New techniques for efficient trapdoor functions and applications

Sanjam Garg, Romain Gay, Mohammad Hajiabadi

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

    4 Scopus citations

    Abstract

    We develop techniques for constructing trapdoor functions (TDFs) with short image size and advanced security properties. Our approach builds on the recent framework of Garg and Hajiabadi [CRYPTO 2018]. As applications of our techniques, we obtain The first construction of deterministic-encryption schemes for block-source inputs (both for the CPA and CCA cases) based on the Computational Diffie-Hellman (CDH) assumption. Moreover, by applying our efficiency-enhancing techniques, we obtain CDH-based schemes with ciphertext size linear in plaintext size.The first construction of lossy TDFs based on the Decisional Diffie-Hellman (DDH) assumption with image size linear in input size, while retaining the lossiness rate of [Peikert-Waters STOC 2008]. Prior to our work, all constructions of deterministic encryption based even on the stronger DDH assumption incurred a quadratic gap between the ciphertext and plaintext sizes. Moreover, all DDH-based constructions of lossy TDFs had image size quadratic in the input size. At a high level, we break the previous quadratic barriers by introducing a novel technique for encoding input bits via hardcore output bits with the use of erasure-resilient codes. All previous schemes used group elements for encoding input bits, resulting in quadratic expansions.

    Original languageEnglish (US)
    Title of host publicationAdvances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
    EditorsYuval Ishai, Vincent Rijmen
    PublisherSpringer Verlag
    Pages33-63
    Number of pages31
    ISBN (Print)9783030176587
    DOIs
    StatePublished - 2019
    Event38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 - Darmstadt, Germany
    Duration: May 19 2019May 23 2019

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume11478 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019
    CountryGermany
    CityDarmstadt
    Period5/19/195/23/19

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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