On the complexity of computing discrete logarithms over algebraic tori

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

    Abstract

    This paper studies the complexity of computing discrete logarithms over algebraic tori. We show that the order certified version of the discrete logarithm over general finite fields (OCDL, in symbols) reduces to the discrete logarithm over algebraic tori (TDL, in symbols) with respect to the polynomial-time Turing reducibility. This reduction means that if the integer factorization can be computed in polynomial time, then TDL is equivalent to the discrete logarithm DL over general finite fields with respect to the Turing reducibility.

    Original languageEnglish
    Title of host publicationCryptology and Network Security - 8th International Conference, CANS 2009, Proceedings
    Pages433-442
    Number of pages10
    DOIs
    Publication statusPublished - 2009 Dec 14
    Event8th International Conference on Cryptology and Network Security, CANS 2009 - Kanazawa, Japan
    Duration: 2009 Dec 122009 Dec 14

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5888 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other8th International Conference on Cryptology and Network Security, CANS 2009
    CountryJapan
    CityKanazawa
    Period09/12/1209/12/14

    Keywords

    • Algebraic tori
    • Order certified discrete logarithms
    • Turing reduction

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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