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Title:
Optimal security proofs for PSS and other signature schemes
Authors: Jean-Sébastien Coron
Abstract:The Probabilistic Signature Scheme (PSS) designed by Bellare and
Rogaway is a signature scheme provably secure against chosen
message attacks in the random oracle model, with a security level equivalent to RSA.
In this paper, we derive a new security proof for PSS in which
a much shorter random salt is used to achieve the same security
level, namely we show that \log_2 q_{sig} bits suffice, where
q_{sig} is the number of signature queries made by the attacker.
When PSS is used with message recovery, a better
bandwidth is obtained because longer messages can now be
recovered. Moreover, we show that this size is optimal: if less
than \log_2 q_{sig} bits of random salt are used, PSS is still
provably secure but no security proof can be tight. This result
is based on a new technique which shows that other
signature schemes such as the Full Domain Hash scheme and
Gennaro-Halevi-Rabin’s scheme have optimal security proofs.
ePrint: https://eprint.iacr.org/2001/062
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