本文選題：混沌序列密碼　切入點(diǎn)：周期特征　出處：《黑龍江大學(xué)》2014年博士論文　論文類型：學(xué)位論文

【摘要】：人們通常借助混沌映射或混沌運(yùn)動獲取通信領(lǐng)域、信息安全領(lǐng)域和計(jì)算機(jī)領(lǐng)域所需的混沌序列密碼,由于混沌運(yùn)動的確定性以及與傳統(tǒng)密碼設(shè)計(jì)需求的相近性,混沌序列密碼受到人們的廣泛關(guān)注和研究。一方面,混沌運(yùn)動的確定性可以使得生成混沌序列密碼的計(jì)算代價遠(yuǎn)小于其他傳統(tǒng)密碼的計(jì)算代價。另一方面,由于混沌運(yùn)動軌道表現(xiàn)出的內(nèi)隨機(jī)性、遍歷性和初值敏感等特性,使得混沌系統(tǒng)相鄰迭代點(diǎn)經(jīng)有限次迭代后可得到完全不同的序列。這種由微小變化引起不同計(jì)算結(jié)果的特性使得混沌序列密碼能夠滿足傳統(tǒng)密碼在擴(kuò)散、偽隨機(jī)兩類重要需求。如基于Logistic映射等經(jīng)典低維映射的混沌序列生成器可以僅使用3至5次浮點(diǎn)四則運(yùn)算能生成一個新的偽隨機(jī)位,并且由混沌映射的初始狀態(tài)仍極難預(yù)測一定時間后的偽隨機(jī)序列�；煦缧蛄忻艽a存在兩方面不足:一是缺少完善的密碼系統(tǒng)安全性和性能分析理論。通常情況下,借助混沌映射或混沌運(yùn)動生成的密碼序列,很難通過數(shù)學(xué)方法找到混沌序列密碼與隨機(jī)序列之間的關(guān)系。評價混沌序列密碼在安全方面的性能還是一個有待解決的難題。二是多數(shù)情況下,混沌序列密碼均表現(xiàn)出隨機(jī)性弱化現(xiàn)象。如混沌序列密碼的周期長度與全部混沌運(yùn)動值域范圍內(nèi)的元素個數(shù)相比存在較大差距,即所謂的混沌“短周期”現(xiàn)象。本文集中研究混沌序列密碼中隨機(jī)弱化現(xiàn)象的檢測與定位。對比典型隨機(jī)序列伯努利實(shí)驗(yàn)序列,重點(diǎn)研究混沌序列密碼在周期現(xiàn)象研究方向存在的影響隨機(jī)性的特征和標(biāo)量,以及這些特征是否具有統(tǒng)計(jì)規(guī)律。探討在不顯著增加計(jì)算代價的前提下,克服或降低這些特征對隨機(jī)弱化現(xiàn)象影響的方法。研究工作和成果包括以下幾個方面:一是依據(jù)二值隨機(jī)序列自身包含的邏輯聯(lián)系,提出了一種擴(kuò)展的周期現(xiàn)象定義;給出了混沌序列密碼的局部周期特性與特定重構(gòu)序列游程特性之間的對應(yīng)關(guān)系;建立了一種檢測序列周期現(xiàn)象的新方法,BSPD(Binary Sequence’s PeriodicDetection)方法,并證明BSPD對于較長周期模板局部周期現(xiàn)象的檢測正確性。二是針對BSPD算法存在的局限性,特別是對BSPD僅能檢出較長周期模板局部周期現(xiàn)象,不能證明可以檢出所有顯示局部周期特征現(xiàn)象等問題,提出了基于頻率的周期現(xiàn)象定義并給出相應(yīng)統(tǒng)計(jì)特征;給出了精確周期、周期性符號、近似周期、顯著局部周期和顯著符號等混沌序列密碼隨機(jī)弱化現(xiàn)象與統(tǒng)計(jì)特征間的對應(yīng)關(guān)系;基于皮爾遜定理,建立了PCDA(Periodicity Component Detecting Algorithm)檢測方法,通過有限延長算法的計(jì)算時間,修正BSPD的兩個局限性。三是基于BSPD算法,討論量化方法對混沌序列密碼隨機(jī)性的影響,對采用經(jīng)典量化方法的混沌系統(tǒng)進(jìn)行局部周期現(xiàn)象分析與驗(yàn)證。得出兩項(xiàng)結(jié)論:一是本研究對混沌短期可預(yù)測性及量化方法選擇難題的猜想普遍存在,二是針對Logistic映射實(shí)驗(yàn)結(jié)果表明,不同的量化方法對相同的實(shí)值混沌序列生成的混沌序列密碼的隨機(jī)性具有不同的影響,統(tǒng)計(jì)BSPD檢測結(jié)果和統(tǒng)計(jì)分析表明,域值量化方法對混沌序列隨機(jī)性的影響小于其他經(jīng)典量化方法。最后,基于分岔圖理論,提出根據(jù)數(shù)字混沌映射關(guān)系從數(shù)字混沌系統(tǒng)的值域中分離隨機(jī)序列的新思想,利用n比特定點(diǎn)整數(shù)精度的Logistic映射,設(shè)計(jì)了一種新的數(shù)字混沌密鑰序列發(fā)生器(EP-PRNG);通過數(shù)學(xué)方法證明了該發(fā)生器輸出的序列周期至少可達(dá)22n?。仿真表明,使用24比特定點(diǎn)整數(shù)精度的Logistic映射時,EP-PRNG生成的混沌序列密碼不但有較長的近似周期,同時也僅存在少量可以被BSPD檢出的隨機(jī)弱化現(xiàn)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.

【學(xué)位授予單位】：黑龍江大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN918.2;O415.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 王國胤,于洪,楊大春;基于條件信息熵的決策表約簡[J];計(jì)算機(jī)學(xué)報(bào);2002年07期

相關(guān)會議論文 前1條

1 陳關(guān)榮;;廣義Lorenz系統(tǒng)及其規(guī)范式[A];第七屆全國非線性動力學(xué)學(xué)術(shù)會議和第九屆全國非線性振動學(xué)術(shù)會議論文集[C];2004年

，

本文編號：1594131