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We introduce a new cryptosystem with trapdoor decryption based on the difficulty ofcomputing discrete logarithms in the class group of the non-maximal imaginary quadraticorder O \Delta q , where \Delta q = \Deltaq2, \Delta square-free and q prime. The trapdoor information is theconductor q. Knowledge of this trapdoor information enables one to switch to and from theideal class group of the maximal order O \Delta , where the representatives of the ideal classes havesmaller coefficients. ...

A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption