基于動(dòng)力學(xué)特性的混沌密碼算法研究
發(fā)布時(shí)間：2019-01-05 21:17
【摘要】：自1965年美國(guó)氣象學(xué)家Lorenz發(fā)現(xiàn)混沌現(xiàn)象以來(lái)，混沌理論受到越來(lái)越多的關(guān)注。混沌系統(tǒng)因具有對(duì)初始值和系統(tǒng)參數(shù)的敏感依賴性、遍歷性和存在周期無(wú)限長(zhǎng)的軌道的性質(zhì)，這些是理想的密碼系統(tǒng)所追求的性質(zhì)。一個(gè)簡(jiǎn)單的混沌動(dòng)力系統(tǒng)卻有著非常復(fù)雜的行為，這些復(fù)雜行為有著很好的密碼學(xué)性質(zhì)，這正是混沌密碼學(xué)的價(jià)值所在。另一方面，建立在數(shù)論、代數(shù)及算法復(fù)雜性理論基礎(chǔ)之上傳統(tǒng)密碼算法正遭遇各種挑戰(zhàn)，隨著密碼分析方法和研究手段的不斷成熟，DES，MD5，SHA1等原來(lái)被認(rèn)為安全的系統(tǒng)最近接連被破解，量子計(jì)算的發(fā)展也對(duì)非對(duì)稱密碼算法造成了巨大威脅。新的密碼設(shè)計(jì)理論正成為一種迫切的需求，而從全新角度進(jìn)行設(shè)計(jì)的混沌密碼算法正是一種良好的替代方案。 然而，現(xiàn)存的混沌密碼算法還存在諸多問(wèn)題，他們往往因?yàn)閯?dòng)力學(xué)特性差或者是算法結(jié)構(gòu)設(shè)計(jì)存在問(wèn)題而被破譯，現(xiàn)有的混沌密碼算法還沒(méi)有一個(gè)得到了廣泛的應(yīng)用。針對(duì)上述問(wèn)題，本文從以下幾個(gè)方面進(jìn)行了研究： （1）研究了混沌系統(tǒng)動(dòng)力學(xué)特性對(duì)密碼算法的影響。通過(guò)對(duì)Lyapunov指數(shù)譜的計(jì)算可以明確混沌系統(tǒng)在哪些參數(shù)區(qū)域是非混沌的，并且可以衡量初始時(shí)刻相鄰軌道隨時(shí)間變化分離的快慢程度.具有恒正的Lyapunov指數(shù)譜在密碼學(xué)中是比較理想的性質(zhì)。混沌系統(tǒng)的極限點(diǎn)集表明了系統(tǒng)長(zhǎng)時(shí)間運(yùn)行后應(yīng)該保持的穩(wěn)定的性質(zhì)，在密碼學(xué)中理想的系統(tǒng)其極限狀況應(yīng)該盡量保持均勻以免泄露系統(tǒng)的特征。復(fù)雜度的研究可以表明系統(tǒng)生成的序列的隨機(jī)的程度，復(fù)雜度高的系統(tǒng)產(chǎn)生的序列往往更難以預(yù)測(cè)。 （2）在分析了上述動(dòng)力學(xué)性質(zhì)后，提出了一類低維的具有Markov分割性質(zhì)的混沌系統(tǒng)T(x, p, sigma)。其將區(qū)間級(jí)別的變換作為分析的基礎(chǔ)，可利用符號(hào)動(dòng)力學(xué)對(duì)其做詳細(xì)的研究�？梢詮睦碚撋献C明它有恒正的Lyapunov指數(shù)，而且其極限分布是均勻分布。通過(guò)參數(shù)的調(diào)整，在近似熵和符號(hào)熵的評(píng)價(jià)標(biāo)準(zhǔn)下它的復(fù)雜度可以遠(yuǎn)高于Logistic映射和Tent映射，利用它產(chǎn)生的序列具有更好的隨機(jī)性。 （3）進(jìn)一步的，，分析了現(xiàn)有混沌圖像加密算法結(jié)構(gòu)存在的問(wèn)題�，F(xiàn)有的混沌圖像加密算法大多是基于Fridrich結(jié)構(gòu)的，它有兩個(gè)部分組成，一個(gè)置亂矩陣，一個(gè)擴(kuò)散函數(shù)。通過(guò)對(duì)被破譯的混沌算法進(jìn)行分析，發(fā)現(xiàn)其擴(kuò)散函數(shù)的設(shè)計(jì)結(jié)構(gòu)過(guò)于簡(jiǎn)單易破解，而置亂矩陣是可逆矩陣，這樣一來(lái)，通過(guò)選擇明文攻擊可以分析出算法的密鑰流，進(jìn)而可以破解出原始明文圖像。 （4）設(shè)計(jì)了一種新的圖像加密算法。利用本文所構(gòu)造的新的混沌系統(tǒng)去設(shè)計(jì)一個(gè)新的密鑰生成函數(shù)，因具備理想的動(dòng)力學(xué)性質(zhì)，其產(chǎn)生的密鑰比較理想；另外，通過(guò)采用不同群中的加法混合運(yùn)算改進(jìn)了圖像加密算法的擴(kuò)散函數(shù)使其難以破解。通過(guò)對(duì)算法基本性質(zhì)的測(cè)試可以看出本文設(shè)計(jì)的算法可以通過(guò)目前圖像加密算法的所有測(cè)試，另外算法可以抵抗通常的攻擊。 （5）在FPGA的平臺(tái)上實(shí)現(xiàn)了本文的混沌圖像加密算法。給出了算法的實(shí)現(xiàn)方法，利用FPGA的平臺(tái)特性優(yōu)化了算法的可并行執(zhí)行部分，并利用流水線技術(shù)做了進(jìn)一步優(yōu)化，使其在資源消耗不多的情況下有不錯(cuò)的計(jì)算速度。 研究結(jié)果表明，本文采用的混沌系統(tǒng)具有比較理想的動(dòng)力學(xué)特性，這些理想的特性使得此系統(tǒng)特別適合用于密碼算法的設(shè)計(jì)。本文設(shè)計(jì)的圖像加密算法安全性高，計(jì)算效率好具有不錯(cuò)的應(yīng)用前景。
[Abstract]:Since 1965, the American meteorologist, Lorenz, has been more and more concerned about the mix-up theory. the hybrid system is of the nature of an ideal cryptographic system due to the nature of the orbit having an infinite length of sensitivity, ergodic, and existence of the initial value and system parameters. A simple hybrid power system has very complex behavior, and these complex behaviors have very good cryptographic properties, which is the value of the hybrid cryptography. On the other hand, the traditional cryptographic algorithm based on the theory of number theory, algebra and algorithm complexity is faced with various challenges, and with the development of the password analysis method and the research means, the systems of DES, MD5, SHA1, etc., which are originally thought to be safe, are recently cracked, The development of quantum computation also poses a great threat to the asymmetric cryptographic algorithm. The new design theory of the code is becoming an urgent need, and the mixed-code algorithm designed from the new angle is a good alternative. However, there are many problems in the existing hybrid cryptographic algorithms, which are often deciphered because of the poor dynamic characteristics or the problems of the structural design of the algorithm, and the existing hybrid cryptographic algorithm has not been widely used. In the light of the above problems, this paper makes a research on the following aspects In this paper, the dynamic characteristics of the hybrid system and the code algorithm are studied in this paper. The influence of the time-varying separation of the adjacent tracks in the initial time can be measured