On the complexity of hyperelliptic discrete logarithm problem

Authors:
Hiroki Shizuya;Toshiya Itoh;Kouichi Sakurai
Affiliations:
Department of Electrical Communications, Faculity of Engineering, Tohoku University, Aramaki, Sendai, Japan and Département d'I.R.O., Université de Montréal, Montréal, Qué ...;Department of Information Processing, The Graduate School at Nagatsuta, Tokyo Institute of Technology, Yokohama, Japan;Computer & Information Systems Laboratory, Mitsubishi Electric Corporation, Kamakura, Japan
Venue:
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Year:
1991

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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.