On the complexity of computing discrete logarithms over algebraic tori

    Research output: Contribution to journalArticle

    Abstract

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

    Original languageEnglish
    Pages (from-to)442-447
    Number of pages6
    JournalIEICE Transactions on Information and Systems
    VolumeE97-D
    Issue number3
    DOIs
    Publication statusPublished - 2014 Jan 1

    Keywords

    • Algebraic tori
    • Order certified discrete logarithm
    • Turing reduction

    ASJC Scopus subject areas

    • Software
    • Hardware and Architecture
    • Computer Vision and Pattern Recognition
    • Electrical and Electronic Engineering
    • Artificial Intelligence

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