Cryptology ePrint Archive: Report 2015/450

Adaptively Secure Computation with Partial Erasures

Carmit Hazay and Yehuda Lindell and Arpita Patra

Abstract: Adaptive security is a strong corruption model that captures ``hacking'' attacks where an external attacker breaks into parties' machines in the midst of a protocol execution. There are two types of adaptively-secure protocols: adaptive with erasures and adaptive without erasures. Achieving adaptivity without erasures is preferable, since secure erasures are not always trivial. However, it seems far harder.

We introduce a new model of adaptive security called adaptive security with partial erasures that allows erasures, but only assumes them in a minimal sense. Specifically, if all parties are corrupted then security holds as long as any single party successfully erases. In addition, security holds if any proper subset of the parties is corrupted without erasures.

We initiate a theoretical study of this new notion and demonstrate that secure computation in this setting is as efficient as static secure computation. In addition, we study the relations between semi-adaptive security~\cite{GarayWZ09}, adaptive security with partial erasures, and adaptive security without any erasures. We prove that the existence of semi-adaptive OT implies secure computation in all these settings.

Category / Keywords: cryptographic protocols / Secure Two-Party Computation, Adaptive Security, Erasure, Non-committing Encryption, Oblivious Transfer

Original Publication (with major differences): PODC 2015

Date: received 11 May 2015, last revised 13 May 2015

Contact author: arpitapatra10 at gmail com

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Version: 20150513:164123 (All versions of this report)

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