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. © 2009 Springer-Verlag.
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CITATION STYLE
Isobe, S., Koizumi, E., Nishigaki, Y., & Shizuya, H. (2009). On the complexity of computing discrete logarithms over algebraic tori. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5888 LNCS, pp. 433–442). https://doi.org/10.1007/978-3-642-10433-6_29
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