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Unconditionally Secure Computation Against Low-Complexity Leakage

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A Correction to this article was published on 24 January 2022

A Correction to this article was published on 26 October 2021

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Abstract

We consider the problem of constructing leakage-resilient circuit compilers that are secure against global leakage functions with bounded output length. By global, we mean that the leakage can depend on all circuit wires and output a low-complexity function (represented as a multi-output Boolean circuit) applied on these wires. In this work, we design compilers both in the stateless (a.k.a. single-shot leakage) setting and the stateful (a.k.a. continuous leakage) setting that are unconditionally secure against \(\mathsf {AC}^0\) leakage and similar low-complexity classes. In the stateless case, we show that the original private circuits construction of Ishai, Sahai, and Wagner (Crypto 2003) is actually secure against \(\mathsf {AC}^0\) leakage. In the stateful case, we modify the construction of Rothblum (Crypto 2012), obtaining a simple construction with unconditional security. Prior works that designed leakage-resilient circuit compilers against \(\mathsf {AC}^0\) leakage had to rely either on secure hardware components (Faust et al., Eurocrypt 2010, Miles-Viola, STOC 2013) or on (unproven) complexity-theoretic assumptions (Rothblum, Crypto 2012).

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Notes

  1. Let \(D'_0,D'_1\) be uniform distributions over 2n-bit strings such that for every \((\mathbf {x},\mathbf {y}) \in D'_b\), \(<\mathbf {x},\mathbf {y}> = b\). IPPP states that it is hard for \(\mathsf {AC}^0\) circuits to distinguish between \(D'_0\) and \(D'_1\) even when given \(f(\mathbf {x})\) and \(g(\mathbf {y})\) for arbitrary polynomial-time computable functions f, g.

  2. The simulator circuit \(\textsf {Simr}\) is the composition of \(\mathsf {RandZero}\) and a preprocessing circuit. The irrelevant wires from preprocessing are discounted when comparing the two distributions.

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Acknowledgements

The first author’s research is supported by Hong Kong RGC GRF CUHK14208215 and CUHK14207618. The second author’s research is supported by ERC Project NTSC (742754), 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. The third author’s research was done in part while visiting Technion, Israel and while at UC Berkeley, USA and supported in part from DARPA/ARL SAFEWARE Award W911NF15C0210, AFOSR Award FA9550-15-1-0274, AFOSR YIP Award, a Hellman Award and research grants by the Okawa Foundation, Visa Inc., and Center for LongTerm Cybersecurity (CLTC, UC Berkeley).

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Authors and Affiliations

  1. Chinese University of Hong Kong, Shatin, Hong Kong

    Andrej Bogdanov

  2. Technion, Haifa, Israel

    Yuval Ishai

  3. Tata Institute of Fundamental Research, Mumbai, India

    Akshayaram Srinivasan

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  1. Andrej Bogdanov
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Correspondence to Akshayaram Srinivasan.

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Bogdanov, A., Ishai, Y. & Srinivasan, A. Unconditionally Secure Computation Against Low-Complexity Leakage. J Cryptol 34, 38 (2021). https://doi.org/10.1007/s00145-021-09402-2

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