Digital signature cannot provide __ for the message

• (a) Integrity
• (b) Confidentiality
• (c) Non-repudiation
• (d) Authentication

Digital signature uses __ for generating valid signature

• (a) Private key ($K_{priv}$)
• (b) Public key ($K_{pub}$)
• (c) Secret key ($K_{secret}$)
• (d) None of the above

Verification Algorithm uses __ for validating digital signature

• (a) Private key ($K_{priv}$)
• (b) Public key ($K_{pub}$)
• (c) Secret key ($K_{secret}$)
• (d) None of the above

Is digital signature scheme possible without public key cryptography?

• (a) Yes
• (b) No
• (c) May exist
• (d) None of the above

Explain the importance of Hashing (using experiment) and explain why Hashing is needed

Consider the digital signature process: $$\text{Signature} = \text{Sign}(H(M), K_{priv})$$ $$\text{Verification} = \text{Verify}(S, H(M), K_{pub})$$

Where:

• $M$ = Original message
• $H(M)$ = Hash of the message
• $K_{priv}$ = Private key
• $K_{pub}$ = Public key
• $S$ = Digital signature

Suggest a scheme that does not use any hashing scheme

Propose an alternative digital signature scheme and discuss:

• Security implications
• Performance considerations
• Practical limitations

Mathematical representation: $\text{Signature} = \text{Sign}(M, K_{priv})$

Explain why digital signature schemes work

Discuss the mathematical foundations including:

• Asymmetric Key Properties: How $K_{pub}$ and $K_{priv}$ are mathematically related
• One-way Functions: The computational difficulty of deriving $K_{priv}$ from $K_{pub}$
• Hash Function Properties:
  • Collision resistance: $H(x) = H(y) \Rightarrow x = y$
  • Preimage resistance: Given $h$, finding $x$ such that $H(x) = h$ is computationally infeasible
• Digital Signature Algorithm (DSA) security proof outline