On the necessity of strong assumptions for the security of a class of asymmetric encryption schemes

Ron Steinfeld, Joonsang Baek, Yuliang Zheng

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    Abstract

    Recently various public key encryption schemes such as DHIES by Abdalla, Bellare and Rogaway and REACT by Okamoto and Pointcheval, whose security against adaptive chosen ciphertext attack (CCA) is based on the Gap problems, have been proposed. Although the Gap problems were proved to be a sufficient assumption for those schemes to be secure against adaptive chosen-cipertext attack, a necessary condition for CCA security of those schemes has not been explicitly discussed.

    In this paper we clarify the necessary condition for CCA security of those schemes. Namely we prove (in the random oracle model) that the Gap Diffie-Hellman is not only sufficient, but also a necessary assumption for the CCA security of DHIES and Diffie-Hellman version of REACT. We also show that our result applies to a wider class of public key encryption schemes. Furthermore we show that our result implies the equivalence, in the random oracle model, between ‘Strong Diffie-Hellman’ and ‘Oracle Diffie-Hellman’ assumptions proposed by Abdalla, Bellare and Rogaway. Our results may be used as criteria for distinguishing public key encryption schemes whose CCA security is based on strong assumptions (such as Gap Diffie-Hellman) from those schemes based on weaker ones (such as Computational Diffie-Hellman).
    Original languageEnglish
    Title of host publicationInformation Security and Privacy
    Subtitle of host publication7th Australasian Conference, ACISP 2002 Melbourne, Australia, July 3-5, 2002 Proceedings
    EditorsLynn Batten, Jennifer Seberry
    Place of PublicationBerlin Germany
    PublisherSpringer
    Pages241-256
    Number of pages16
    ISBN (Print)3540438610
    DOIs
    Publication statusPublished - 2002
    EventAustralasian Conference on Information Security and Privacy 2002 - Melbourne, Australia
    Duration: 3 Jul 20025 Jul 2002
    Conference number: 7th
    https://link.springer.com/book/10.1007/3-540-45450-0 (Proceedings)

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer
    Volume2384
    ISSN (Print)0302-9743

    Conference

    ConferenceAustralasian Conference on Information Security and Privacy 2002
    Abbreviated titleACISP 2002
    CountryAustralia
    CityMelbourne
    Period3/07/025/07/02
    Internet address

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