代数攻击的基本思想是将密码算法的安全性完全规约到关于密钥的多变元非线性方程系统的求解问题上。近年来, 基于代数攻击的分析方法, 包括标准代数攻击、快速代数攻击、cube攻击（选择IV代数攻击）等已经对序列密码的设计和分析产生了重大影响。本申请项目关注基于代数攻击的序列密码逆向分析方法研究, 主要研究内容有: 序列的谱攻击和谱免疫度的研究; LFSR和NFSR复合结构下的序列密码模型所对应方程系统的特点和规律分析; 对Trivium算法的cube攻击的改进。通过本项目的研究工作, 可以为序列密码代数攻击逆向分析的进一步发展提供理论支撑和应用指导。

The basic principle of algebraic attacks is to express the whole cipher as a large system of multivariate algebraic equations, which can be solved to recover the secret key. Recently, standard algebraic attacks, fast algebraic attacks and cube attacks have given great influence on the design and analysis of stream ciphers. In this project, we focus on analysis methods of stream ciphers based on algebraic attacks and the main contents of the project consist of three problems: research on spectral attacks and the spectral immunity of periodic sequences; algebraic attacks on some typical models of stream ciphers; improvement of cube attacks on Trivium. Our aims are to provide more theoretical foundations and technologies for further applications of algebraic attacks.