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EUROCRYPT
1998
Springer

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

9 years 3 months ago
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.
Detlef Hühnlein, Michael J. Jacobson Jr., Sac
Added 05 Aug 2010
Updated 05 Aug 2010
Type Conference
Year 1998
Where EUROCRYPT
Authors Detlef Hühnlein, Michael J. Jacobson Jr., Sachar Paulus, Tsuyoshi Takagi
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