Cryptology ePrint Archive: Report 2001/062

Optimal security proofs for PSS and other signature schemes

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.

Category / Keywords: public-key cryptography / Probabilistic Signature Scheme, provable security, random oracle model.

Date: received 6 Aug 2001

Contact author: coron at clipper ens fr

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Version: 20010813:174454 (All versions of this report)

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