【作者】 王大虎；

【导师】 魏学业；

【作者基本信息】 北京交通大学 ， 交通信息工程及控制， 2007， 博士

【摘要】 保密通信是研究信息安全有效传输的技术和理论，一直是关系国计民生和国家安全亟需解决的重大理论和技术难题。非线性理论是研究关于客观世界复杂动力学系统一般规律的科学，一度成为国内外研究热点和前沿课题。利用非线性理论来解决保密通信中的关键技术问题具有重要的理论和实际意义。从上世纪八十年代，利用混沌理论设计保密通信系统的思想受到了越来越多的关注。通常讲，目前存在两种不同的混沌保密通信研究范式，一种是对称保密通信系统，另一种是非对称保密通信系统。本文首先讨论非对称混沌保密通信系统，也就是位于混沌理论和非对称密码学理论之间的研究领域。本文的第二个重点将非线性理论应用到信息隐藏和数字水印中，并取得了一些初步成果。本文基于非线性理论的保密通信研究成果可以归纳为以下三个的部分：提出了一个基于扩展Chebyshev多项式的单向陷门函数，并验证了其是安全和可行的；由此设计了公钥加密、密钥交换、身份认证和数字签名等安全协议；另外研究了信息隐藏和脆弱数字水印相关的问题，提出了相应的基于复合混沌映射的信息隐藏和水印算法，并进行了性能分析。本文的主要成果可以总结以下几点：1．Ljupco Kocarev等人于2003年针对Chcbyshev多项式良好的混沌和半群特性，提出了一种混沌公钥加密算法。但是由于三角函数的固有周期性，攻击者在已知密文的条件下很容易解出明文，使得攻击容易得逞。基于此，本文给出了改进的基于Chebyshev多项式公钥加密算法方案。2．本文研究了Chebyshev多项式和扩展的Chebyshev多项式迭代公式的性质，以及在不同的有限环、有限域和有限域的扩域中，研究了离散Chebyshev问题的困难性。得到如下结论：在迭代参数为整数的条件下，扩展的Chebyshev多项式的计算复杂度等同于离散对数问题和大素数分解的难题。但是由于扩展的Chebyshev多项式用来构成公钥算法时不需要得到一个大素数的过程，其效率要高于RSA，EIGamal算法。3．将Chebyshev多项式结合模运算，将其定义在实数域上进行了扩展，通过理论证明、实验和数据分析，总结出实数域Chebyshev多项式应用于公钥密码的一些性质，根据这些性质，指出Pina Bergamo等人提出的混沌公钥密码中的破解方法是可以避免的。经研究发现实数域上扩展的Chebyshev多项式函数作为公钥加密体系的基础是可行的。4．利用Chebyshev迭代公式固有的半群特性以及模运算的性质，构造了一类具有单向带陷门函数，并将其应用到公钥密码学中。先后提出了基于扩展的Chebyshev多项式的公钥加密、密钥交换协议、网络身份认证协议以及数字签名协议。并从合理性、可行性、安全性和有效性进行了相关分析。结果表明这些算法是行之有效的。5．Di Xiao等人于2005年提出了一种基于混沌映射的可否认认证方案，该方案利用混沌模型分别构造了一个混沌密钥交换协议和公钥加密以及一个混沌Hash函数。本文对其算法进行了分析，发现它在已知密文攻击下是不安全的，在此基础上提出了改进方案。6．对单一Logistic映射的周期性进行了分析，指出其应用在信息隐藏和数字水印领域的缺陷；同时提出了优化的方案即采用复合混沌映射来生成所需要的伪随机序列。基于此，提出了一种基于复合混沌映射和图像融合的数字隐藏技术，充分利用复合混沌映射生成的混沌序列的初值敏感性，达到隐藏的信息目的。实验结果也表明本方法具有较好的隐藏效果以及对一般图象处理具有一定程度的鲁棒性和安全性。7．提出了一种基于复合混沌模型的脆弱水印算法，从理论上分析和验证了算法的检测精确性。脆弱水印算法利用复合混沌动力方程动态地生成认证水印，灵活地控制了定位精度和准确性，且能抵抗局部替换等伪认证。基于整数小波的空频篡改估脆弱算法不仅能准确地判断空间篡改的位置，还能估计图像经历了哪种滤波，在一定程度上能够判断复合篡改的攻击。图像的完整性认证既不需要原始图像，也不需要原始水印，是一种盲检算法。更多还原

