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I’ve a signature scheme for 1024‒bit RSA with a 65537 exponent. The signed message is constructed as follows:

760‒Bits fully_user_controlled_message_content+8 Bits incremental nonce+sha256(fully_user_controlled_message_content+Nonce)

Verification then consists of:

  • the nonce in the remainder must be ++prev_nonce
  • sha256(remainder from Signature>>768bits) must be equal to sha256(fully_user_controlled_message_content+Nonce)

Breaking 1024‒bit RSA is impossible for small organizations. However, for large messages only the least 264 bits of the signed message are randomized.

Does this enable Oracle attacks? Does the random padding of the least significant bits introduce vulnerabilities that allow forging a signature?

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  • $\begingroup$ So the message of a fixed size is small enough to be signed without being hashed. Each signing request to the Oracle costs about $20. $\endgroup$ Mar 31 at 18:16

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