Proxy cryptosystems are classified into proxy decryption systems and proxy re-encryption systems on the basis of a proxy's role. In this paper, we propose an ID-based proxy cryptosystem with revocability and hierarchical confidentialities. In our scheme, on receiving a ciphertext, the proxy has the rights to perform the following three tasks according to the message confidentiality levels of the sender's intention: (1) to decrypt the ciphertext on behalf of the original decryptor; (2) to re-encrypt the ciphertext such that another user who is designated by the original decryptor can learn the message; (3) to do nothing except for forwarding the ciphertext to the original decryptor. Our scheme supports revocability in the sense that it allows proxy's decryption and re-encryption rights to be revoked even during the valid period of the proxy key without changing the original decryptor's public information. We prove that our proposal is indistinguishable against chosen identity and plaintext attacks in the standard model. We also show how to convert it into a system against chosen identity and ciphertext attacks by using the Fujisaki-Okamoto transformation.

With the flourish of applications based on the Internet of Things (IoT), privacy issues have been attracting a lot of attentions. Although the concept of privacy homomorphism was proposed along with the birth of the well-known RSA cryptosystems, cryptographers over the world have spent about three decades for finding the first implementation of the so-called fully homomorphic encryption (FHE). Despite of, currently known FHE schemes, including the original Gentry's scheme and many subsequent improvements as well as the other alternatives, are not appropriate for IoT-oriented applications because most of them suffer from the problems of inefficient key size and noisy restraining. In addition, for providing fully support to IoT-oriented applications, symmetric fully homomorphic encryptions are also highly desirable. This survey presents an analysis on the challenges of designing secure and practical FHE for IoT, from the perspectives of lightweight requirements as well as the security requirements. In particular, some issues about designing noise-free FHE schemes would be addressed.