中文摘要：

已有基于证书代理重加密方案的构造严重依赖双线性对运算，计算效率不高。针对这一问题，提出了一个高效的基于证书代理重加密方案。所提出方案的加密算法无须作双线性对运算，而其他算法至多作一次双线性对运算，因此显著提高了方案的计算性能。与现有基于证书代理重加密方案相比，该方案具有计算效率高和通信带宽低的优点。基于q-mBDHI问题和1-BDHI问题的困难性假设，该方案在随机预言模型下被严格证明满足适应性选择密文攻击下的密文不可区分安全性，即满足选择密文安全性。

英文摘要：

The previous constructions of certificate-based proxy re-encryption are heavily dependent on the costly bilinearpairings,and thus have low computation efficiency.To solve this problem,an efficient certificate-based proxy re-encryptionscheme with bilinear pairings is developed.This new scheme significantly reduces the computation cost because it requirescomputing no bilinear pairings in the encryption algorithm and at most one bilinear pairing in other algorithms.Comparedwith the previous certificate-based proxy re-encryption schemes,it enjoys obvious advantage in both the computation efficiencyand the communication cost.In the random oracle model,the proposed scheme is formally proven to achieve indistinguishabilityagainst adaptively chosen-ciphertext attacks(i.e.,chosen-ciphertext security)under the hardness assumptionof the modified Bilinear Diffie-Hellman Inversion for q-values(q-mBDHI)problem and the1-Bilinear Diffie-HellmanInversion(1-BDHI)problem.