A Fast Semantically Secure Public Key Cryptosystem Based on Factoring

The cryptosystem proposed by Koyama is not semantically secure. Also, it is not secure against partial known plaintext attack, linearly related plaintext attack and low exponent attack. In this paper we propose a cryptosystem over singular cubic curve using the idea of Koyama and Kouichi et al. Our proposed cryptosystem is approximately two times faster than the cryptosystem given by Kouichi et al. with the same security label and more efficient than the Koyama scheme at higher security label. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme.