How Intractable Is the Discrete Logarithm for a General Finite Group?

@inproceedings{Okamoto1992HowII,
  title={How Intractable Is the Discrete Logarithm for a General Finite Group?},
  author={Tatsuaki Okamoto and Kouichi Sakurai and Hiroki Shizuya},
  booktitle={EUROCRYPT},
  year={1992}
}
GDL is the discrete logarithm prablem for a general finite group G. This paper gives a characterization for the intractability of GDL from the viewpoint of computational complexity theory. It is shown that GDL ∈ NP ∩ co-AM, assuming that G is in NP ∩ co-NP, and that the group law operation of G can be cxecuted in a polynomial time of the element size. Furthermore, as a natural probabilistic extension, the complexity of GDL is investigated under the assumption that the group law operation is… CONTINUE READING

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