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[Keyword] order certified discrete logarithm(1hit)

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  • On the Complexity of Computing Discrete Logarithms over Algebraic Tori

    Shuji ISOBE  Eisuke KOIZUMI  Yuji NISHIGAKI  Hiroki SHIZUYA  

     
    PAPER-Fundamentals of Information Systems

      Vol:
    E97-D No:3
      Page(s):
    442-447

    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.