For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
Substitution boxes （S-boxes） are often used as the most important nonlinear components in many symmetric encryption algorithms. The cryptographic properties of an S-box directly affect the security of the whole ciph...Substitution boxes （S-boxes） are often used as the most important nonlinear components in many symmetric encryption algorithms. The cryptographic properties of an S-box directly affect the security of the whole cipher system. Recently, generalized global avalanche characteristics （GGAC） were introduced to measure the correlation between two arbitrary Boolean functions. In this paper, to better evaluate the security of an S-box, we present two cross-correlation indicators for it. In addition, by studying the related properties of the cross-correlation between two balanced Boolean func- tions, we propose the lower bounds on the sum-of-squares indicator related to GGAC for two balanced functions and also for an S-box.展开更多
This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above B...This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.展开更多
Covariate-adaptive randomisation has a more than 45 years of history of applications in clinical trials,in order to balance treatment assignments across prognostic factors that may have influence on the outcomes of in...Covariate-adaptive randomisation has a more than 45 years of history of applications in clinical trials,in order to balance treatment assignments across prognostic factors that may have influence on the outcomes of interest.However,almost no theory had been developed for covariate-adaptive randomisation until a paper on the theory of testing hypotheses published in 2010.In this article,we review aspects of methodology and theory developed in the last decade for statistical inference under covariate-adaptive randomisation.Wefocus on issues such as whether a conventional procedure valid under the assumption that treatments are assigned completely at random is still valid or conservative when the actual randomisation is covariateadaptive,how a valid inference procedure can be obtained by modifying a conventional method or directly constructed by stratifying the covariates used in randomisation,whether inference procedures have different properties when covariate-adaptive randomisation schemes have different degrees of balancing assignments,and how to further adjust covariates in the inference procedures to gain more efficiency.Recommendations are made during the review and further research problems are discussed.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
基金Supported by the National Natural Science Foundation of China ( 60603012)the Foundation of Hubei Provincial Department of Education, China (D200610004)
文摘For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
文摘Substitution boxes （S-boxes） are often used as the most important nonlinear components in many symmetric encryption algorithms. The cryptographic properties of an S-box directly affect the security of the whole cipher system. Recently, generalized global avalanche characteristics （GGAC） were introduced to measure the correlation between two arbitrary Boolean functions. In this paper, to better evaluate the security of an S-box, we present two cross-correlation indicators for it. In addition, by studying the related properties of the cross-correlation between two balanced Boolean func- tions, we propose the lower bounds on the sum-of-squares indicator related to GGAC for two balanced functions and also for an S-box.
基金supported by the National Basic Research Program of China under Grant No.2011CB302400
文摘This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.
基金supported by the National Natural Science Foundation of China(11831008)the U.S.National Science Foundation(DMS-1914411).
文摘Covariate-adaptive randomisation has a more than 45 years of history of applications in clinical trials,in order to balance treatment assignments across prognostic factors that may have influence on the outcomes of interest.However,almost no theory had been developed for covariate-adaptive randomisation until a paper on the theory of testing hypotheses published in 2010.In this article,we review aspects of methodology and theory developed in the last decade for statistical inference under covariate-adaptive randomisation.Wefocus on issues such as whether a conventional procedure valid under the assumption that treatments are assigned completely at random is still valid or conservative when the actual randomisation is covariateadaptive,how a valid inference procedure can be obtained by modifying a conventional method or directly constructed by stratifying the covariates used in randomisation,whether inference procedures have different properties when covariate-adaptive randomisation schemes have different degrees of balancing assignments,and how to further adjust covariates in the inference procedures to gain more efficiency.Recommendations are made during the review and further research problems are discussed.
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
