查询词典 signature of permutation

We provide a substitution box, exponential permutation which has much measurable security, and give a enumerating result and a fast algorithm of calculating such permutation. An almost perfect nonlinear exponential permutation with high algebric degree is proposed. with some discussion on how to select the parameters of such permutation. The experimental result shows us a conjecture that there exists no such permutation over even dimensional space. As a way of generating substitution boxes, we briefly point out the cryptographic weakness of the exponential functions derived from such permutation. We also present two new cryptographic indexes, fixed point and cyclic structure, on which we investigate the performance of such permutation. Finally, we give a viewpoint about the application of correlation immune functions in designing substitution boxes.

提供了一种可度量安全强度的代换盒－幂置换；详细阐述了幂置换的实现和计数问题；给出了一种计算幂置换的快速算法；从几乎完善非线性幂置换角度讨论了幂置换参数的选取，并提出了一种高次几乎完善非线性置换；通过试验给出了关于偶数维空间上几乎完善非线性幂置换的一个猜想；简要给出了由幂置换派生出的幂函数的密码局限性；针对幂置换，提出了两个密码安全指标：不动点和循环结构；证明了幂置换在这两个指标下的密码性能；简要讨论了相关免疫函数与代换盒设计的关系。

The orbits of the point stabilizer of a finite permutation group are called the suborbits of the permutation group. The determination of the suborbits of a permutation group is one of the basic problems in the permutation group theory. It plays an important role in the study of combinatorial structures.

一个有限传递置换群的点稳定子群的轨道称为该群的次轨道，决定一个置换群的次轨道结构是置换群理论的基本问题之一，它在组合结构的研究中有着重要的应用。

The main content of this thesis includes six parts. First of all, it is a comprehensive systematic introduction about RSA algorithm including the present application situation and principle of RSA algorithm----producing big prime numbers and secret keys, the encryption arithmetic for information and the decryption for secret information, which establish the theory foundation for achieving concrete; secondly, it introduces some basic conception of RSA digital signature and theory of digital signature realizing process; thirdly, it introduces the basic principle of MD5 algorithm; fourthly, it states design and realization of RSA digital signature in detail. The main modules includes producing RSA secret keys, implementation of RSA encryption algorithm and decryption algorithm, producing message digest and realizing digital signature and verification by RSA; the fifth, it carries on testing entirely, analyzing and improving for this system;The sixth, it analyses the security of RSA digital signature and points out the development direction of RSA digital signature.

本文主要研究的内容包括：第一，对RSA算法进行了全面系统的介绍，包括RSA算法的应用现状和原理—大素数的产生、密钥对的产生、对明文的加密运算和密文的解密运算，为具体实现打下了理论基础；第二，介绍了RSA数字签名的一些基本概念和数字签名的理论实现过程；第三，对MD5算法基本原理的介绍；第四，详述了RSA数字签名的设计与实现，主要实现的模块包括RSA密钥的产生，RSA加密算法和解密算法的实现，消息摘要MD的生成以及利用RSA算法实现数字签名和签名的验证；第五，对该系统进行了整体的测试和分析改进；第六，分析了RSA数字签名的安全性，指出了RSA数字签名的发展方向。

Characteristics of a number of gates from the set of all generalized Toffoli gates are studied. Any permutation S is proved to be generated by a n-cycle δ and a permutation τ=i(subscript j, i together. It shows that any neighboring 2-cycle permutation can be generated by at most two NOT gates without ancilla bit.

本文研究了生成Toffoli门集合的可逆逻辑门数的特点，证明了任意置换S可以由n-轮换δ和一个置换τ=i(下标 j，i生成，同时证明了相邻2-轮换可由至多两个NOT门在不增加额外信息位的情况下生成。

After comparing the two type of tests,we came to some conclusions.The tests based on binomial test can be regarded as some kind of permutation tests under certain definition of "permutaton".If the tests are related to statistics,then whether they can be viewed as permutation tests depends on if the value of the probability,p,is known where p is the population parameter in the null hypothesis.For tests like Kolmogorov goodness-of-fit test,since the statistics is calculated based on empirical distribution function,hence no matter how we repermutate the observations,the order statistics is the same.This kind of tests can't be regarded as permutation tests.

我们得到的结论为：在一般的无母数检定中，如果检定与binomial test相关，基本上都可以视作排列检定的一种；与卡方检定相关的检定，基本上和p值已知或是未知有关，这个p值为原始假设下所要检定的母体机率值；其他检定如Kolmogorov goodness-of-fit test，由於统计量的值是根据empirical distribution function决定，而不论如何重新排列样本，其顺序统计量都不变，所以无法视为一种排列检定。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

An almost perfect nonlinear exponential permutation with high algebric degree is proposed, with some discussion on how to select the parameters of such permutation. The experimental result shows us a conjecture that there exists no such permutation over even dimensional space.

作者所取得的主要研究结果如下：(1)讨论了分组密码的条件攻击和技术攻击方法；全面总结了分组密码算法设计应当遵循的七项准则；概括了分组密码的四种强化技术；设计了一种新的三重加密方案NTE。

The four round MISTY-type and the three round dual MISTY-type transformation are optimized by replacing the first round pseudorandom permutation with XOR-universal permutation and employing identical pseudorandom permutation in the second and the third round.

在保持其安全性不变的情况下，把4轮MISTY结构中第1轮的伪随机置换，用一个XOR-泛置换代替，第2，第3轮采用相同的伪随机置换，3轮结构中第1轮的伪随机置换用XOR-泛置换代替，其它轮相同。

In terms of Latin squares, an isotopy is given by a permutation of rows α, a permutation of columns β, and a permutation on the underlying element set γ.

在拉丁方中，三元组由第α和第β列的一个置换以及其余集合上的一个置换γ给出。

If the sequence is already in the last permutation, then next_permutation reorders the sequence to be the lowest permutation and returns false. Otherwise, it transforms the input sequence into the next permutation, which is the lexicographically next ordered sequence and returns true.

如果序列已经是在最后一个排列中，则 next_permutation 将序列重新排列为最低排列并返回 false；否则，它将输入序列变换为下一个排列，即字典序的下一个排列，并返回 true。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。