公钥密码分析中的格方法与代数攻击

项目名称： 公钥密码分析中的格方法与代数攻击

项目编号： No.61472417

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： 胡磊

作者单位： 中国科学院信息工程研究所

项目金额： 80万元

中文摘要： 公钥密码是现代信息系统安全性的重要保障。本项目的出发点是研究公钥密码系统两种恒等关系--线性恒等关系和高阶恒等关系相结合的攻击方法，即公钥密码的基于格基归约求解和代数方程求解相结合的分析方法，旨在得到低复杂度的代数密码分析新方法。主要研究破解纠错码、格和多变量多项式公钥密码中的格基归约求解--代数方程求解的分析方法，研究纠错码、格和多变量公钥密码中的广播攻击、重放攻击、差错攻击分析方法，研究以离散对数、因子分解、向量背包等困难假设为基础设计的公钥密码变型的格基归约求解--代数方程求解的分析方法，以及研究ECC、RSA、SM2等常规公钥密码的基于格和代数攻击的广播模式下的新攻击方法。本项目的研究以后量子公钥密码的分析为主要载体，对于我们理解和设计安全的可抵御量子计算机攻击的公钥密码具有重要意义。

中文关键词： 密码系统；公钥密码；后量子密码；格方法；代数攻击

英文摘要： Public key cryptography is an important technology for ensuring the security of modern information systems. The starting point of the present proposal is to study methods which combine linear identical relations and high order identical relations derived from cryptographic systems to attack public key cryptographic systems, and to obtain cryptographic analysis methods with low complexity by applying lattice basis reduction algorithms to solve linear identical relations and algebraic equation solving algorithms to high order identical relations. The project will mainly study how to combine lattice basis reduction and algebraic equation solving algorithms to analyze and break public key cryptographic systems based on error coding, lattices, or multivariate polynomials; research how to launch broadcast, multiple transmission or fault injection attacks on such cryptographic systems; study how to apply combined lattice basis reduction and algebraic equation solving methods to analyze public key cryptographic variant schemes based on discrete logarithm, integer factorization, or vector knapsack problems; and present new combined broadcast-type attacks on conventional ECC, RSA and SM2 cryptosystems. The project will focus on the analysis of post quantum public key cryptography which is regarded to resist against quantum computer attacks and achieve obvious effect on understanding and designing secure public key cryptography.

英文关键词： cryptographic system;public key cryptography;post-quantum cryptography;lattice method;algebraic attack