Hash Functions and Digital Signatures Questions and Answers

Answer: D

A Certification Authority authenticates the public keys of subscribers.

A CA issues digital certificates that bind a subscriber's identity to that subscriber's public key, signed with the CA's own private key. Anyone who trusts the CA can then trust that the public key really belongs to the named person, and so verify that person's digital signatures.

A CA never sees or certifies subscribers' private keys, which must stay secret. Hash functions are standard algorithms needing no certification, and DES keys belong to symmetric encryption, not to digital signatures.

Answer: B

Only (1) is a possible violation.

A birthday attack finds two messages with the same hash, which takes about \(2^{n/2}\) work for an \(n\)-bit hash. The sender S controls what is signed, so S can prepare a pair, M and a fraudulent M', with equal hashes, sign M, and later claim that the signature was on M'. The signature is valid for both.

A third party or the receiver R faces a message M already fixed and signed by S. To substitute another message they would need a second message matching that particular hash, a second-preimage attack needing about \(2^{n}\) work, not a birthday attack. So (2) and (3) are not birthday-attack violations.

Answer: B

The possible violation is I only.

A birthday attack finds two different messages with the same hash. The signer S can prepare such a pair in advance, sign the harmless one, and later claim the signature was on the other, because the signature covers only the hash. S can do this because S holds the private key and chooses what to sign.

A third party or the receiver R does not control which message S signs and cannot sign a new message without S's private key, so finding a colliding pair does not let them substitute a message S signed. That rules out options including II or III.