS) Digital Signature Standard (DSS) Digital Signature Algorithm (DSA) Digital Signature Algorithm (DSA) Appendix: Discrete Logarithm Appendix: Discrete Logarithm

Digital Signature: The Big Picture

Digital Signature Process: Evolution Signing and verifying algorithms Signing and verifying algorithms Need for keys Need for keys Signing the Digest Signing the Digest Need for CAs (trusted third parties) Need for CAs (trusted third parties)

Need for CAs (trusted third parties)

Services provided Digital Signatures Message Authentication Message Authentication Message Integrity Message Integrity Nonrepudation (CAs) Nonrepudation (CAs) Does not provide privacy (confidentiality) Does not provide privacy (confidentiality)

Digital Signature Standard (DSS) US Govt approved signature scheme US Govt approved signature scheme designed by NIST & NSA in early 90's designed by NIST & NSA in early 90's published as FIPS-186 in 1991 published as FIPS-186 in 1991 revised in 1993, 1996 & then 2000 revised in 1993, 1996 & then 2000 uses the SHA hash algorithm (original SHA-1) uses the SHA hash algorithm (original SHA-1) DSS is the standard, DSA is the algorithm DSS is the standard, DSA is the algorithm FIPS (2000) includes alternative RSA & elliptic curve signature variants FIPS (2000) includes alternative RSA & elliptic curve signature variants Latest version is FIPS (June 2009) Latest version is FIPS (June 2009)

Digital Signature Algorithm (DSA) creates a 320 bit signature creates a 320 bit signature with bit key security with bit key security smaller and faster than RSA smaller and faster than RSA a digital signature scheme only a digital signature scheme only security depends on difficulty of computing discrete logarithms security depends on difficulty of computing discrete logarithms variant of ElGamal [ELGA85] & Schnorr [SCHN91] schemes variant of ElGamal [ELGA85] & Schnorr [SCHN91] schemes

Digital Signature Algorithm (DSA)

Glossary

Digital Signature Algorithm (DSA): Key Generation have shared global public key values (p,q,g): have shared global public key values (p,q,g): choose q, a 160 bit choose q, a 160 bit choose a large prime p = 2 L choose a large prime p = 2 L where L= 512 to 1024 bits and is a multiple of 64 where L= 512 to 1024 bits and is a multiple of 64 and q is a prime factor of (p-1) and q is a prime factor of (p-1) choose g = h (p-1)/q choose g = h (p-1)/q where h 1 where h 1 users choose private & compute public key: users choose private & compute public key: choose x<q choose x<q compute y = g x (mod p) compute y = g x (mod p)

Digital Signature Algorithm (DSA): Signing to sign a message M the sender: to sign a message M the sender: generates a random signature key k, k<q generates a random signature key k, k<q nb. k must be random, be destroyed after use, and never be reused nb. k must be random, be destroyed after use, and never be reused then computes signature pair: then computes signature pair: r = (g k (mod p))(mod q) s = (k -1.H(M)+ x.r)(mod q) sends signature (r,s) with message M sends signature (r,s) with message M

Digital Signature Algorithm (DSA): Verification having received M & signature (r,s) having received M & signature (r,s) to verify a signature, recipient computes: to verify a signature, recipient computes: w = s -1 (mod q) u1= (H(M).w)(mod q) u2= (r.w)(mod q) v = (g u1.y u2 (mod p)) (mod q) if v=r then signature is verified if v=r then signature is verified

Correctness of the algorithm

Digital Signature Algorithm (DSA): An Example Alice chooses q = 101 and p = Alice selects e 0 = 3 and calculates e 1 = e 0 (p−1)/q mod p = Alice chooses d = 61 as the private key and calculates e 2 = e 1 d mod p = Now Alice can send a message to Bob. Assume that h(M) = 5000 and Alice chooses r = 61: Alice sends M, S 1, and S 2 to Bob. Bob uses the public keys to calculate V.

Digital Signature Algorithm (DSA) Please refer to the following document for further information: Please refer to the following document for further information: /fips_186-3.pdf /fips_186-3.pdf

A last word..

Appendix: Discrete Logarithm If g and h are elements of a finite cyclic group G then a solution x of the equation g x = h is called a discrete logarithm to the base g of h in the group G. If g and h are elements of a finite cyclic group G then a solution x of the equation g x = h is called a discrete logarithm to the base g of h in the group G.finitecyclic groupfinitecyclic group

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