Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

0 IntroductionThe Orthomorphic permutation is one kind of the com-pleteness mapped,andis also the especial Boolean per-mutation. The Boolean permutations have good characteristicsin cryptosystems .It can be consideredthe permutationthat isany cryptosystems lacking outstretched information. For ex-ample,DES(data encryption standard) , which is a standardencryption system,is the permutationin whichthe proclai medin writing controlled by the secret key and RSA( Rivest ,Shamir , Adleman) is a…     

关于正形置换的构造

基于正形置换的定义,给出一个实用的正形置换构造算法及其应用,得到全部16次正形置换的计数为244 744 192;通过求解有限域Fm2上矩阵的逆矩阵,给出一个简捷的Fm2上与一个置换对应的置换多项式构造方法,得到了有限域F42上的全部正形置换多项式,并且证明其多项式次数均小于14.证明了有限域Fm2上置换多项式的多项式次数均小于2m-1.     

Quick trickle permutation based on quick trickle characteristic sequence

0　IntroductionAblockcipherwithoutdataextensionorexpressionisaper mutation .Thesecurityofablockcipherschemeiscorrela tivewiththe permutations.Quicktrickle permutation[1 ] canmakethedatadisorderedwhenactingatthedataandmakeallprobabledistancebetweentwoelementsappear,soithasgoodcryptographicpropertiesandcanbeusedintheblockcipherwhichrequireshighsecurity.Aprivatekeyblockcipherisapermutationinn dimensionvectorspaceoverF2 atthecontrolofakey[2 ,3] .Moreover,manyblockciphersusepermutationstoexecuteso…     

Improved zero-sum distinguisher for full round <Emphasis Type="Italic">Keccak-f</Emphasis> permutation

Keccak is one of the five hash functions selected for the final round of the SHA-3 competition,and its inner primitive is a permutation called Keccak-f.In this paper,we observe that for the inverse of the only nonlinear transformation in Keccak-f,the algebraic degree of any output coordinate and the one of the product of any two output coordinates are both 3,which is 2 less than its size of 5.Combining this observation with a proposition on the upper bound of the degree of iterated permutations,we improve the zero-sum distinguisher for the Keccak-f permutation with full 24 rounds by lowering the size of the zero-sum partition from 21590 to 21575.     

多输出m值逻辑函数的谱特征

讨论了剩余类环上多输出多值逻辑函数的谱特征,给出了多输出m值逻辑函数的广义一阶Chrestenson谱与单输出m值逻辑函数Chrestenson谱之间的关系,得到了多输出m值逻辑函数的广义一阶Chrestenson谱与其函数之间的转换公式,接着给出了多输出m值逻辑函数的广义一阶Chrestenson谱的概率表示式.同时讨论了多输出m值逻辑函数的广义一阶Chrestenson线性谱和循环谱之间的关系,并给出了这两种谱之间的关系式.     

n阶排列中相同逆序数的排列个数递推算法

用生成函数(母函数)讨论了n阶排除中具有相同逆序数k的排列个数d(n,k)的新递推公式,将d(n,k)的计算转化成其生成函数的计算,从而得到一个可以用计算机完成的算法.     

基于可逆Hash函数的DES型超伪随机置换的新构造

为优化Luby和Rackoff给出的DES型置换的构造,给出4-轮DES型超伪随机置换的构造ψ（h,f,f,h^-1）,指出首末两轮双对称ε-△-通用可逆Hash函数和中间两轮DES-型随机置换的组合构造是超伪随机置换．构造降低了对首末轮函数的要求,提高了DES型超伪随机置换在运算和密钥使用方面的效率．     

An Improved Genetic Algorithm for Problem of Genome Rearrangement

In view of the fact that the problem of sorting unsigned permutation by reversal is NP-hard, while the problem of sorting signed permutation by reversal can be solved easily, in this paper, we first transform an unsigned permutation of length n,π （π1 ,… ,πn）, into a set S（π） containing 2^n signed permutations, so that the reversal distance of π is equal to the reversal distance of the optimal signed permutation in S（π）. Then analyze the structural features of S（π） by creating a directed graph and induce a new computing model of this question. Finally, an improved genetic algorithm for solving the new model is proposed. Experimental results show that the proposed model and algorithm is very efficient in practice.     

浅谈置换符号的几种表示法

文章讨论置换符号的三种表示法,利用逆序数和对换的个数来表示置换符号的方法。通过这两种方法提出了置换的循环结构来定义置换的符号,而且举例说明。     

Formulations of some bit switching functions in DES

In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realized by using table look-up technique in the implementation of the cryptosystem. This paper presents explicit formulas for the initial permutation IP, its inverse IP-1 , the expansion function E, and the permuted choice PC₁. It also gives the program realizations of these functions in C++ applying these formulas. With the advantage of the omission of the storage space for these matrixes and the tedious inputs of tables in the implementations of DES, our experimental results shows that the explicit formulas are useful in some situations, such as wireless sensor networks where the memory capacity is limited, especially when the size of file for encrypting is not too large, preferably smaller than 256KB.     

A note on m -weights of linear codes

m-weight, as a new generalization of classical Hamming weight, was discussed in this paper. A condition for the existence of linear codes of certainm-weights was given; the Singleton bound, Plotkin bound and Sphere Parking bound of Hamming weight were correspondingly generalized to them-weight. Foundation item: Supported by the National Program on Basic Sciences (973 Program, G1999075102) Biography: YUAN Yuan (1979-), female, Ph. D candidate, research directions: combination and codes.     

