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Journal Articles Algorithmica Year : 2021

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

Abstract

We address the problem of speeding up group computations in cryptography using a single untrusted computational resource. We analyze the security of two efficient protocols for securely outsourcing (multi-)exponentiations. We show that the schemes do not achieve the claimed security guarantees and we present practical polynomial-time attacks on the delegation protocols which allow the un-trusted helper to recover part (or the whole) of the device's 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 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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Dates and versions

hal-02899803 , version 1 (15-07-2020)

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Celine Chevalier, Fabien Laguillaumie, Damien Vergnaud. Privately Outsourcing Exponentiation to a Single Server: Cryptanalysis and Optimal Constructions. Algorithmica, 2021, 83 (1), pp.72-115. ⟨10.1007/s00453-020-00750-2⟩. ⟨hal-02899803⟩
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