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New Protocols for Secure Equality Test and Comparison

  • Geoffroy Couteau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10892)

Abstract

Protocols for securely comparing private values are among the most fundamental building blocks of multiparty computation. introduced by Yao under the name millionaire’s problem, they have found numerous applications in a variety of privacy-preserving protocols; however, due to their inherent non-arithmetic structure, existing construction often remain an important bottleneck in large-scale secure protocols.

In this work, we introduce new protocols for securely computing the greater-than and the equality predicate between two parties. Our protocols rely solely on the existence of oblivious transfer, and are \(\textsf {UC}\)-secure against passive adversaries. Furthermore, our protocols are well suited for use in large-scale secure computation protocols, where secure comparisons (\(\mathsf {SC}\)) and equality tests (\(\mathsf {ET}\)) are commonly used as basic routines: they perform particularly well in an amortized setting, and can be preprocessed efficiently (they enjoy an extremely efficient, information-theoretic online phase). We perform a detailed comparison of our protocols to the state of the art, showing that they improve over the most practical existing solutions regarding both communication and computation, while matching the asymptotic efficiency of the best theoretical constructions.

Keywords

Two-party computation Equality test Secure comparison Oblivious transfer 

Notes

Acknowledgements

We thank David Pointcheval for insightful discussions and comments, and Thomas Schneider for pointing out inaccuracies in our cost estimations for the garbled circuit-based constructions of equality tests and secure comparison. The author was supported by ERC grant 339563 (project CryptoCloud) and ERC grant 724307 (project PREP-CRYPTO).

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Authors and Affiliations

  1. 1.Karsruhe Institute of TechnologyKarlsruheGermany

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