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Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW

Authors Gilad Asharov , Ran Cohen , Oren Shochat

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Author Details

Gilad Asharov
  • Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel
Ran Cohen
  • Efi Arazi School of Computer Science, Reichman University, Herzliya, Israel
Oren Shochat
  • Department of Computer Science, Bar-Ilan University, Ramat-Gan Israel

Funding

  • Asharov, Gilad: Sponsored by the Israel Science Foundation (grant No. 2439/20), by JPM Faculty Research Award, by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 891234.
  • Cohen, Ran: Research partially supported by NSF grant no. 2055568.
  • Shochat, Oren: Sponsored by the Israel Science Foundation (grant No. 2439/20).

Cite AsGet BibTex

Gilad Asharov, Ran Cohen, and Oren Shochat. Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITC.2022.15

Abstract

Adaptive security is a highly desirable property in the design of secure protocols. It tolerates adversaries that corrupt parties as the protocol proceeds, as opposed to static security where the adversary corrupts the parties at the onset of the execution. The well-accepted folklore is that static and adaptive securities are equivalent for perfectly secure protocols. Indeed, this folklore is backed up with a transformation by Canetti et al. (EUROCRYPT'01), showing that any perfectly secure protocol that is statically secure and satisfies some basic requirements is also adaptively secure. Yet, the transformation results in an adaptively secure protocol with inefficient simulation (i.e., where the simulator might run in super-polynomial time even if the adversary runs just in polynomial time). Inefficient simulation is problematic when using the protocol as a sub-routine in the computational setting. Our main question is whether an alternative efficient transformation from static to adaptive security exists. We show an inherent difficulty in achieving this goal generically. In contrast to the folklore, we present a protocol that is perfectly secure with efficient static simulation (therefore also adaptively secure with inefficient simulation), but for which efficient adaptive simulation does not exist (assuming the existence of one-way permutations). In addition, we prove that the seminal protocol of Ben-Or, Goldwasser and Wigderson (STOC'88) is secure against adaptive, semi-honest corruptions with efficient simulation. Previously, adaptive security of the protocol, as is, was only known either for a restricted class of circuits, or for all circuits but with inefficient simulation.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • secure multiparty computation
  • perfect security
  • adaptive security
  • BGW protocol

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