A new encryption algorithm over elliptic curve

Various public key encryption systems have been proposed in modern information techology. Some of them have also been used in various applications, such as E-commerce and mobile database. This paper proposes two secure receipt oriented encryption systems. The decryptioner's private keys could be changed with the different time periods. This case would be very useful in some practical scenarios, for instance, in a mobile database environment. Besides the semantic security, the proposed schemes have the backward-and-future security, a new security requirement for semantically secure encryption schemes. In terms of construction, the two schemes are based on the pairings over elliptic curves. Also, this paper provides a heuristic security analysis for the underlying system