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
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
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.
