Cryptology ePrint Archive: Report 2016/191

Optimal Security Proofs for Signatures from Identification Schemes

Eike Kiltz and Daniel Masny and Jiaxin Pan

Abstract: We perform a concrete security treatment of digital signature schemes obtained from canonical identification schemes via the Fiat-Shamir transform. If the identification scheme is rerandomizable and satisfies the weakest possible security notion (key-recoverability), then the implied signature scheme is unforgeability against chosen-message attacks in the multi-user setting in the random oracle model. The reduction loses a factor of roughly Qh, the number of hash queries. Previous security reductions incorporated an additional multiplicative loss of N, the number of users in the system. As an important application of our framework, we obtain a concrete security treatment for Schnorr signatures.

Our analysis is done in small steps via intermediate security notions, and all our implications have relatively simple proofs. Furthermore, for each step we show the optimality of the given reduction via a meta-reduction.

Category / Keywords: public-key cryptography / Signatures, Identification, Schnorr, tightness

Date: received 23 Feb 2016, last revised 29 Nov 2017

Contact author: eike kiltz at rub de

Available format(s): PDF | BibTeX Citation

Note: This work subsumes and extends ePrint report 2015/1122.

Version: 20171129:205054 (All versions of this report)

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