Improving Security of strongqstrong-SDH Based Digital Signatures.pdfVIP

Improving Security of strongqstrong-SDH Based Digital Signatures.pdf

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Fuchun Guo , Yi Mu, Willy Susilo In Eurocrypt 2009, Hohenberger and Waters pointed out that a complex- ity assumption, which restricts the adversary to a single correct response, seems inherently more reliable than their flexible counterparts. The q-SDH assumption is less reliable than standard assumptions because its solution allows exponential answers. On the other hand, the q-SDH assumption ex- hibits the nice feature of tight reducion in security proof. In this paper, we propose a variant of the q-SDH assumption, so that its correct answers are polynomial and no longer exponentially many. The new assumption is much more reliable and weaker than the original q-SDH assumption. We propose a new digital signature scheme that can tightly reduce the security to the proposed assumption in the standard model. We show that our signature scheme shares most properties with the q-SDH based signature schemes. We also propose a new approach to construct fully secure signatures from weakly secure signature against known-message attacks. Although our se- curity transformation is conditional and not completely generic, it offers another efficient approach to construct fully secure signatures. Keywords: Digital Signatures, q-SDH Assumption, Security Proof Digital signatures are a central primitive in modern cryptography. The security proof of a signature scheme is usually based on a complexity as- sumption. The q-Strong Diffie-Hellman (q-SDH) assumption [4] has become a common assumption used for a catalogue of signatures. Digital signatures [4, 5, 12] based on the q-SDH assumption have many good properties. For example, the

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