几类密码方案的格分析优化技术

项目名称： 几类密码方案的格分析优化技术

项目编号： No.61502488

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： 许军

作者单位： 中国科学院信息工程研究所

项目金额： 20万元

中文摘要： 同态加密方案可解决数据及操作委托给第三方时的保密问题；泄漏容忍加密方案是由于侧信道攻击对原密码方案安全性的威胁而设计的；非线性伪随机数生成器是一类重要的生成器。同态加密方案、泄漏容忍加密方案、非线性随机数生成器是密码学目前的研究热点。本课题以分析这三类密码方案的安全性为目标，研究它们的基于格的分析方法，结合线性化技术、变量替换等相关理论和方法提出格分析优化技术，期望得到低复杂度的格分析方法。主要研究内容包括：1）研究基于近似公因子问题及相关问题的同态加密方案的格分析优化技术；2）研究安全性可转化成求解隐藏数问题及变种的泄漏容忍加密方案的格分析优化技术； 3）研究与模逆隐藏数问题有内在联系的逆生成器的格分析优化技术； 4）研究这三类密码方案安全参数的选取。本课题的研究对于密码方案的设计提出指导性意见，对于推动格分析优化技术的发展以及将该技术应用到更多的领域具有重要的理论和现实意义。

中文关键词： 密码方案；密码分析；格分析方法；格分析优化技术；线性化技术

英文摘要： Homomorphic encryption schemes can solve the confidentiality problem of data and operations entrusted to the third party. Leakage-resilient encryption schemes are designed for resisting side channel attacks which threaten the security of the original cryptosystems. Nonlinear pseudo random-number generators are a kind of important generators. Homomorphic encryption schemes, leakage-resilient encryption schemes and nonlinear pseudo-random number generators are the current hot topics of cryptography. This research project is targeted to analyze the security of these three classes of cryptosystems and study lattice-based cryptanalysis about them. By utilizing the relevant theories and methods of linearization technique and variable substitutions, etc, we propose the optimized technique of lattice analysis and hopefully obtain a method of lattice analysis with low complexity. The main research contents are as follows: 1) study the optimized technique of lattice analysis of homomorphic encryption schemes based on the approximate common divisor problem and other relevant problems, 2) study the optimized technique of lattice analysis of leakage-resilient encryption schemes whose security can be reduced into solving the hidden number problem or its variants, 3) study the optimized technique of lattice analysis of the security on the inversive generator which has inner connection with the modular inversion hidden number problem, 4) study the selection of security parameters about these three classes of cryptosystems. This research project provides guidance on the design of cryptosystems. It also has important theoretical and practical significance on promoting the development of the optimized technique of lattice analysis and applying this technique to more areas.

英文关键词： cryptographic scheme;cryptanalysis;method of lattice analysis;optimized technique of lattice analysis;linearization technique