An efficient probabilistic public-key cryptosystem over quadratic fields quotients

@article{Castagnos2007AnEP,
  title={An efficient probabilistic public-key cryptosystem over quadratic fields quotients},
  author={Guilhem Castagnos},
  journal={Finite Fields and Their Applications},
  year={2007},
  volume={13},
  pages={563-576}
}
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. 
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