中文摘要：

云计算中现有同态公钥算法计算复杂度大，不能很好满足云计算高效快速的要求。针对具有很高计算效率的基于中国剩余定理的快速公钥算法进行同态特性研究，研究结果表明算法仅支持一次乘法同态操作；提出将现有算法降维改进，使改进后的算法具有加法、标量乘法和多次乘法的同态特性；分析了改进后算法的安全理论基础和语义安全特性，并基于改进后的算法设计了序列安全比较协议，通过与现有两种公钥算法进行对比，表明了改进后的算法具有安全高效的特性。

英文摘要：

Homomorphic public-key cryptosystems used in the cloud computing are huge in complexity, which influence the effi ciency of the cloud computing. The fast public-key cryptosystem based on Chinese remainder theorem is researched, which is ef ficient, and prove that it only supports the multiplication of two ciphertexts. This cryptosystem is improved by reducing its di- mension and the proof of the improved cryptosystem＇s homomorphic characteristic is provided, and the analysis of the secure basement and semantic security of this cryptosystem is giver. A secure comparison protocol of two sequences is designed using this cryptosystem, the result shows its efficiency and security compared with ELGamal and Paillier.