基于LFSR高次剩余问题构造公钥密码体制的研究

Research on the Construction of Public-Key Cryptosystems Based on LFSR Residuosity Problem

该文对用线性反馈移位寄存器(LFSR)构造公钥密码体制做了进一步的研究,定义了LFSR的高次(非)剩余问题,基于新的困难问题探讨了构造一种加解密不同于GH的密码原型,并给出了具体的加解密过程,证明了它的可行性;在此基础上,进一步把该体制改进为概率加密体制,克服了GH加密确定性的缺点,同时对体制的安全性和效率做了初步分析,具有单向性和语意安全性,最后证明了该体制的单向性等价于LFSR高次剩余问题,语意安全性等价于LFSR判断高次剩余问题。

Further research on the construction of public-key cryptosystem based on Linear Feedback Shift Register （LFSR） is provided, and the LFSR higher （non） residuosity problem is defined. Based on new intractability problems a new public-key encryption primitive with encryption/decryption procedures differ from GH is investigated. The encryption and decryption procedures are specified. It is further improved to be a probabilistic encryption scheme. Efficiency and security analysis of the proposed encryption scheme is provided. It has properties of one-wayness and semantic security. The one-wayness and semantic security are equivalent to higher LFSR residuosity and decisional LFSR residuosity problems respectively.