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Privately Outsourcing Exponentiation to a Single Server: Cryptanalysis and Optimal Constructions

Céline Chevalier 1 Fabien Laguillaumie 2, 3 Damien Vergnaud 4, 5 
3 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We address the problem of speeding up group computations in cryptography using a single untrusted computational resource. We analyze the security of an efficient protocol for securely outsourcing multi-exponentiations proposed at ESORICS 2014. We show that this scheme does not achieve the claimed security guarantees and we present practical polynomial-time attacks on the delegation protocol which allow the untrusted helper to recover part (or the whole) of the device secret inputs. We then provide simple constructions for outsourcing group exponentiations in different settings (e.g. public/secret, fixed/variable bases and public/secret exponents). Finally, we prove that our attacks on the ESORICS 2014 protocol are unavoidable if one wants to use a single untrusted computational resource and to limit the computational cost of the limited device to a constant number of (generic) group operations. In particular, we show that our constructions are actually optimal in terms of operations in the underlying group.
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Submitted on : Monday, October 3, 2016 - 3:32:38 PM
Last modification on : Friday, July 1, 2022 - 3:51:36 AM

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Céline Chevalier, Fabien Laguillaumie, Damien Vergnaud. Privately Outsourcing Exponentiation to a Single Server: Cryptanalysis and Optimal Constructions. Computer Security - ESORICS 2016, Sep 2016, Heraklion, Greece. pp.261-278, ⟨10.1007/978-3-319-45744-4_13⟩. ⟨hal-01375817⟩



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