Discuss concept of Digital Signature along with DSA?

It looked towards message authentication but does not address issues of lack of trust. Digital signatures provide the ability to:

  1. verify author, date & time of signature
  2. authenticate message contents
  3. be verified by third parties to resolve disputes

hence include authentication function with additional capabilities. Figures describe the model of digital signature and digital signature with hash function in both the fig. respectively

Fig. Digital Signature Model

Fig. Digital Signature Model with Hash Function

Possible Attacks and Forgeries:

  1. attacks
    • key-only attack
    • known message attack
    • generic chosen message attack
    • directed chosen message attack
    • adaptive chosen message attack
  2. break success levels
    • total break
    • selective forgery
    • existential forgery

Digital Signature Requirements:
It must depend on the message signed. It must use information unique to sender to prevent both forgery and denial. It must be relatively easy to produce. It must be relatively easy to recognize & verify. It should be computationally infeasible to forge with new message for existing digital signature and with fraudulent digital signature for given message. It should be be practical save digital signature in storage.

Digital Signature Standard (DSS):
US Govt approved signature scheme designed by NIST & NSA in early 90’s and published as FIPS-186 in 1991. It is revised in 1993, 1996 & then 2000 uses the SHA hash algorithm. DSS is the standard, DSA is the algorithm. FIPS 186-2 (2000) includes alternative RSA & elliptic curve signature variants. DSA is digital signature only unlike RSA. It is a public-key technique.

Digital Signature Algorithm (DSA): It creates a 320 bit signature with 512-1024 bit security. It is smaller and faster than RSA a digital signature scheme only. Security depends on difficulty of computing discrete logarithms.

DSA Key Generation:

  1. have shared global public key values (p,q,g):
    • choose 160-bit prime number q
    • choose a large prime p with 2L-1 < p < 2L
      • where L= 512 to 1024 bits and is a multiple of 64
      • such that q is a 160 bit prime divisor of (p-1)
    • choose g = h(p-1)/q
      • where 1<h<p-1 and h(p-1)/q mod p > 1
  2. users choose private & compute public key:
    • choose random private key: x<q
    • compute public key: y = gx mod p

DSA Signature Creation:

  1. To sign a message M the sender:
    • generates a random signature key k, k<q
    • nb. k must be random, be destroyed after use, and never be reused
  2. then computes signature pair:
    r = (gk mod p)mod q
    s = [k-1(H(M)+ xr)] mod q
  3. sends signature (r,s) with message M

DSA Signature Verification:
It is having received M & signature (r,s) to verify a signature, recipient computes:
w = s-1 mod q
u1= [H(M)w ]mod q
u2= (rw)mod q
v = [(gu1 yu2)mod p ]mod q
if v=r then signature is verified

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