A Cryptosystem Based on Non-maximal Imaginary Quadratic Orders with Fast Decryption

We introduce a new cryptosystem with trapdoor decryption based on the di culty of computing discrete logarithms in the class group of the non-maximal imaginary quadratic order O q , where q = q2 , square-free and q prime. The trapdoor information is the conductor q. Knowledge of this trapdoor information enables one to switch to and from the class group of the maximal order O , where the representatives of the ideal classes have smaller coe cients. Thus, the decryption procedure may be performed in the class group of O rather than in the class group of the public O q , which is much more e cient. We show that inverting our proposed cryptosystem is computationally equivalent to factoring the non-fundamental discriminant q which is intractable for a suitable choice of and q. We also describe how signature schemes in O q may be set up using this trapdoor information. Furthermore, we illustrate how one may embed key escrow capability into classical imaginary quadratic eld cryptosystems.

• Type: Conference
• Year: 1998
• Where: EUROCRYPT
• Authors: Detlef Hühnlein, Michael J. Jacobson Jr., Sachar Paulus, Tsuyoshi Takagi
• Keywords: Class Group, Cryptology, EUROCRYPT 1998, Trapdoor Decryption, Trapdoor Information