多输出函数的自相关函数特征及Walsh谱特征

给出了多输出函数自相关函数的定义,并得到了多输出函数的自相关函数特征和Walsh谱特征的关系式;证明了多输出函数的Walsh谱的两种变换的关系式、Plancheral公式、能量守恒公式、卷积公式;得到了谱的平稳性．有助于进一步研究多输出函数的密码学性质．     

最大线性正形置换及其性质

根据最大线性正形置换可以用于密码体制中非线性置换的构造，利用有限域上的多项式理论以及矩阵理论，研究了最大线性正形置换T的性质．给出了T的幂仍就是最大线性正形置换的充分条件，证明了T的特征多项式为F2上的本原多项式，进一步证明了F2^n为T的不可约空间．     

基于重构子互相关的BOC无模糊度跟踪方法

针对BOC体制信号的自相关函数具有多峰性质导致BOC存在的模糊跟踪问题,提出了子互相关函数概念及基于重构子互相关函数的无模糊度跟踪方法.通过分析对比各子互相关函数,重构生成仅具有单一相关峰并保持BOC窄相关特性的相关函数.以BOC(1,1)和BOC(10,5)为例进行仿真与分析,模糊度有效性表明本文方法相比ASPeCT与BPSK-like能够更好地去除副峰且保持窄相关,鉴相曲线表明对于BOC(1,1)与BOC(10,5),本文方法相对BPSK-like的线性区域斜率增益分别为5.2 dB与7.2 dB,抗多径性能表明本文方法相比ASPeCT与BPSK-like的多径误差最小,抗噪声性能表明对于BOC(1,1)与BOC(10,5)本文方法相比BPSK-like的码跟踪误差标准差分别减少了0.046 Tc与0.030 Tc.     

On the Symmetry Classes of Functions

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.     

潮间带贝克喜盐草土壤种子库空间分布及其生物影响因素

【目的】为探讨贝克喜盐草(Halophila beccarii Ascherson)种群更新及濒危机制,研究其土壤种子库空间分布特征及其生物影响因素。【方法】对广西合浦榕根山、防城港交东、防城港山心3个贝克喜盐草典型分布点进行调查取样,统计(或称量)样品种子、直立茎、雌花、果实数量、地上部分生物量和地下部分生物量。【结果】从水平方向分布来看,相同方向上不同距离处贝克喜盐草土壤种子库密度差异不显著,海草场潮沟、外海、海岸方向一侧的土壤种子库密度在榕根山和交东分别为271粒/m~2、180粒/m~2、52粒/m~2和52粒/m~2、23粒/m~2、16粒/m~2,差异显著,可见该海草种子水平空间分布格局受到落潮水流与落潮后流向潮沟的微水流的影响,受距离影响较弱;垂直方向上,上层(0~4cm)、中层(4~8cm)、下层(8~12cm)土壤底质中贝克喜盐草种子数量分别占总量的73.0%、20.8%和6.2%,上层土壤中种子数量显著高于中层和下层(P0.05),表明绝大部分的种子分布于土壤表层(0~8cm);贝克喜盐草海草场土壤种子库密度与其种群雌花密度、直立茎密度存在极显著线性正相关关系,其相关系数r分别为0.722 9(P0.01)、0.845 1(P0.01),与果实密度、地上部分生物量及总生物量呈多项式曲线关系。【结论】贝克喜盐草土壤种子库的水平空间分布受潮沟、入海河流等外界环境和地上植被的种群属性、种子自身特性等因素的影响,垂直方向上主要分布在表层底质中,且地上植被的种群属性是决定土壤种子库密度的关键因素。     

广西南丹山口林场引种秃杉的栽培技术初探

【目的】为解决杉木长期连栽产量递减的问题,总结杉木轮换树种秃杉(Taiwania flousiana)的引种栽培技术。【方法】从秃杉种源选择、种子采集、壮苗培育技术、造林技术设计与实施等方面对南丹山口林场引种秃杉栽培资料进行分析。【结果】样地测定显示,8年生、11年生、14年生、17年生的秃杉林分平均胸径依次为10.7cm,12.7cm,14.1cm,20.8cm;平均树高分别为8.6m,11.9m,13.3m,17.3m;林分平均蓄积量依次为93.428m3/hm2,153.418m3/hm2,203.824m3/hm2,223.400m3/hm2。秃杉林分各项生长量指标分别超过同等立地条件的杉木二代林的8.8%~112.0%。【结论】山口林场秃杉的引种栽培技术有一定的推广价值。     

一类排列的计数问题

应用容斥原理解决了不含连续数对的一系列排列的计数问题。并将其进行了推广。     

Dependence of mutual information of big protein sequence

The mutual information function is used to describe the auto-correlation of amino acids in protein. We find two interesting phenomenon: (1) for any given big protein, the mutual information function l(k) is almost a const, where k is the length of gap. (2) for any two sequence similar proteins, the mutual information are nearly the same. As a consequent, we may use mutual information of protein as a character for sequences comparison. Foundation item: Supported by the National Natural Science Foundation of China (30170214) Biography: Shi Feng ( 1966-), male, Ph. D, Associate professor, research direction: bioinformatics.     

多值复制生成序列的自相关函数

介绍了以p进制码为复制信息,用平移复制生成多复数值序列的方法,讨论了复制生成序列的性质和复制生成序列的自相关函数.依据序列的复制特性,给出了一个复制生成序列自相关函数的计算公式及相应的数学证明.最后指出了离散奎斯特恩逊函数的自相关函数的计算方法,为将复制生成序列应用于工程实践,提供了理论基础.