Relationships among the computational powers of breaking discrete log cryptosystems

Kouichi Sakurail, Hiroki Shizuya

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

    17 Citations (Scopus)

    Abstract

    We investigate the complexity of breaking cryptosystems of which security is based on the discrete logarithm problem. We denote the algorithms of breaking the Diffie-Hellman’s key exchange scheme by DH, the Bellare-Micali’s non-interactive oblivious transfer scheme by BH, the ElGamal’s public-key cryptosystem by EG, the Okamoto’s conference-key sharing scheme by CONF, and the Shamir’s 3-pass key-transmission scheme by BPASS, respectively. We show a relation among these cryptosystems that (Formula Presented) where (Formula Presented) denotes the polynomial-time functionally many-teone reducibility, i.e. a function version of the (Formula Presented) -reducibility. We further give some condition in which these algorithms have equivalent difficulty. Namely, 1. If the complete factorization of p - 1 is given, i.e. if the the discrete logarithm problem is a certified one, then these cryptosystems are equivalent w.r.t. expected polynomial-time functionally Turing reducibility. 2. If the underlying group is the Jacobian of an elliptic curve over 2pwith a prime order, then these cryptosystems are equivalent w.r.t. polynomial-time functionally many-to-one reducibility. We also discuss the complexity of several languages related to those computing problems.

    Original languageEnglish
    Title of host publicationAdvances in Cryptology — EUROCRYPT 1995 - International Conference on the Theory and Application of Cryptographic Techniques, Proceedings
    EditorsJean-Jacques Quisquater, Louis C. Guillou
    PublisherSpringer Verlag
    Pages341-355
    Number of pages15
    ISBN (Print)3540594094, 9783540594093
    DOIs
    Publication statusPublished - 1995
    EventInternational Conference on theTheory and Applications of Cryptographic Techniques, EUROCRYPT 1995 - Saint-Malo, France
    Duration: 1995 May 211995 May 25

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume921
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    OtherInternational Conference on theTheory and Applications of Cryptographic Techniques, EUROCRYPT 1995
    Country/TerritoryFrance
    CitySaint-Malo
    Period95/5/2195/5/25

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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