Discussion
A sender 'S' sends a message 'M' to receiver 'R', which is digitally signed by 'S' with its private key. In this scenario, one or more of the following security violations can take place.
(1) 'S' can launch a birthday attack to replace M with a fraudulent message.
(2) A third party attacker can launch a birthday attack to replace 'M' with a fraudulent message.
(3) 'R' can launch a birthday attack to replace 'M' with a fraudulent message.
Which of the following are possible security violations ?
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.
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