【作者】 刘连浩；

【导师】 罗安； 陈松乔；

【作者基本信息】 中南大学 ， 计算机应用技术， 2006， 博士

【摘要】 AES／Rijndael是2000年公布的对敏感数据加密的美国高级加密标准，现在已基本成为商业数据加密的国际标准。AES(Advanced Encryption Standard)的密码分析和应用研究已越来越受到人们的重视。短分组加密技术是在实际应用中使用较多的一种加密技术，如预付费代码表计中使用的就是短分组加密技术。因此，研究解决基于AES的短分组加密及应用中的关键技术问题是当前国内预付费代码表计行业所急需的，对国民经济的发展具有十分重要的意义。本文对AES／Rijndael进行了深入的研究，内容包括：Rijndael算法的基本原理和设计准则，Sbox的代数性质，积分攻击与代数攻击，对AES几种功耗分析方法进行了比较分析研究，设计了基于AES的短分组加密算法，成功实现了预付费代码表计的加密通信。主要成果有：(1)研究分析了S-盒的代数表达式，给出了S-盒9项代数表达式和逆S-盒255项代数表达式；指出S-盒仿射变换周期为4和迭代周期小于88；提出了构造S-盒的改进方案，改进方案构造的S-盒在严格雪崩准则距离、代数表达式、仿射变换周期和迭代周期上都具有较好的代数性质。(2)对Rijndael算法积分攻击和代数攻击进行了分析。研究了Square-5和Square-6攻击，得出的结论是：随着加密轮数的增加，其攻击复杂度超过了穷举搜索，Square攻击对Rijndael算法还不构成威胁。到目前为止，Rijndael的连分式表示、AES嵌入BES以及XSL攻击对Rijndael算法还不构成威胁，Rijndael算法是目前最安全的分组加密算法。(3)对Rijndael算法进行功耗分析。得出结论是：功耗分析的最好的部件为非线性函数，1阶DPA有奇异峰值现象，功耗统计分析的状态位数越多(即高阶DPA)，奇异峰值现象越不明显；CPA分析的效果要好于DPA。提出了基于Walsh谱的功耗分析方法，给出了功耗分析与非线性度的关系，指出了不可能设计出抗功耗分析与抗线性、差分攻击同时最优的S-盒函数。(4)设计并实现了基于AES的6位、8位、12位、16位、32位十进制数短分组加密算法。该算法的最大特点是做到安全的短分组加密、在加密和解密过程中能做到十进制数的明文和密文长度相等，满足特殊行业对加密算法的要求，如预付费代码表计加密。(5)提出了预付费代码表计加密通信工作方式，建立了系统内密钥分配和动态密钥产生的模型，对预付费代码表计进行了仿真实验，对短分组加密算法进行了Square攻击，并对短分组加密系统进行性能测试，各项指标满足实际应用需要。更多还原

【Abstract】 AES/Rijndael algorithm is the Advanced Encryption Standard ofAmerica that is finalized to encrypt the sensitive data in 2000 has becomethe international standard in commerce field. The cryptanalysis andapplication study of AES are becoming more and more importance. Inpractical life, short-block encryption technology is widely applied, suchas pre-payment code-meter. It is necessary to study the key problems inshort block encryption and its application for pre-payment code-meterindustry, which is of great significance to the development of the nationaleconomy.AES/Rijndael algorithm is investigated in this thesis. Researchershave focused on developing the basic principle and design rule ofRijndael algorithm, the algebraic property of S-box, integral attack andalgebraic attack. Several methods of power analysis are compared andstudied. And the short-block encryption algorithm based on AES isdesigned and pre-payment code-meter communications is successfullyrealized. The key contributions follow below.(1) The algebraic expression of S-box is studied, the algebraicexpression with 9 items of S-box and the algebraic expression ofInvS-box with 255 items are given; it is pointed out that the periods ofaffined transformation is 4 and periods of iterative-output is less than 88;an improved method of S-box is proposed, and the new S-box have betteralgebraic properties in strict avalanche criterion, algebraic expression,affined transformation periods and iterative-output periods.(2) Integral attack and algebraic attack of Rijndael are analyzed, theSquare-5 attack and Square-6 attack are studied. Thus it draws theconclusion that the attack complexity of Square attack exceeds exhaustedsearch with encryption round increases. Square attack,conjoint-denominator expression of Rijndael, AES embedded in BES andXSL attack would fail against Rijndael by far. So Rijndael is the safest block cipher.(3) Power analysis of Rijndael is carded through. It is discoveredthat the best component of power analysis is nonlinear function. There issome ghost peak phenomena in DPA. There are more state bits in powerstatistic analysis (viz. high order DPA). The phenomena of ghost peakare less obvious. The effect of CPA analysis is better than DPA’s. Thepower analysis method based on Walsh spectral is proposed, and therelation between power analysis and nonlinear degree is presented. Theconclusion goes that it is impossible to design a S-box that can resist inan optimal way to linear, differential and DPA attacks.(4) The decimal short-block encryption algorithm based on AESused in practical application with the block size 6, 8, 12, 16, 32 bits isdesigned in the thesis. The main characteristic of this algorithm is that itis a safe short-block encryption algorithm and the cipher has the samesize of the corresponding plaintext, so the algorithm can meet the specialrequirement of special industry, for example, the secret communication ofpre-payment code-meter industry.(5) Encryption communication mode of pre-payment code-meter isproposed, models of key allocation and dynamic key creation in systemare established, experiments and simulations of pre-payment code-meterare carried through, Square attack against short-block encryptionalgorithm is executed, tests of short-block encryption system are alsocarried through, and all the performances meet the practical applications.更多还原