Tight Proofs for Signature Schemes without Random Oracles

  • Sven Schäge
Conference paper

DOI: 10.1007/978-3-642-20465-4_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6632)
Cite this paper as:
Schäge S. (2011) Tight Proofs for Signature Schemes without Random Oracles. In: Paterson K.G. (eds) Advances in Cryptology – EUROCRYPT 2011. EUROCRYPT 2011. Lecture Notes in Computer Science, vol 6632. Springer, Berlin, Heidelberg


We present the first tight security proofs for two general classes of Strong RSA based signature schemes. Among the affected signature schemes are the Cramer-Shoup, Camenisch-Lysyanskaya, Zhu, and Fischlin signature scheme. We also present two bilinear variants of our signature classes that produce short signatures. Similar to before, we show that these variants have tight security proofs under the the Strong Diffie-Hellman (SDH) assumption. We so obtain very efficient SDH-based variants of the Cramer-Shoup, Fischlin, and Zhu signature scheme and the first tight security proof of the recent Camenisch-Lysyanskaya scheme that was proposed and proven secure under the SDH assumption. Central to our results is a new proof technique that allows the simulator to avoid guessing which of the attacker’s signature queries are re-used in the forgery. In contrast to previous proofs, our security reduction does not lose a factor of q here.


signature class tight security SRSA SDH standard model 
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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Sven Schäge
    • 1
  1. 1.Horst Görtz Institute for IT-SecurityRuhr-University of BochumGermany

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