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Adaptive Pseudo-free Groups and Applications

Dario Catalano 1 Dario Fiore 2 Bogdan Warinschi 3
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : In this paper we explore a powerful extension of the notion of pseudo-free groups, proposed by Rivest at TCC 2004. We identify, motivate, and study pseudo-freeness in face of adaptive adversaries who may learn solutions to other non-trivial equations before having to solve a new non-trivial equation. We present a novel, carefully crafted definition of adaptive pseudo-freeness that walks a fine line between being too weak and being unsatisfiable. We show that groups that satisfy our definition yield, via a generic construction, digital and network coding signature schemes. Finally, we obtain concrete constructions of such schemes in the RSA group by showing this group to be adaptive pseudo-free. In particular, we demonstrate the generality of our framework for signatures by showing that most existing schemes are instantiations of our generic construction.
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https://hal.inria.fr/hal-01110376
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Submitted on : Wednesday, January 28, 2015 - 9:47:22 AM
Last modification on : Thursday, July 1, 2021 - 5:58:06 PM

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Dario Catalano, Dario Fiore, Bogdan Warinschi. Adaptive Pseudo-free Groups and Applications. EUROCRYPT 2011 - 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, May 2011, Talinn, Estonia. pp.207-233, ⟨10.1007/978-3-642-20465-4_13⟩. ⟨hal-01110376⟩

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