For the drawbacks of low key updating efficiency and high decryption cost of the Revocable Identity-Based Encryption (RIBE), which make it unsuitable for lightweight devices, an RIBE with Outsourcing Decryption and member revocation (RIBE-OD) was proposed. Firstly, a full binary tree was created and a random one-degree polynomial was picked for each node of this tree. Then, the one-degree polynomial was used to create the private keys of all the users and the update keys of the unrevoked users by combining the IBE scheme based on exponential inverse model and the full subtree method, and the revoked users' decryption abilities were deprived due to not obtaining their update keys. Next, the majority of decryption calculation was securely outsourced to cloud servers after modifying the private key generation algorithm by the outsourcing decryption technique and adding the ciphertext transformation algorithm. The lightweight devices were able to decrypt the ciphertexts by only performing a little simple computation. Finally, the proposed scheme was proved to be secure based on the Decisional Bilinear Diffie-Hellman Inversion (DBDHI) assumption. Compared with Boldyreva-Goyal-Kumar (BGK) scheme, the proposed scheme not only improves the efficiency of key updating by 85.7%, but also reduces the decryption cost of lightweight devices to an exponential operation of elliptic curve, so it is suitable for lightweight devices to decrypt ciphertexts.

Since the encryption algorithm of Hierarchical Identity-Based Encryption (HIBE) is unsuitable for the lightweight devices, a fully secure Hierarchical Identity-Based Online/Offline Encryption (HIBOOE) scheme was proposed. This scheme introduced the online/offline cryptology into HIBE, and divided the encryption algorithm into two stages. Firstly, the offline encryption preprocessed most of heavy computations before knowing the message and the recipient, then the online encryption could be performed efficiently to produce the ciphertext once the recipient's identity and the message were got. The experiment results show that the proposed scheme greatly improves the encryption efficiency, and gets suitable for power-constrained devices. Moreover it is proven fully secure.

The existing public key encryption schemes with auxiliary inputs are impractical since they are only of Indistinguishability under Chosen Plaintext Attack (IND-CPA) security. This paper constructed a novel public-key encryption scheme resilient to auxiliary input leakage, which was based on CS '98 encryption scheme and Goldreich-Levin theorem over large field GF(q). The proposed scheme was based on Indistinguishability under Adaptive Chosen Ciphertext Attack (IND-CCA2) security, allowing an attacker to query decryption oracle with auxiliary input leakage when it tried to attack the challenge ciphertext. Compared with the BHHO (Boneh, Halevi, Hamburg, Ostrovsky) encryption scheme, the proposed scheme realizes the more strict IND-CCA2 security in spite of the encryption's and decryption's overhead being nearly doubled.

The existing Identity-Based Online/Offline Encryption (IBOOE) schemes do not allow the attacker to choose the target identity adaptively, since they are only proven to be secure in the selective model. This paper introduced the online/offline technology into fully secure Identity-Based Encryption (IBE) schemes, and proposed a fully secure IBOOE scheme. Based on three static assumptions in composite order groups, this scheme was proven to be fully secure with the dual system encryption methodology. Compared with the famous IBOOE schemes, the proposed scheme not only greatly improves the efficiency of the online encryption, but also can meet the demands for complete safety in the practical systems.