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中文摘要：
基于二次剩余和高次剩余的困难问题，通过选择适当的参数，在不增加密文长度的情况下，对Paillier和Pointcheval提出的公钥概率加密体制的效率和加密的明文长度进行改进，能以更高的效率加密｜n｜＋k bit长度的明文消息，并分析了改进后加密体制的效率和安全性，改进加密体制的安全性与原加密体制的安全性、模n的高次剩余问题以及二次剩余问题等价．与原Paillier-Pointcheval加密体制相比，改进的加密体制具有加、解密效率高，传输数据量低，加密明文长等特点．
英文摘要：
Based on the intractable problems of nth residuosity and quadratic residuosity, by choosing proper parameters and without increasing the length of ciphertexts, the efficiency and the size of plaintexts of a probabilistic public-key encryption scheme proposed by Paillier and Pointcheval were improved. The improved encryption scheme can encrypt ｜n｜ ＋ k bit messages with higher efficiency. Security and efficiency analysis of the improved encryption scheme were also provided, and the security of the improved scheme is equivalent to that of the original encryption scheme, the higher residuosity problem and quadratic residuosity problem modulo n. Compared to the original Paillier-Pointcheval encryption scheme, the improved encryption scheme has features of higher efficiency, lower traffic date and larger size of plaintexts.
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