正形置换小波变换的一类密码学应用研究
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摘要
现代密码算法都是在计算安全的前提下展开的。随着计算能力的提高,密码技术的安全性受到了很大威胁。研究如何提高分组密码算法的安全性具有重要的学术价值和广泛的应用前景。
论文的主要工作及创新点如下所述：
1.推导出在上正形置换一个精确的计数下界。正形置换枚举和计数的研究是正形置换的研究热点之一。论文利用正形拉丁方截集构造正形置换的方法,在前人工作的基础上,推导出一个更精确的计数下界。说明在上正形置换的存在性及其丰富性。
2.为提高传统分组密码算法的安性,论文提出对数据进行逐级换位、映射的模型,并将其定义为生长树(G-T)。G-T是一种能够应用于密码学中,提高数据安全性的新思路。G-T将各级经过Fk算子处理后的数据块作为各低维空间中某个向量正交基的系数矩阵,通过将低维空间中一系列点进行变换,合成为高维空间上的一个点,使用G-T逐级变换,能够实现数据块的重组。
3.提出借鉴遗传算法构建算子Fk,使用小波逆变换构建算子φ的思路来实现G-T算法。即：使用换位算子和小波包函数的逆向变换逐级实现G-T算法的正变换；使用小波包函数的正向变换,对算子Fk求逆,逐级恢复原始输入码流。对该G-T算法的性能进行的实验和分析说明了在G-T算法控制下,对输入码流进行逐级变换,能够增加穷举攻击者的测算次数,从而提高码流的安全性。
4.针对G-T算法计算复杂的缺陷,提出了利用正形置换及有限域小波实现生长树算法FW-GT。其算子Fk和算子φ分别由正形置换及有限域小波构造生成。基于正形置换的算子Fk具有计算复杂度较低,安全性较高的特点;利用有限域GF(2)上的小波变换构造出算子φ,解决了小波变换引起计算复杂度较高的问题。实验说明,当变换数据量在32k以上时,FW-GT算法的运算时间仅为G-T算法运算时间的一半以下。通过使用FW-GT对明文数据进行预处理,能够使数据具有典型分组密码攻击方法(差分分析、线性分析)的免疫性,从而提高码流安全性。
With the improvement of computing capability, the security of cipher has been queried extensively. It is urgent to study how to enhance cipher (especially block cipher) security intensity. This study has some academic value and application prospect.
Main work and innovations in this thesis are as follows:
1. An excellent lower bound of orthomorphism over Galois field GF(2") was derived. Enumerations and counting of orthomorphism is one of the research hotspot in the study of orthomorphism. Based on the construction of Latin Square transversal, an excellent lower bound of orthomorphism was derived. It shows the existence and plentifulness of orthomorphism over GF(2").
2. A novel model of recurrent transposition and mapping was proposed in this thesis, to guarantee the security of classical block ciphers. It was named as Grow Tree (G-T). G-T could be used in cryptography to improve data security. The clue of G-T is: consider each data block as the coefficient matrix for orthogonal basis in lower dimensional space. Map the coefficient matrix in lower dimensional space to higher dimensional space.
3. It was proposed in this thesis a class of G-T based on crossover operator, mutation operator in genetic algorithm and wavelet transform. Ie. Forward G-T transform should transfer data by operator Fk and the inverse wavelet transformation. Experiments and analysis show the improvement of data security.
4. It was proposed in this thesis another grow tree based on orthomorphism and finite filed wavelet-FW-GT, to improve G-T's computation speed and security intensity. Based on orthomorphism, perators Fk has the merits of low computational complexity and high security intensity. Based on binary filed wavelet transform, peratorφdiscarded the problem of high computational complexity. Experiments show when input data is above 32k, the operation time of FW-GT is only half of G-T. Using FW-GT to transfer data before coding, could improve data anti-attack ability, and improve data security intensity.
论文的主要工作及创新点如下所述：
1.推导出在
2.为提高传统分组密码算法的安性,论文提出对数据进行逐级换位、映射的模型,并将其定义为生长树(G-T)。G-T是一种能够应用于密码学中,提高数据安全性的新思路。G-T将各级经过Fk算子处理后的数据块作为各低维空间中某个向量正交基的系数矩阵,通过将低维空间中一系列点进行变换,合成为高维空间上的一个点,使用G-T逐级变换,能够实现数据块的重组。
3.提出借鉴遗传算法构建算子Fk,使用小波逆变换构建算子φ的思路来实现G-T算法。即：使用换位算子和小波包函数的逆向变换逐级实现G-T算法的正变换；使用小波包函数的正向变换,对算子Fk求逆,逐级恢复原始输入码流。对该G-T算法的性能进行的实验和分析说明了在G-T算法控制下,对输入码流进行逐级变换,能够增加穷举攻击者的测算次数,从而提高码流的安全性。
4.针对G-T算法计算复杂的缺陷,提出了利用正形置换及有限域小波实现生长树算法FW-GT。其算子Fk和算子φ分别由正形置换及有限域小波构造生成。基于正形置换的算子Fk具有计算复杂度较低,安全性较高的特点;利用有限域GF(2)上的小波变换构造出算子φ,解决了小波变换引起计算复杂度较高的问题。实验说明,当变换数据量在32k以上时,FW-GT算法的运算时间仅为G-T算法运算时间的一半以下。通过使用FW-GT对明文数据进行预处理,能够使数据具有典型分组密码攻击方法(差分分析、线性分析)的免疫性,从而提高码流安全性。
With the improvement of computing capability, the security of cipher has been queried extensively. It is urgent to study how to enhance cipher (especially block cipher) security intensity. This study has some academic value and application prospect.
Main work and innovations in this thesis are as follows:
1. An excellent lower bound of orthomorphism over Galois field GF(2") was derived. Enumerations and counting of orthomorphism is one of the research hotspot in the study of orthomorphism. Based on the construction of Latin Square transversal, an excellent lower bound of orthomorphism was derived. It shows the existence and plentifulness of orthomorphism over GF(2").
2. A novel model of recurrent transposition and mapping was proposed in this thesis, to guarantee the security of classical block ciphers. It was named as Grow Tree (G-T). G-T could be used in cryptography to improve data security. The clue of G-T is: consider each data block as the coefficient matrix for orthogonal basis in lower dimensional space. Map the coefficient matrix in lower dimensional space to higher dimensional space.
3. It was proposed in this thesis a class of G-T based on crossover operator, mutation operator in genetic algorithm and wavelet transform. Ie. Forward G-T transform should transfer data by operator Fk and the inverse wavelet transformation. Experiments and analysis show the improvement of data security.
4. It was proposed in this thesis another grow tree based on orthomorphism and finite filed wavelet-FW-GT, to improve G-T's computation speed and security intensity. Based on orthomorphism, perators Fk has the merits of low computational complexity and high security intensity. Based on binary filed wavelet transform, peratorφdiscarded the problem of high computational complexity. Experiments show when input data is above 32k, the operation time of FW-GT is only half of G-T. Using FW-GT to transfer data before coding, could improve data anti-attack ability, and improve data security intensity.
引文
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