Multi-output Gaussian Process Regression Model with Combined Kernel Function for Polyester Esterification Processes

In polyester fiber industrial processes,the prediction of key performance indicators is vital for product quality.The esterification process is an indispensable step in the polyester polymerization process.It has the characteristics of strong coupling,nonlinearity and complex mechanism.To solve these problems,we put forward a multi-output Gaussian process regression(MGPR)model based on the combined kernel function for the polyester esterification process.Since the seasonal and trend decomposition using loess(STL)can extract the periodic and trend characteristics of time series,a combined kernel function based on the STL and the kernel function analysis is constructed for the MGPR.The effectiveness of the proposed model is verified by the actual polyester esterification process data collected from fiber production.

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

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

Relationship between Multi-Output Partially Bent Functions and Multi-Output Bent Functions

In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent functions is given in Theorem 4, which includes Walsh spectrum expression and function expression. This shows that multi-output partially Bent functions and multi-output Bent functions can define each other in principle. So we obtain the general method to construct multi-output partially Bent functions from multi-output Bent functions.

On the construction of cryptographically strong Boolean functions with desirable trade-off

This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2)n→GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties: nl(f)=22k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic of f satisfying σf=24k+23k+2+23k+23k?2 and the absolute avalanche characteristic of ?f satisfying ?f=2k+1. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions.

Find Better Boolean Functions in the Affine Equivalence Class

The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.

Global Avalanche Characteristics of Boolean Functions by Concatenation

In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,for the function f = f_1‖f_2,the cross-correlation function of f_1,f_2 in the special condition are studied.In this case,f,f_1,f_2 must be in desired form.By computing their sum-of-squares indicators,the crosscorrelation function between f_1,f_2 is obtained.Secondly,for the function g = f_1‖f_2‖f_3‖f_4,by analyzing the relation among their auto-correlation functions,their sum-of-squares indicators are investigated.Based on them,the sum-of-squares indicators of functions obtained by Canteaut et al.are investigated.The results show that the correlation property of g is good when the correlation properties of Boolean functions f_1,f_2,f_3,f_4 are good.

ENUMERATING CORRELATION-IMMUNE BOOLEAN FUNCTIONS OF ORDER ONE

A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.

Evolutionary Design of Boolean Functions

We use evolutionaly computing to synthesize Boolean functions randomly Byusing specific crossover and mutation operator, in evolving process and modifying search space andfitness function, we get some high non-linearity functions which have other good cryptographycharacteristics such as autocorrelation etc Comparing to other heuristic search techniques,evolutionary computing approach is more effective because of global search strategy and implicitparallelism.

IMPROVEMENT OF THE ALGORITHM PRINCIPLES FOR MINIMIZATION OF MULTI-OUTPUT FUNCTIONS

In this paper,the application of extraction principle for logic function minimiza-tion to multi-output case is studied.A defect in original algorithm in dealing with multi-outputextrema is made up,and on this base,three kinds of less-than terms in different conditions aredefined.In addition,three kinds of generalized definition of less-than terms are given,so as to findout more efficiently the covers with minimal number of terms and irredundant function outputs.This work makes the multi-output extraction principle closer to perfection.An algorithm basedon the work is presented.

Spectral Characteristics of the Best Affine Approach of Multi-Output m-Valued Logical Functions

This paper discusses the best affine approach （BAA） of multi-output m-valued logical functions. First, it gives the spectra of rate of accordance between multi-output m-valued logical functions and their affine functions, then analyzes the BAA of multi-output m-valued logical functions and finally gives the spectral characteristics of BAA of multi-output m-valued logical functions.

