A research on new public-key encryption schemes

We investigate the properties of Lucas Sequence, and propose a new variant of (probabilistic) public-key encryption scheme based on Lucas sequence. Then we provide security analysis of the encryption schemes. The one-wayness of the proposed scheme is equivalent to Partial LUC-DL problem in ZN. For the proposed probabilistic encryption scheme, its semantic security is equivalent to Decisional LUC-DH problem in ZN. At last, we briefly analyze the efficiency of the proposed schemes.