Research on the Construction of Public-Key Cryptosystems Based on LFSR Residuosity Problem
基于LFSR高次剩余问题构造公钥密码体制的研究

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.