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Unconditionally Secure Computation Against Low-Complexity Leakage

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Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

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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. 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. 2.

    The simulator circuit \(\mathsf {Simr}\) 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 is 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. University of California, Berkeley, USA

    Akshayaram Srinivasan

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  1. Andrej Bogdanov
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  2. Yuval Ishai
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Correspondence to Andrej Bogdanov or Yuval Ishai .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Bogdanov, A., Ishai, Y., Srinivasan, A. (2019). Unconditionally Secure Computation Against Low-Complexity Leakage. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11693. Springer, Cham. https://doi.org/10.1007/978-3-030-26951-7_14

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