基于LFSR高次剩余问题构造公钥密码体制的研究

姜正涛; 柳毅; 王育民

基于LFSR高次剩余问题构造公钥密码体制的研究

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出版历程
- 收稿日期: 2004-09-09
- 修回日期: 2005-04-21
- 刊出日期: 2006-03-19

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

摘要

摘要: 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。
- 公钥加密体制;LFSR 高次(非)剩余;单向性;语意安全性
Abstract: 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.

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