Abstract
We give a characterization for the intractability of hyperelliptic discrete logarithm problem from a viewpoint of computational complexity theory. It is shown that the language of which complexity is equivalent to that of the hyperelliptic discrete logarithm problem is in NP ∩ co-AM, and that especially for elliptic curves, the corresponding language is in NP ∩ co-NP. It should be noted here that the language of which complexity is equivalent to that of the discrete logarithm problem defined over the multiplicative group of a finite field is also characterized as in NP ∩ co-NP.
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CITATION STYLE
Shizuya, H., Itoh, T., & Sakurai, K. (1991). On the complexity of hyperelliptic discrete logarithm problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 547 LNCS, pp. 337–351). Springer Verlag. https://doi.org/10.1007/3-540-46416-6_29
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