密码算法的组件设计与分析

发布时间：2018-04-14 02:17

本文选题：完全非线性函数 + 原像分布　；参考：《国防科学技术大学》2014年博士论文

【摘要】：现代社会,信息的安全防护问题日益凸显。密码学作为信息安全领域的支撑,获得了人们的高度关注。密码算法的组件设计与分析正是其中的一个研究热点,对于序列密码和分组密码体制均具有重要的理论与现实意义。在此背景下,本文围绕着密码算法的组件设计理论与分析方法两部分展开研究。密码函数(包括布尔函数和向量值布尔函数)是密码算法的核心组件,其安全性受到差分均匀度、代数免疫度等指标的制约。在本文前半部分,有限域上差分均匀度达到最优的向量值布尔函数——完全非线性函数的原像分布问题与指数和的值分布问题先后得到讨论;然后,本文又研究了具有最大代数免疫的布尔函数的计数问题。分组密码算法因其速度快、易实现等特点,在数据加密、数字签名等方面得到广泛应用。本文的后半部分研究了中间相遇攻击和积分攻击、不可能差分攻击等分组密码分析方法,并据此对Zodiac、RC6两种常见分组密码算法进行了安全性分析。在密码算法的组件设计理论研究方面,本文取得的主要成果有:(1)证明了当(?)(x)为GF(q~m)上Dembowski-Ostrom函数或Coulter-Matthews函数时,从GF(q~m) 到GF(q)的完全非线性函数tr(a(?)(x))的原像分布恰有两种取值,其中一种取值对应GF(q~m) 所有平方剩余元,另一种取值对应GF(q~m) 所有非平方剩余元。(2)利用有限域上二次型理论,刻画了三类GF(q)到GF(q)上的完全非线性函数(?)(x)指数和的值分布特征;进而得到了序列间的相关分布特征和线性码的权分布特征。(3)研究了偶数元MAI布尔函数和1阶弹性的MAI布尔函数的计数问题。给出偶数元MAI布尔函数个数的一个新下界,该下界优于已有结果。关于1阶弹性的MAI布尔函数,首次提出了一个有意义的计数下界。在密码算法的分析方法研究方面,本文取得的主要成果有:(1)研究了Zodiac算法抵抗中间相遇攻击的能力。找到了Zodiac算法新的9轮区分器和10轮区分器,基于这两个区分器分别对15轮和完整16轮Zodiac算法进行了中间相遇攻击。结果表明完整16轮Zodiac-128/192/256是不抗中间相遇攻击的。(2)重点研究低轮RC6算法对积分攻击和不可能差分攻击的免疫能力,对4轮RC6算法实施了积分攻击并对5轮RC6算法实施了不可能差分攻击,攻击结果均优于穷尽搜索。但是对轮数更多的RC6算法实施以上攻击较为困难。由此说明使用数据依赖循环确实在很大程度上增强了算法的扩散性能。
[Abstract]:In modern society, the problem of information security protection is increasingly prominent.Cryptography, as the support of information security field, has been highly concerned by people.The component design and analysis of cryptographic algorithms is one of the research hotspots, which has important theoretical and practical significance for both sequential cipher and block cipher systems.Under this background, this paper focuses on the component design theory and analysis method of cryptographic algorithm.Cryptographic function (including Boolean function and vector-valued Boolean function) is the key component of cryptographic algorithm. Its security is restricted by the index of difference uniformity and algebraic immunity.In the first half of this paper, the problem of the distribution of the original image and the value of the exponential sum of the vector valued Boolean function with the difference uniformity reaching the optimum on the finite field has been discussed successively.In this paper, we also study the counting problem of Boolean functions with maximum algebraic immunity.Block cipher algorithm is widely used in data encryption and digital signature because of its high speed and easy implementation.In the second half of this paper, the block cipher analysis methods, such as middle encounter attack, integral attack and impossible differential attack, are studied, and the security of two common block cipher algorithms, Zodiacan RC6, is analyzed.In terms of the component design theory of cryptographic algorithms, the main results obtained in this paper are: 1) it is proved that when the Dembowski-Ostrom function or Coulter-Matthews function is a Dembowski-Ostrom function or a Coulter-Matthews function, there are exactly two values for the original image distribution of the complete nonlinear function from Dembowski-Ostrom to Coulter-Matthews).One value corresponds to all square residual elements and the other corresponds to all non-square residual elements. (2) by using the theory of quadratic form over finite field, the distribution characteristics of completely nonlinear function sum on three classes of GFQ) to GFGQ) are described.Furthermore, the correlation distribution between sequences and the weight distribution of linear codes are obtained.) the counting problem of MAI Boolean functions of even number elements and MAI Boolean functions of order 1 elasticity is studied.A new lower bound for the number of MAI Boolean functions in even number elements is given, which is superior to the existing results.For MAI Boolean functions of order 1 elasticity, a meaningful lower bound of counting is presented for the first time.In the analysis of cryptographic algorithms, the main achievements of this paper are: 1) the ability of Zodiac algorithm to resist the middle encounter attack is studied.A new 9-wheel discriminator and 10-round discriminator for Zodiac algorithm are found. Based on the two discriminators, 15 rounds and 16 full rounds of Zodiac algorithm are attacked in the middle of the encounter respectively.The results show that the complete 16-round Zodiac-128/192/256 is not resistant to intermediate encounter attack.) the immune ability of low wheel RC6 algorithm to integral attack and impossible differential attack is studied.Four rounds of RC6 algorithm are attacked with integral and five rounds of RC6 algorithm with impossible differential attack. The result of attack is superior to exhaustive search.However, it is difficult to implement the above attack on the RC6 algorithm with more rounds.It is shown that the diffusion performance of the algorithm is greatly enhanced by using the data dependent loop.
【学位授予单位】：国防科学技术大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.1

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