Université de Liège
The authors present a new probabilistic cryptosystem working in quadratic field's 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.