A clarification in Signature schemes for Strong Unforgeability.

Question

Signature scheme is strongly unforgeable. "making the message m being signed depend on the randomness r — we break the proof of security for the underlying signature."

From Paper: Strongly Unforgeable Signatures Based on Computational Diffie-Hellman - Dan Boneh, Emily Shen, and Brent Waters.

Can some one point out how a scheme can be broken when the message being signed depends on the randomness?

Thanks. Please let me know if I am not clear. The paper has it all.

Answer 1

Their comment was not meant to apply to all signature schemes, just the specific construction they are talking about in that paragraph. (Also, it was not meant as a formal statement; it was just mentioned as part of the intuition for their construction.)