SPN型分组密码的新型代数分析方法研究

项目名称： SPN型分组密码的新型代数分析方法研究

项目编号： No.61502008

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 崔杰

作者单位： 安徽大学

项目金额： 20万元

中文摘要： 代数分析被认为是分组密码最有效的密码分析技术之一。现有代数分析方法F4、XL、XSL等存在假设条件过多和效率低下的问题。本项目研究基于Gröbner基的SPN型分组密码代数分析方法，从理论与实践上提高分组密码的代数分析效率，同时为构建新型安全轻量级分组密码提供理论和技术支持。首先，采用方程系统优化策略，探索通过选择合理的项序及变量次序构造SPN型分组密码的零维Gröbner基；其次，以零维Gröbner基构造为基础，研究SPN型分组密码的Gröbner基分析理论，构建SPN型分组密码的Gröbner基分析方案；最后，采用异域迁移方法和密钥相关性理论，建立SPN型分组密码的统一表示模型，以降低方程系统的求解复杂度，为解决分组密码的代数分析难题探寻一条新的途径。本项目注重研究的可持续性和可移植性、理论和技术上的前瞻性和应用的有效性，研究成果将对完善分组密码代数分析的理论基础和技术框架提供支持。

中文关键词： 代数分析；Gröbner基；替换-置换网络；分组密码；轻量级分组密码

英文摘要： Algebraic analysis is considered to be one of the most effective techniques of cryptanalysis of block ciphers. Nowadays, there exist several problems in the algebraic analysis methods which include F4, XL, XSL, etc, such as too many assumptions, inefficiencies and so on. This project studies the algebraic cryptanalysis method based on Gröbner basis for SPN-style block ciphers, aims at improving the efficiency of block cipher algebraic cryptanalysis theoretically and practically. At the same time, it can also provide theoretical and technical support in building the new secure lightweight block ciphers. First, we will construct the SPN-style block ciphers’ zero-dimensional Gröbner basis through using equation system optimization strategy and choosing suitable term order and variable order. Second, based on the construction of zero-dimensional Gröbner basis, we will study the SPN-style block ciphers’ Gröbner basis cryptanalysis theories to construct Gröbner basis cryptanalysis schemes for SPN-style block ciphers. Finally, we will adopt the different fields transferring method and the key correlation theory to establish the unified representation model, which helps to reduce the complexity of solving the equation system and explore a new approach to solving the algebraic cryptanalysis problems of block ciphers. The project emphasizes the sustainability and portability of research, theoretical and technical prospective and the effectiveness of applications. Our study results will provide support in perfecting the theoretical basis and technical framework of the block ciphers algebraic cryptanalysis.

英文关键词： Algebraic Cryptanalysis;Gröbner Basis;SPN（Substitution-Permutation Network）;Block Cipher;Lightweight Block Cipher