混沌序列密码周期现象的检测与抵抗研究

发布时间：2018-03-10 16:24

本文选题：混沌序列密码　切入点：周期特征　出处：《黑龙江大学》2014年博士论文　论文类型：学位论文

【摘要】：人们通常借助混沌映射或混沌运动获取通信领域、信息安全领域和计算机领域所需的混沌序列密码,由于混沌运动的确定性以及与传统密码设计需求的相近性,混沌序列密码受到人们的广泛关注和研究。一方面,混沌运动的确定性可以使得生成混沌序列密码的计算代价远小于其他传统密码的计算代价。另一方面,由于混沌运动轨道表现出的内随机性、遍历性和初值敏感等特性,使得混沌系统相邻迭代点经有限次迭代后可得到完全不同的序列。这种由微小变化引起不同计算结果的特性使得混沌序列密码能够满足传统密码在扩散、伪随机两类重要需求。如基于Logistic映射等经典低维映射的混沌序列生成器可以仅使用3至5次浮点四则运算能生成一个新的伪随机位,并且由混沌映射的初始状态仍极难预测一定时间后的伪随机序列。混沌序列密码存在两方面不足:一是缺少完善的密码系统安全性和性能分析理论。通常情况下,借助混沌映射或混沌运动生成的密码序列,很难通过数学方法找到混沌序列密码与随机序列之间的关系。评价混沌序列密码在安全方面的性能还是一个有待解决的难题。二是多数情况下,混沌序列密码均表现出随机性弱化现象。如混沌序列密码的周期长度与全部混沌运动值域范围内的元素个数相比存在较大差距,即所谓的混沌“短周期”现象。本文集中研究混沌序列密码中随机弱化现象的检测与定位。对比典型随机序列伯努利实验序列,重点研究混沌序列密码在周期现象研究方向存在的影响随机性的特征和标量,以及这些特征是否具有统计规律。探讨在不显著增加计算代价的前提下,克服或降低这些特征对随机弱化现象影响的方法。研究工作和成果包括以下几个方面:一是依据二值随机序列自身包含的逻辑联系,提出了一种扩展的周期现象定义;给出了混沌序列密码的局部周期特性与特定重构序列游程特性之间的对应关系;建立了一种检测序列周期现象的新方法,BSPD(Binary Sequence’s PeriodicDetection)方法,并证明BSPD对于较长周期模板局部周期现象的检测正确性。二是针对BSPD算法存在的局限性,特别是对BSPD仅能检出较长周期模板局部周期现象,不能证明可以检出所有显示局部周期特征现象等问题,提出了基于频率的周期现象定义并给出相应统计特征;给出了精确周期、周期性符号、近似周期、显著局部周期和显著符号等混沌序列密码随机弱化现象与统计特征间的对应关系;基于皮尔逊定理,建立了PCDA(Periodicity Component Detecting Algorithm)检测方法,通过有限延长算法的计算时间,修正BSPD的两个局限性。三是基于BSPD算法,讨论量化方法对混沌序列密码随机性的影响,对采用经典量化方法的混沌系统进行局部周期现象分析与验证。得出两项结论:一是本研究对混沌短期可预测性及量化方法选择难题的猜想普遍存在,二是针对Logistic映射实验结果表明,不同的量化方法对相同的实值混沌序列生成的混沌序列密码的随机性具有不同的影响,统计BSPD检测结果和统计分析表明,域值量化方法对混沌序列随机性的影响小于其他经典量化方法。最后,基于分岔图理论,提出根据数字混沌映射关系从数字混沌系统的值域中分离随机序列的新思想,利用n比特定点整数精度的Logistic映射,设计了一种新的数字混沌密钥序列发生器(EP-PRNG);通过数学方法证明了该发生器输出的序列周期至少可达22n?。仿真表明,使用24比特定点整数精度的Logistic映射时,EP-PRNG生成的混沌序列密码不但有较长的近似周期,同时也仅存在少量可以被BSPD检出的随机弱化现象。
[Abstract]:People usually use chaos mapping or chaotic motion capture communication, chaotic sequence cipher field of information security and computer field required, due to proximity and the traditional password design requirements determine the chaotic motion, chaotic sequence cipher by extensive attention and research. On the one hand, the computational cost of determining can make the computational cost of generation chaotic sequence cipher is far less than other traditional password chaos. On the other hand, due to chaotic motions exhibit intrinsic randomness, ergodicity and initial value sensitivity characteristics of the adjacent iterative chaotic system by finite iterations can be obtained after the sequence is completely different. This characteristic by small changes caused by different calculation results the chaotic sequence cipher can satisfy the traditional password in the proliferation of pseudo random two important needs. Based on Logistic mapping and other classic low dimensional mapping Chaotic sequence generator can be shot using only 3 to 5 times the floating-point four operations can generate a new pseudo-random bit, and the initial state of a chaotic mapping is still very difficult to predict the pseudo random sequence after a certain period of time. Chaotic sequence cipher has two shortcomings: one is the lack of perfect system security and code the performance analysis theory. Usually, the password by chaotic mapping or chaotic motion sequence generation, to find the relationship between chaotic sequences with random sequences is very difficult by mathematical methods. The performance evaluation of chaotic cipher sequences in terms of security is still a problem to be solved is two. In most cases, showed a chaotic sequence cipher random weakening phenomenon. Such as the number of cycle length of chaotic cipher sequences and chaotic