Fast RSA-type Schemes Based on Pell. Equations over ZN

Abstract

In this paper, we propose two new fast RSA-type schemes based on Pell equations over the ring Zn * .The decryption speed of the proposed schemes is about two times as fast as that of the RSA scheme for a 2 lonN-bit long message. The encryptions speed of our schemes is about 1.5 times slower than that of the RSA scheme. So, our schemes can be used in communications between a smart card and a larger computer. In addition, we also prove that the proposed schemes are as secure as the RSA scheme against the ciphertext attack.