本文为沙特阿卜杜拉国王科技大学（作者：Naif B. Abdulwahed）的硕士论文，共134页。

本文介绍了一种新的基于混沌的高级加密标准（AES）。AES是美国国家标准与技术研究院（NIST）于2001年制定的一种著名的加密算法，本文通过将AES算法的两个原始模块S-Box和密钥调度模块替换为另外两个基于混沌的模块，对AES算法的性能进行了研究。在设计新的模块时，考虑了三个混沌系统：具有乘法非线性的Lorenz系统、具有符号模块非线性的Chen系统和具有阶梯非线性的一维多尺度系统。在对三个系统的输出应用后处理技术，然后执行NIST SP.800-22统计测试后，对其初始条件的敏感性和伪随机数发生器（PRNG）进行评估。

本文提出了一种基于三个混沌系统的AES动态S盒硬件实现方案。此外，基于图形分析、Walsh-Hadamard谱分析和图像加密分析，开发了一个完整的MATLAB软件包来分析混沌产生的S盒。虽然这些S盒是动态的，意味着每当密钥改变时，它们都会被重新生成，但分析结果表明，这些S盒具有严格雪崩准则（SAC）和非线性等优良特性，并在图像加密中得到了应用。此外，本文还提出了一种新的基于Lorenz混沌的AES密钥扩展方案。许多研究者指出AES原有的密钥扩展方法存在一些缺陷，从而提出了基于混沌的密钥扩展方案。通过频率测试和SAC测试，从混淆和扩散的角度对新提出的密钥调度方案进行了分析和评估。结果表明，新的密钥调度方案比原AES密钥调度方案和其他文献中的密钥调度方案更安全。然后利用分治的概念对所提出的设计进行改进，以提高运算速度。这样的增强不仅使AES算法更安全，而且使AES更快，因为它现在可以在更高的频率上工作，并且更高效。

This thesis introduces a new chaos-based Advanced Encryption Standard(AES). The  AES  is a  well-known  encryption algorithm  that  was standardized  by  U.S National Institute  of  Standard and  Technology  (NIST) in  2001.  The thesis investigates and explores the behavior of the AES algorithm byreplacing two of its original modules, namely the S-Box and the Key Schedule,with two other chaos-based modules. Three chaos systems are considered indesigning the new modules which are Lorenz system with multiplicationnonlinearity, Chen system with sign modules nonlinearity, and 1D multiscrollsystem with stair case nonlinearity. The three systems are evaluated on theirsensitivity to initial conditions and as Pseudo Random Number Generators (PRNG)after applying a post-processing technique to their output then performing NISTSP. 800-22 statistical tests. The thesis presents a hardware implementation ofdynamic S-Boxes for AES that are populated using the three chaos systems.Moreover, a full MATLAB package to analyze the chaos generated  S-Boxes based  on  graphical analysis,  Walsh-Hadamard  spectrum analysis, and image encryptionanalysis is developed. Although these S-Boxes are dynamic, meaning they areregenerated whenever the encryption key is changed, the analysis results showthat such S-Boxes exhibit good properties like the Strict Avalanche Criterion(SAC) and the nonlinearity and in the application of image encryption.Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for theAES. Many researchers have pointed out that there are some defects in theoriginal key expansion of AES and thus have motivated such chaos-based keyexpansion proposal.  The  new proposed  key  schedule is  analyzed  and assessed  in  terms of confusion  and  diffusion by  performing  the frequency  and  SAC test  respectively. The obtainedresults show that the new proposed design is more secure than the original  AES key  schedule  and other  proposed  designs in  the  literature.   The proposed design is then enhanced to increase the operating speedusing the divide-and-conquer  concept.  Such enhancement,  did  not only make  the  AES algorithm more secure, but also enabled the AES to be faster, as it cannow operate on higher frequencies, and more area-efficient. 

1.         引言

2.         密码学与AES

3.         CB-PRNG的数字实现

4.         用于AES的新的基于混沌的S盒

5.         用于AES的新的改进的基于混沌的密钥扩展

6.         结论

附录 布尔函数的Walsh-Hadamard变换

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