基于反馈移位寄存器的流密码相关问题研究

项目名称： 基于反馈移位寄存器的流密码相关问题研究

项目编号： No.61472120

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 曾祥勇

作者单位： 湖北大学

项目金额： 83万元

中文摘要： 随着代数攻击和快速代数攻击等密码分析理论与技术的发展，基于线性反馈移位寄存器的流密码的安全受到了严重威胁。近年来，非线性反馈移位寄存器逐渐成为密钥流生成器的一种重要设计原件，非线性序列作为驱动已经成为基于反馈移位寄存器的流密码设计的新趋势。本项目将集中研究用于基于反馈移位寄存器流密码的布尔函数和非线性反馈移位寄存器。具体地，我们将运用代数学、编码学、组合学和计算机代数等工具，构造具有较好抗代数攻击、快速代数攻击和其它优良密码学性质的布尔函数，研究Fibonacci型非线性反馈移位寄存器的圈结构，探讨以Grain和Trivium算法中的非线性反馈移位寄存器为原型的Galois型非线性反馈移位寄存器的密码学性质，并讨论有限域上序列的非线性复杂度和k次复杂度等问题。这些研究对发展基于反馈移位寄存器的流密码设计与分析的方法和技术具有重要的理论意义和应用价值。

中文关键词： 流密码；布尔函数；代数免疫；伪随机序列；非线性反馈移位寄存器

英文摘要： With the development of the theory and techniques of algebraic attacks and fast algebraic attacks, the security of the stream ciphers based on linear feedback shift registers has been seriously threatened. In recent years, nonlinear feedback shift registers have been important cryptographic primitives in the design of keystream generators, and that nonlinear sequences are used as driving sequences has been a new trend in the design of stream ciphers based on feedback shift registers.This project will focus on studying Boolean functions and nonlinear feedback shift registers used in stream ciphers based on feedback shift registers. Specifically, by applying the tools of algebra, coding theory, combinatorics and computer algebra, we will propose some constructions of Boolean functions having good behavior against algebraic attacks, fast algebraic attacks and possessing other desired cryptographic properties, investigate the cycle structure of Fibonacci nonlinear feedback shift registers, analyze the cryptographic properties of Galois nonlinear feedback shift registers coming from Grain and Trivium alogrithms, and study the nonlinear complexity and k-th order complexity of sequences over finite fields. These studies have important theoretical and practical value for developing methods and techniques in the design and analysis of stream ciphers based on feedback shift registers.

英文关键词： stream cipher;Boolean function;algebraic immunity;pesudorandom sequence;nonlinear feedback shift register