How to construct secure proxy cryptosystem

Proxy cryptosystem, first proposed by Mambo and Okamoto [M.Mambo, E. Okamoto, Proxy cryptosystem: delegation of a power to decrypt ciphertexts, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E80-A/1 (1997) 54-63], allows the original decryptor to delegate his decrypting capability to the proxies. However, until now, no practical proxy cryptosystem modes are proposed. Therefore, in this paper, we present a novel proxy cryptosystem model: proxy cryptosystem based on time segmentation. Under this mode, a security analysis model will be proposed. Furthermore, a proxy cryptosystem scheme is presented as an example. We will show that the proposed scheme is proven security in the proposed security analysis model. Finally, we will give the ID-based version of this construction.