by the calculation of the Lyapunov exponent spectrum. Slow degree. The Lyapunov exponent spectrum with constant positive is more ideal in cryptography The limit point set of the hybrid system shows the stable property that should be kept after the system is running for a long time. The limit condition of the ideal system in cryptography should be kept as uniform as possible in order to avoid the leakage system. The study of complexity can indicate the random degree of the system generated by the system, and the sequence generated by the system with high complexity tends to be more difficult. In this paper, a class of low-dimensional hybrid system T (x, p, s) with Markov-splitting properties is proposed after analyzing the dynamic properties. igma). It uses the transformation of the interval level as the basis for the analysis and can be done using the symbolic dynamics In this paper, we can theoretically prove that it has a constant positive Lyapunov exponent and its limit distribution It is a uniform distribution. By adjusting the parameters, its complexity can be much higher than the Logistic mapping and the Tent mapping under the evaluation criteria of the approximate entropy and the symbol entropy. good randomness. (3) Further, the existing hybrid image encryption algorithm is analyzed The existing hybrid image encryption algorithm is based on the Fridrich structure, which consists of two parts, a scrambling matrix, It is found that the design structure of the diffusion function is too simple and easy to crack, and the scrambling matrix is a reversible matrix, so that the key stream of the algorithm can be analyzed by selecting the plaintext attack, which can then be cracked. The original plain text image is shown. (4) It is designed In this paper, a new key generation function is designed by using the new hybrid system constructed in this paper. Because of the ideal dynamic property, the key generated by the new key generation function is ideal; in addition, the expansion of the image encryption algorithm is improved by using the addition and mixing operation in different groups. The hash function makes it difficult to crack. By testing the basic properties of the algorithm, it can be seen that the algorithm designed in this paper can pass all the tests of the current image encryption algorithm, and the other algorithms can resist the usual attack. (5) It is implemented on the platform of the FPGA In this paper, the hybrid image encryption algorithm is given. The implementation method of the algorithm is given. The executable part of the algorithm is optimized by using the platform characteristics of the FPGA, and further optimization is made by using the pipeline technology, so that it is not much consumed in the resource consumption. The results show that the hybrid system used in this paper has the ideal dynamic characteristics, and these ideal characteristics make the system It is especially suitable for the design of the cipher algorithm. The security of the image encryption algorithm designed in this paper is high,
【學(xué)位授予單位】：中國(guó)科學(xué)院研究生院(長(zhǎng)春光學(xué)精密機(jī)械與物理研究所)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN918.4;O415.5
[Abstract]:Since 1965, the American meteorologist, Lorenz, has been more and more concerned about the mix-up theory. the hybrid system is of the nature of an ideal cryptographic system due to the nature of the orbit having an infinite length of sensitivity, ergodic, and existence of the initial value and system parameters. A simple hybrid power system has very complex behavior, and these complex behaviors have very good cryptographic properties, which is the value of the hybrid cryptography. On the other hand, the traditional cryptographic algorithm based on the theory of number theory, algebra and algorithm complexity is faced with various challenges, and with the development of the password analysis method and the research means, the systems of DES, MD5, SHA1, etc., which are originally thought to be safe, are recently cracked, The development of quantum computation also poses a great threat to the asymmetric