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A Leakage-Resilient Ciphertext-Policy Attribute-based Encryption (LR-CP-ABE) not only supports the fine-grained access control to encrypted data but also guarantees the security of the data under the side-channel attacks. However, the leakage rate in the existing schemes is low or related to the number of attributes. It will make these schemes suffer from continual attacks. In addition, all of them almost not consider the leakage of the users' privacy and rely on the composite order groups which will threaten the privacy security of the users and depress the users in practice. In this paper, we aim at solving the above problems and propose a scheme with the improving leakage rate in the prime order group. In the proposed scheme, an extension of the lattice-based trapdoor is used to make it achieve the maximum leakage rate $1-o(1)$ . Moreover, it achieves the anonymity which can protect the privacy of the receivers. The proposed scheme can be reduced to the standard assumption-Decision Linear (DLIN) assumption in the selective security model and resist the Chosen Plaintext Attacks (CPA security). At last, the performance comparisons are given to confirm the efficiency and security of the proposed scheme.

Since cloud computing has been playing an increasingly important role in real life, the privacy protection in many fields has been paid more and more attention, especially, in the field of personal health record (PHR). The traditional ciphertext-policy attribute-based encryption (CP-ABE) provides the fine-grained access control policy for encrypted PHR data, but the access policy is also sent along with ciphertext explicitly. However, the access policy will reveal the users' privacy, because it contains too much sensitive information of the legitimate data users. Hence, it is important to protect users' privacy by hiding access policies. In most of the previous schemes, although the access policy is hidden, they face two practical problems: 1) these schemes do not support large attribute universe, so their practicality in PHR is greatly limited and 2) the cost of decryption is especially high since the access policy is embedded in the ciphertext. To address these problems, we construct a CP-ABE scheme with efficient decryption, where both the size of public parameters and the cost of decryption are constant. Moreover, we also show that the proposed scheme achieves full security in the standard model under static assumptions by using the dual system encryption method.