motion of all range elements there is a big gap compared to the so-called chaotic "short cycle" phenomenon. This paper focuses on the detection and location of the weakening of random chaotic sequence cipher. In contrast to the classical random sequence Bernoulli experimental sequence, features and effects of scalar stochastic focusing on chaotic cipher sequences exist in the direction of cycle, and whether these characteristics are discussed. Statistical law without significantly increasing the computational cost of the method. To overcome or reduce the influence of these characteristics on random weakening phenomena. Research work and achievements include the following aspects: one is based on two valued logic with random sequence contains the proposed definition of an extended cycle phenomenon; the relationship between the local periodicity of chaotic cipher sequences and sequence specific reconstruction run characteristics are given; a new method was established for detecting sequence cycle phenomenon, BSPD (Binary Sequence s PeriodicDetection) method, and prove that for BSPD The correct detection of local periodic phenomenon of long period template. Two is in view of the limitations of BSPD algorithm, especially for BSPD can only be detected in the local cycle phenomenon of long period template, not be detected all showed the local cycle characteristic phenomena, proposed the definition of periodic phenomena based on frequency and the corresponding statistical characteristics are given; exact periodic, periodic symbol, approximate period, correlation between the local cycle and significant symbols of chaotic sequence cipher random weakening and statistical characteristics between; based on the Pearson theorem, established the PCDA (Periodicity Component Detecting Algorithm) detection method, extend the calculation time by two, the limitations of the modified BSPD. The three is based on the BSPD algorithm, discuss the influence of quantization method for chaotic sequence cipher randomness, the chaotic system using the classical quantization method The analysis and verification of local periodic phenomenon. Draw two conclusions: one is the research of chaotic short-term and quantitative method to predict the selection problem of conjecture exists generally, two is for the Logistic mapping experiments show that with different influence of random chaotic sequence cipher quantization method of different chaotic sequences of the same generation. Statistical BSPD test results and statistical analysis showed that the effect of threshold quantization method for chaotic random sequence is less than other classical quantitative methods. Finally, based on the theory of bifurcation diagram, this paper proposes a new idea for separation of random sequences from the range of digital chaotic system according to the digital chaotic mapping, Logistic mapping using n bit fixed-point integer precision design. A new digital chaotic key sequence generator (EP-PRNG); through the mathematical method that the cycle of the sequence generator output at least up to 22n. Copy? It is shown that the chaotic sequence ciphers generated by EP-PRNG not only have a longer approximate period, but also have only a small number of random weakening phenomena that can be detected by BSPD when using 24 bits integer Logistic mapping with integer accuracy.

【学位授予单位】：黑龙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.2;O415.5

【参考文献】