Security of Cryptosystems Based on Class Groups of Imaginary Quadratic Orders

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.

• Type: Conference
• Year: 2000
• Where: ASIACRYPT
• Authors: Safuat Hamdy, Bodo Möller
• Keywords: ASIACRYPT 2000, Class Groups, Cryptology, Discrete Logarithms, Imaginary Quadratic Orders