本文選題：偽隨機(jī)序列 + 相關(guān)免疫　； 參考：《西安電子科技大學(xué)》2014年博士論文

【摘要】：偽隨機(jī)序列在模擬仿真、通信系統(tǒng)、軟件測(cè)試以及密碼學(xué)領(lǐng)域都有著廣泛的應(yīng)用。流密碼體制在資源極端受限的領(lǐng)域及需要極高加解密速度的地方依然具有不可比擬的優(yōu)勢(shì)。以往的流密碼通常采用硬件實(shí)現(xiàn)，而軟件實(shí)現(xiàn)效率較低。如何彌補(bǔ)流密碼在軟件方面的弱點(diǎn)，發(fā)揮其優(yōu)勢(shì)，設(shè)計(jì)具有穩(wěn)定性高、速度快和占用資源少的流密碼算法一直是眾多密碼學(xué)家追求的目標(biāo)。 流密碼的優(yōu)勢(shì)是簡(jiǎn)單快速，特別是硬件實(shí)現(xiàn)模塊體積小，運(yùn)行速度遠(yuǎn)高于其他密碼體制。流密碼的劣勢(shì)是僅適用于持續(xù)的保密通信，不適用于靈活的文件加解密。流密碼，特別是其使用的偽隨機(jī)序列在各個(gè)系統(tǒng)中的廣泛應(yīng)用，使得流密碼仍然是密碼學(xué)研究的熱點(diǎn)。密鑰流生成器的設(shè)計(jì)與分析永遠(yuǎn)是流密碼學(xué)研究的中心課題，在這個(gè)領(lǐng)域的研究工作一直都是生機(jī)勃發(fā)，成果倍出。 本文在總結(jié)已有研究結(jié)果的基礎(chǔ)上，，也做了一些有益的嘗試和探索，主要取得以下成果： 1．通過(guò)分析一般布爾函數(shù)的Walsh譜，得到了布爾函數(shù)相關(guān)免疫性的一個(gè)判定條件，給出了n元布爾函數(shù)f(x)是m階相關(guān)免疫的充分條件，并給出了一些相關(guān)免疫布爾函數(shù)的性質(zhì)；通過(guò)討論相關(guān)免疫的和函數(shù)的相關(guān)免疫性，得出了有限個(gè)相關(guān)免疫和函數(shù)為相關(guān)免疫的等價(jià)條件。 2．通過(guò)對(duì)兩個(gè)級(jí)數(shù)互素的LFSR誘導(dǎo)出的乘積序列的分析，得到周期序列的自相關(guān)函數(shù)與乘積序列的重量之間的關(guān)系，由此得到兩個(gè)周期互素的m序列的乘積序列的自相關(guān)函數(shù)的值及其在一個(gè)周期內(nèi)的Hamming重量。 3.通過(guò)對(duì)任意有限個(gè)級(jí)數(shù)互素的m序列的乘積序列的相關(guān)分析，得出對(duì)于任意l個(gè)m序列的乘積序列，其自相關(guān)函數(shù)永遠(yuǎn)是l+1值函數(shù)，且其主峰值R Y(0)很高。 4.基于抵抗BAA攻擊和基于穩(wěn)定性理論的其它攻擊，利用鐘控方法產(chǎn)生的控制序列，并對(duì)鐘控序列生成器的內(nèi)部結(jié)構(gòu)作一定的改進(jìn)，使其各個(gè)移位寄存器產(chǎn)生相互控制的關(guān)系，構(gòu)造了“互控”鐘控移位寄存器模型（該模型及所謂“互控”的概念由本論文作者提出，參見本論文“攻讀博士學(xué)位期間的研究成果”部分），分析了其輸出序列的偽隨機(jī)性質(zhì)，證明了由其產(chǎn)生的序列具有大的周期及相當(dāng)高的線性復(fù)雜度。通過(guò)分析指出，“互控”鐘控移位寄存器序列綜合了安全性和穩(wěn)定性指標(biāo)，理論上是可行的，并且軟件實(shí)現(xiàn)效率較高，具有一定的實(shí)用價(jià)值。
[Abstract]:Pseudorandom sequences are widely used in simulation, communication systems, software testing and cryptography. Stream cryptosystems still have incomparable advantages in areas where resources are extremely limited and where very high encryption and decryption speed is required. In the past, stream ciphers were usually implemented by hardware, but the efficiency of software implementation was low. How to make up for the weakness of stream cipher in software, give full play to its advantages, design a stream cipher algorithm with high stability, high speed and less resources has been the goal pursued by many cryptographers. The advantage of stream cipher is that it is simple and fast, especially the hardware implementation module is small in size and runs much faster than other cryptosystems. The disadvantage of stream cipher is that it is only suitable for continuous secure communication, not for flexible file encryption and decryption. Stream cipher, especially its pseudorandom sequences, is widely used in various systems, which makes stream cipher still a hotspot in cryptography. The design and analysis of key stream generator is always the central subject of stream cryptography. On the basis of summarizing the existing research results, this paper has also made some useful attempts and explorations, and has mainly achieved the following results: 1. By analyzing the Walsh spectrum of general Boolean functions, a criterion for the correlation immunity of Boolean functions is obtained. The sufficient conditions for n-variable Boolean functions to be m-order correlated immunity are given, and some properties of correlated immune Boolean functions are given. By discussing the correlation immunity of the sum function of the correlation immunity, we obtain the equivalent conditions for the finite number of correlation immunity and function to be the correlation immunity. 2. By analyzing the product sequence induced by LFSR of two series, the relation between the autocorrelation function of periodic sequence and the weight of product sequence is obtained. The value of autocorrelation function of the product sequence of m sequence of two periodic coprimes and its Hamming weight in one period are obtained. 3. Through the correlation analysis of the product sequences of the m sequences of any finite series, it is concluded that for the product sequences of any l m sequences, the autocorrelation function is always a l 1 valued function, and its principal peak value R Y 0) is very high. 4. Based on resisting the BAA attack and other attacks based on the stability theory, the control sequence generated by the clock control method is used, and the internal structure of the clock-controlled sequence generator is improved to make each shift register control each other. A clock-controlled shift register model of "mutual control" is constructed (this model and the concept of "intercontrol" are put forward by the author of this paper. See part of this paper "the research results during the study of doctoral degree"), the pseudorandom nature of the output sequence is analyzed. It is proved that the sequence produced by it has large period and high linear complexity. Through analysis, it is pointed out that the "mutual control" clock-controlled shift register sequence integrates the security and stability indexes, is feasible in theory, and has high efficiency in software implementation, and has certain practical value.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN918

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 胡予濮,魏仕民,肖國(guó)鎮(zhèn);廣義Legendre序列和廣義Jacobi序列的線性復(fù)雜度[J];電子學(xué)報(bào);2000年02期

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