Security of Cryptosystems Based on Class Groups of Imaginary Quadratic Orders

Authors:
Safuat Hamdy;Bodo Möller
Affiliations:
-;-
Venue:
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Year:
2000

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Abstract

In this work we investigate the difficulty of the discrete logarithm problem in class groups of imaginary quadratic orders. In particular, we discuss several strategies to compute discrete logarithms in those class groups. Based on heuristic reasoning, we give advice for selecting the cryptographic parameter, i.e. the discriminant, such that cryptosystems based on class groups of imaginary quadratic orders would offer a similar security as commonly used cryptosystems.