【Abstract】 Secure communication technology is involved in the transmission of information safe and efficient, and concerned with national security and the national economy and the people’s livelihood. At the same time, nonlinear science is concerned about exploring the law of complex system, and become the focus and hotspot of researching. Therefore, it is significant theoretically and practically to adapt non-linear theory to constructing the system of secure communication.Since 1980s, the idea of using chaotic systems to design secure communication system has attracted more and more attention. The use of chaos in cryptography depends on the natural relation between the two research areas: strong dynamical properties of chaotic systems imply strong cryptographical properties of cryptosystems, and the basic way to make cryptosystems with good strong cryptographical properties implies quasi-chaos. Generally speaking, there are two paradigms of applying chaos for secure applications: symmetrical secure communication and asymmetrical secure communication. This dissertation firstly focuses on asymmetrical secure communication, i.e., the area lying between chaos theory and pure cryptography in asymmetrical secure communication system. Meanwhile, we apply non-linear theory to information hiding and digital watermark and gain some elementary results.Our contributions in this dissertation involve the following three aspects about non-linear secure communication: theoretical analyses results in a one-way trapdoor function based on extended Chebyshev polynomials and the verification of the feasibility and security. Further few secure algorithms are presented. In the end, the methods of information hiding and fragile digital watermark are researched, and the algorithms about them based on multi-chaos map present. The main achievements contained in this dissertation are as follows:1. In 2003, Ljupco Kocarev etc used the properties of chaos and semi-group, and proposed a public-key cipher based on Chebyshev polynomials. But any attacker easily gets the plaintext message given known ciphertext for the inherent periodic property of trigonometric function. Thus, an improved public-key encryption project which is based on Chebyshev polynomials, is presented.2. It is investigated for the properties of Chebyshev polynomials and extended Chebyshev iteration formula, and the difficulty of discrete Chebyshev problem. And the conclusion has been reached that if the iteration parameters are integer, the compute complexity of extended Chebyshev polynomials is the same as discrete logarithm problem and integer factoring problem.Because that the public-key encryption scheme based on extended Chebyshev polynomials doesn’t need a large prime, the efficiency is higher than conventional RSA and EIGamal algorithms, and at least no lower than them.3. By combining Chebyshev polynomials with modulus compute, extending Chebyshev polynomials’ definition domain to real number, the following conclusion has been drawn by theoretic verification and data analyses: based on the properties of extended Chebyshev polynomials in real number, the proposed break scheme from Pina Bergamo et al can be avoided. And it is feasible to use extended Chebyshev polynomials to construct public-key encryption in theory.4. A one-way trapdoor function based on the properties of semi-group and modulus compute of Chebyshev polynomials iteration formula has been constructed and applied to public-key cryptography. The relative public-key encryption, key exchange, authentication identity and digital signal schemes are presented. These are proven as feasible and efficient.5. In 2005, Di Xiao proposed an entire deniable protocol based on chaotic maps, which used chaotic model to a chaotic key exchange scheme and a chaotic hash function. After the analysis of the algorithms, the scheme above is insecure. Thus an improved scheme is presented.6. A single Logistic map is analysed, the fault of its application to the field of information hiding and digital watermarking found, and the relative optimal project based on multi-chaos map present.To use the property of dependence on initial value,we present the digital hiding algorithm based on multi-chaos map and image mergence.It is proven that the algorithm is robust,secure.7. An fragile watermarking with high precision based on multi-chaotic model is proposed, and detection accuracy is also proposed and analyzed. The fragile watermark algorithm, which uses chaotic systems to produce watermark dynamically, can control location precision and resist pse- udo-authentication. Tampering estimation algorithm in spatial and frequency domain based on integer DWT domain not only can decide the position of spatial tampering, but also estimate the sorts of filtering that the image has undergone. The integrity authentication process is completely blind which requires neither the original image nor the original watermark.更多还原