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Secure Computation with Preprocessing via Function Secret Sharing

  • Elette BoyleEmail author
  • Niv Gilboa
  • Yuval Ishai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11891)

Abstract

We propose a simple and powerful new approach for secure computation with input-independent preprocessing, building on the general tool of function secret sharing (FSS) and its efficient instantiations. Using this approach, we can make efficient use of correlated randomness to compute any type of gate, as long as a function class naturally corresponding to this gate admits an efficient FSS scheme. Our approach can be viewed as a generalization of the “TinyTable” protocol of Damgård et al. (Crypto 2017), where our generalized variant uses FSS to achieve exponential efficiency improvement for useful types of gates.

By instantiating this general approach with efficient PRG-based FSS schemes of Boyle et al. (Eurocrypt 2015, CCS 2016), we can implement useful nonlinear gates for equality tests, integer comparison, bit-decomposition and more with optimal online communication and with a relatively small amount of correlated randomness. We also provide a unified and simplified view of several existing protocols in the preprocessing model via the FSS framework.

Our positive results provide a useful tool for secure computation tasks that involve secure integer comparisons or conversions between arithmetic and binary representations. These arise in the contexts of approximating real-valued functions, machine-learning classification, and more. Finally, we study the necessity of the FSS machinery that we employ, in the simple context of secure string equality testing. First, we show that any “online-optimal” secure equality protocol implies an FSS scheme for point functions, which in turn implies one-way functions. Then, we show that information-theoretic secure equality protocols with relaxed optimality requirements would follow from the existence of big families of “matching vectors.” This suggests that proving strong lower bounds on the efficiency of such protocols would be difficult.

Notes

Acknowledgements

Research supported by ERC Project NTSC (742754). E. Boyle additionally supported by ISF grant 1861/16 and AFOSR Award FA9550-17-1-0069. N. Gilboa additionally supported by ISF grant 1638/15, ERC grant 876110, and a grant by the BGU Cyber Center. Y. Ishai additionally supported by ISF grant 1709/14, NSF-BSF grant 2015782, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.IDCHerzliyaIsrael
  2. 2.Ben Gurion UniversityBeershebaIsrael
  3. 3.TechnionHaifaIsrael

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