The Nonlinear Filter Boolean Function of LILI-128 Stream Cipher Generator Is Successfully Broken Based on the Complexity of Nonlinear 0 1 Symbol Sequence

The nonlinear filter Boolean function of LILI-128 stream cipher generator is studied in this paper. First we measure the complexity of the stream ciphers sequence of LILI-128 stream cipher generator and obtain the shortest bit stream sequence reconstructed Boolean function of nonlinear filter in LILI-128 stream cipher generator. Then the least nonlinear Boolean function of generating stream cipher sequence is reconstructed by clusterig, nonlinear predictive and nonlinear synchronization from shortest bit stream sequence. We have verified the correctness of our reconstruction result by simulating the block diagram of Lili-128 keystream generator using our getting Boolean function and implement designers’ reference module of Lili-128 stream cipher public online, and two methods produce the same synchronous keystream sequence under same initial state, so that our research work proves that the nonlinear Boolean function of LILI-128 stream cipher generator is successfully broken.

Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation

To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to construct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is determined for the number of Boolean functions with maximum algebraic immunity.

A Review of Lightweight Cryptographic Schemes and Fundamental Cryptographic Characteristics of Boolean Functions

In this paper, we survey a number of studies in the literature on improving lightweight systems in the Internet of Things (IoT). The paper illustrates recent development of Boolean cryptographic function Application and how it assists in using hardware such as the internet of things. For a long time there seems to be little progress in applying pure mathematics in providing security since the wide progress made by George Boole and Shannon. We discuss cryptanalysis of Boolean functions to avoid trapdoors and vulnerabilities in the development of block ciphers. It appears that there is significant progress. A comparative analysis of lightweight cryptographic schemes is reported in terms of execution time, code size and throughput. Depending on the schemes and the structure of the algorithms, these parameters change but remain within reasonable values making them suited for Internet of things applications. The driving force of lightweight cryptography (LWC) stems mainly from its direct applications in the real world since it provides solutions to actual problems faced by designers of IoT systems. Broadly speaking, lightweight cryptographic algorithms are designed to achieve two main goals. The first goal of a cryptographic algorithm is to withstand all known cryptanalytic attacks and thus to be secure in the black-box model. The second goal is to build the cryptographic primitive in such a way that its implementations satisfy a clearly specified set of constraints that depend on a case-by-case basis.

ON THE DEGREE OF COMPLETENESS OF CRYPTOGRAPHIC FUNCTIONS

This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.

有向根树上局部更新函数为NAND或NOR的广义并序动力系统的固定点

研究对象为有向根树上的广义并序动力系统,其局部更新函数为NAND或NOR。为了研究这类广义并序动力系统中的固定点的个数及状态,采用结构分析法和分类讨论法,得到了此类动力系统中关于固定点的确切结果。证明了这类广义并序动力系统中的固定点状态完全由有向根树中的自环决定。离散动力系统是数学建模的重要工具,该文可为离散动力系统的研究提供新的思路。

非线性可分Boolean函数分解及神经网络实现

对于2n个顶点用"0"或"1"标记的n维超方体,利用n输入Boolean函数f的输出vi(i=0,1,…,2n-1)与偏移量σi的关系,用一组平行的超平面实现分隔n维超方体顶点。从而,实现非线性可分Boolean函数的分解及二进神经网络隐层神经元的实现。同时,给出几个例子说明分解方法以及其有效性。

Boolean函数与某些变元无关的充要条件

本文首先用第二种谱方法给出了Boolean函数与某些变元无关的一个充要条件.其次用"函数的特征矩阵"给出了Boolean函数与某些变元无关的一些充要条件.

二进神经网络的Boolean函数化简

利用二进神经网络方法对Boolean函数逻辑化简具有理论研究与实际应用意义。通过二进神经网络化简复杂非线性可分Boolean函数的方法,说明对非线性可分Boolean函数化简采用二进神经网络方法能够取得比传统方法更加高效、简便的化简。同时,给出几个二进神经网络化简非线性可分Boolean函数的实例,具体说明该方法的有效性。

The structure of canalizing functions

The structure of a canalizing function is discussed. Using a new matrix product, namely semitensor product, the logical function is expressed in its matrix form. From its matrix expression, a criterion is obtained to test whether a logical function is a canalizing function. Then a formula is obtained to calculate the number of canalizing functions. Moreover, an algorithm is presented to generate canalizing functions. Finally, some results obtained are extended to seminested canalizing functions.