cryptographic algorithm. The new design theory of the code is becoming an urgent need, and the mixed-code algorithm designed from the new angle is a good alternative. However, there are many problems in the existing hybrid cryptographic algorithms, which are often deciphered because of the poor dynamic characteristics or the problems of the structural design of the algorithm, and the existing hybrid cryptographic algorithm has not been widely used. In the light of the above problems, this paper makes a research on the following aspects In this paper, the dynamic characteristics of the hybrid system and the code algorithm are studied in this paper. The influence of the time-varying separation of the adjacent tracks in the initial time can be measured by the calculation of the Lyapunov exponent spectrum. Slow degree. The Lyapunov exponent spectrum with constant positive is more ideal in cryptography The limit point set of the hybrid system shows the stable property that should be kept after the system is running for a long time. The limit condition of the ideal system in cryptography should be kept as uniform as possible in order to avoid the leakage system. The study of complexity can indicate the random degree of the system generated by the system, and the sequence generated by the system with high complexity tends to be more difficult. In this paper, a class of low-dimensional hybrid system T (x, p, s) with Markov-splitting properties is proposed after analyzing the dynamic properties. igma). It uses the transformation of the interval level as the basis for the analysis and can be done using the symbolic dynamics In this paper, we can theoretically prove that it has a constant positive Lyapunov exponent and its limit distribution It is a uniform distribution. By adjusting the parameters, its complexity can be much higher than the Logistic mapping and the Tent mapping under the evaluation criteria of the approximate entropy and the symbol entropy. good randomness. (3) Further, the existing hybrid image encryption algorithm is analyzed The existing hybrid image encryption algorithm is based on the Fridrich structure, which consists of two parts, a scrambling matrix, It is found that the design structure of the diffusion function is too simple and easy to crack, and the scrambling matrix is a reversible matrix, so that the key stream of the algorithm can be analyzed by selecting the plaintext attack, which can then be cracked. The original plain text image is shown. (4) It is designed In this paper, a new key generation function is designed by using the new hybrid system constructed in this paper. Because of the ideal dynamic property, the key generated by the new key generation function is ideal; in addition, the expansion of the image encryption algorithm is improved by using the addition and mixing operation in different groups. The hash function makes it difficult to crack. By testing the basic properties of the algorithm, it can be seen that the algorithm designed in this paper can pass all the tests of the current image encryption algorithm, and the other algorithms can resist the usual attack. (5) It is implemented on the platform of the FPGA In this paper, the hybrid image encryption algorithm is given. The implementation method of the algorithm is given. The executable part of the algorithm is optimized by using the platform characteristics of the FPGA, and further optimization is made by using the pipeline technology, so that it is not much consumed in the resource consumption. The results show that the hybrid system used in this paper has the ideal dynamic characteristics, and these ideal characteristics make the system It is especially suitable for the design of the cipher algorithm. The security of the image encryption algorithm designed in this paper is high,
【學(xué)位授予單位】：中國(guó)科學(xué)院研究生院(長(zhǎng)春光學(xué)精密機(jī)械與物理研究所)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN918.4;O415.5
【參考文獻(xiàn)】
相關(guān)期刊論文 前10條
1 蔡軍輝;雷仲魁;孫繼如;;基于FPGA的數(shù)字視頻加解密系統(tǒng)設(shè)計(jì)[J];信息化研究;2009年11期
2 章明朝;于曉;李佩s
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