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2018 | OriginalPaper | Buchkapitel

Leakage-Resilient Cryptography from Puncturable Primitives and Obfuscation

verfasst von : Yu Chen, Yuyu Wang, Hong-Sheng Zhou

Erschienen in: Advances in Cryptology – ASIACRYPT 2018

Verlag: Springer International Publishing

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Abstract

In this work, we develop a framework for building leakage-resilient cryptosystems in the bounded leakage model from puncturable primitives and indistinguishability obfuscation (\(i\mathcal {O}\)). The major insight of our work is that various types of puncturable pseudorandom functions (PRFs) can achieve leakage resilience on an obfuscated street.

First, we build leakage-resilient weak PRFs from weak puncturable PRFs and \(i\mathcal {O}\), which readily imply leakage-resilient secret-key encryption. Then, we build leakage-resilient publicly evaluable PRFs (PEPRFs) from puncturable PEPRFs and \(i\mathcal {O}\), which readily imply leakage-resilient key encapsulation mechanism and thus public-key encryption. As a building block of independent interest, we realize puncturable PEPRFs from either newly introduced puncturable objects such as puncturable trapdoor functions and puncturable extractable hash proof systems or existing puncturable PRFs with \(i\mathcal {O}\). Finally, we construct the first leakage-resilient public-coin signature from selective puncturable PRFs, leakage-resilient one-way functions and \(i\mathcal {O}\). This settles the open problem posed by Boyle, Segev, and Wichs (Eurocrypt 2011).

By further assuming the existence of lossy functions, all the above constructions achieve optimal leakage rate of \(1 - o(1)\). Such a leakage rate is not known to be achievable for weak PRFs, PEPRFs and public-coin signatures before. This also resolves the open problem posed by Dachman-Soled, Gordon, Liu, O’Neill, and Zhou (PKC 2016, JOC 2018).

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Vorheriges Kapitel How to Securely Compute with Noisy Leakage in Quasilinear Complexity

Nächstes Kapitel Unbounded Inner Product Functional Encryption from Bilinear Maps

This is sometimes called second pre-image resistant functions.

Leftover hash lemma could be interpreted as a leakage-resilient fact, which stipulates \(\mathsf {ext}(x, s)\) is close to uniform even given a correlated value z, as long as s is a random seed chosen independently and x still has high min-entropy given leakage z.

Goldreich-Levin theorem can be interpreted as a leakage-resilient assumption, which states that if h is one-way then \(\mathsf {hc}(x)\) is pseudorandom even in the presence of h(x). Here \(\mathsf {hc}\) serves as a computational randomness extractor and h(x) could be viewed as leakage on x.

Following current conventions, we do not regard hash proof systems [CS02] as a general assumption.

A signature is secret-coin if its security breaks down when the randomness used in the signing procedure is revealed. On the contrary, a signature is public-coin if it stays secure even when the random coins used in the signing procedure are revealed (i.e., provided in-the-clear by the signature). In other words, public-coin signature is secure even when the entire random coins used for signing are leaked.

In selective security model, the adversary must declare the message \(m^*\) on which it will make a forgery before seeing the verification key, but then can adaptively make signing queries on messages distinct from \(m^*\).

In the case of our adaptively secure construction, a signature additionally contains a public coin of size \(\lambda ^c\) for any constant \(c < 1\).

Note that this dilemma does not occur in the case of encryption, since the argument in the final game is information-theoretic.

Without loss of generality, we assume that \(k(\{x^*\})\) includes the information of \(x^*\) in plain.

In a PEPRF, when the input x is not in \(L_{pk}\), its PRF value \(F_{sk}(x)\) may not be well defined and will be denoted by a distinguished symbol \(\bot \).

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Titel: Leakage-Resilient Cryptography from Puncturable Primitives and Obfuscation
verfasst von: Yu Chen
Yuyu Wang
Hong-Sheng Zhou
Verlag: Springer International Publishing
Buch: Advances in Cryptology – ASIACRYPT 2018
Print ISBN: 978-3-030-03328-6

Electronic ISBN: 978-3-030-03329-3

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-030-03329-3_20

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