An efficient probabilistic public-key cryptosystem over quadratic fields quotients

We present a new probabilistic cryptosystem working in quadratic fields quotients. Computation in such objects can be done efficiently with Lucas sequences which help to design a fast system. The security of the scheme is based on the LUC problem and its semantic security on a new decisional problem. This system appears to be an alternative to schemes based on the RSA primitive and has a full computational cost smaller than the El Gamal EC cryptosystem.