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 generalize...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.展开更多
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 function...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.展开更多
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 ...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.展开更多
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 res...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)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. 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. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6展开更多
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,f...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.展开更多
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, ...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.展开更多
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-lineari...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.展开更多
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,thr...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.展开更多
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 o...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 constmct 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 deter- mined for the number of Boolean functions with rmximum algebraic immunity.展开更多
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 func...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.展开更多
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 sho...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.展开更多
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 ...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.展开更多
Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated ...Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated to aligned spaces which is similar to the one we have given for switching functions associated to finite topological spaces.展开更多
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 a...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.展开更多
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 d...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.展开更多
We construct an infinite family of minimal linear codes over the ring F_(2)+u F_(2).These codes are defined through trace functions and Boolean functions.Their Lee weight distribution is completely computed by Walsh t...We construct an infinite family of minimal linear codes over the ring F_(2)+u F_(2).These codes are defined through trace functions and Boolean functions.Their Lee weight distribution is completely computed by Walsh transformation.By Gray mapping,we obtain a family of minimal binary linear codes from a generic construction,which have prominent applications in secret sharing and secure two-party computation.展开更多
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) .
文摘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.
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) the Doctorate Foundation ofInstitute of Information Engineering (YP20014401)HenanInno-vation Project for University Prominent Research Talents(2003KJCX008)
文摘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.
文摘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.
文摘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)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. 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. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6
基金Sponsored by the National Natural Science Foundations of Anhui Higher Education Institutions of China(Grant No.KJ2014A220,KJ2014A231)the Anhui Provincial Natural Science Foundation(Grant No.1608085MF143)the Key Program in the Youth Elite Support Plan in Universities of Anhui Province(Grant No.gxyq ZD2016112)
文摘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.
文摘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.
文摘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.
文摘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.
基金This work was supported by the National Natural Science Foundation of China under Grants No. 61103191, No. 61070215 the Funds of Key Lab of Fujian Province University Network Security and Cryptology under Crant No. 2011003 and the Open Research Fund of State Key Laboratory of Inforrmtion Security.
文摘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 constmct 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 deter- mined for the number of Boolean functions with rmximum algebraic immunity.
基金Supported by the Opening Research Foundation of the State Key Laboratory of Information Security (2005-01-02)
文摘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.
文摘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.
基金Natural Science Foundation of Shanghai,China(No.19ZR1402300)。
文摘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.
文摘Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated to aligned spaces which is similar to the one we have given for switching functions associated to finite topological spaces.
文摘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.
基金Supported by the National Key Basic Research Program of China(No.2013CB834204)
文摘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.
基金National Natural Science Foundation of China(12201171)。
文摘We construct an infinite family of minimal linear codes over the ring F_(2)+u F_(2).These codes are defined through trace functions and Boolean functions.Their Lee weight distribution is completely computed by Walsh transformation.By Gray mapping,we obtain a family of minimal binary linear codes from a generic construction,which have prominent applications in secret sharing and secure two-party computation.
