On generic constructions of circularly-secure, leakage-resilient public-key encryption schemes

Mohammad Hajiabadi, Bruce M. Kapron, Venkatesh Srinivasan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    3 Scopus citations

    Abstract

    We propose generic constructions of public-key encryption schemes, satisfying key-dependent message (KDM) security for projections and different forms of key-leakage resilience, from CPA-secure private-key encryption schemes with two main abstract properties: (1) a form of (additive) homomorphism with respect to both plaintexts and randomness, and (2) reproducibility, providing a means for reusing encryption randomness across independent secret keys. More precisely, our construction transforms a private-key scheme with the stated properties (and one more mild condition) into a public-key one, providing:–KDM-projection security, an extension of circular security, where the adversary may also ask for encryptions of negated secret key bits;–a (1− o(1)) resilience rate in the bounded-memory leakage model of Akavia et al. (TCC 2009); and–Auxiliary-input security against subexponentially-hard functions. We introduce homomorphic weak pseudorandom functions, a homomorphic version of the weak PRFs proposed by Naor and Reingold (FOCS’95) and use them to realize our base encryption scheme. We in turn obtain homomorphic weak PRFs from homomorphic hash-proof systems (HHPS). We also show how the base encryption scheme may be realized using subgroup indistinguishability (implied, in particular, by quadratic residuosity (QR) and decisional composite residuosity (DCR)). As corollaries of our results, we obtain (1) the first multiple-key projection-secure bit-encryption scheme (as well as the first scheme with a (1 − o(1)) resilience rate) based solely on the HHPS assumption, and (2) a unifying approach explaining the results of Boneh et al. (CRYPTO’08) and Brakerski and Goldwasser (CRYPTO’10). Finally, by observing that Applebaum’s KDM amplification method (EUROCRYPT’11) preserves both types of leakage resilience, we obtain schemes providing at the same time high leakage resilience and KDM security against any fixed polynomial-sized circuit family.

    Original languageEnglish (US)
    Title of host publicationPublic-Key Cryptography – PKC 2016 - 19th IACR International Conference on Practice and Theory in Public-Key Cryptography, Proceedings
    EditorsChen-Mou Cheng, Kai-Min Chung, Bo-Yin Yang, Giuseppe Persiano
    PublisherSpringer Verlag
    Pages129-158
    Number of pages30
    ISBN (Print)9783662493861
    DOIs
    StatePublished - 2016
    Event19th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2016 - Taipei, Taiwan, Province of China
    Duration: Mar 6 2016Mar 9 2016

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9615
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference19th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2016
    CountryTaiwan, Province of China
    CityTaipei
    Period3/6/163/9/16

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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