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Private Circuits: A Modular Approach

  • Prabhanjan Ananth
  • Yuval Ishai
  • Amit Sahai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10993)

Abstract

We consider the problem of protecting general computations against constant-rate random leakage. That is, the computation is performed by a randomized boolean circuit that maps a randomly encoded input to a randomly encoded output, such that even if the value of every wire is independently leaked with some constant probability \(p > 0\), the leakage reveals essentially nothing about the input.

In this work we provide a conceptually simple, modular approach for solving the above problem, providing a simpler and self-contained alternative to previous constructions of Ajtai (STOC 2011) and Andrychowicz et al. (Eurocrypt 2016). We also obtain several extensions and generalizations of this result. In particular, we show that for every leakage probability \(p<1\), there is a finite basis \(\mathbb {B}\) such that leakage-resilient computation with leakage probability p can be realized using circuits over the basis \(\mathbb {B}\). We obtain similar positive results for the stronger notion of leakage tolerance, where the input is not encoded, but the leakage from the entire computation can be simulated given random \(p'\)-leakage of input values alone, for any \(p<p'<1\). Finally, we complement this by a negative result, showing that for every basis \(\mathbb {B}\) there is some leakage probability \(p<1\) such that for any \(p'<1\), leakage tolerance as above cannot be achieved in general.

We show that our modular approach is also useful for protecting computations against worst case leakage. In this model, we require that leakage of any \(\mathbf{t}\) (adversarially chosen) wires reveal nothing about the input. By combining our construction with a previous derandomization technique of Ishai et al. (ICALP 2013), we show that security in this setting can be achieved with \(O(\mathbf{t}^{1+\varepsilon })\) random bits, for every constant \(\varepsilon > 0\). This (near-optimal) bound significantly improves upon previous constructions that required more than \(\mathbf{t}^{3}\) random bits.

Notes

Acknowledgements

We thank Jean-Sébastien Coron, Stefan Dziembowski, and Sebastian Faust for helpful discussions. The second author was supported in part by ERC grant 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 a DARPA/ARL SAFEWARE award, NSF Frontier Award 1413955, and NSF grant 1619348, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through the ARL under Contract W911NF-15-C-0205. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.CSAIL, MITCambridgeUSA
  2. 2.TechnionHaifaIsrael
  3. 3.UCLALos AngelesUSA

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