Global Avalanche Characteristics of Boolean Functions by Concatenation

Global Avalanche Characteristics of Boolean Functions by Concatenation

TP918.1; 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., f1‖f2 and f1‖f2‖f3‖f4. Firstly, for the function f = f1‖f2 , the cross?correlation function of f1 , f2 in the s...

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Veröffentlicht in:哈尔滨工业大学学报（英文版） 2016-06, Vol.23 (3), p.91-96
Hauptverfasser: Zepeng Zhuo?,Jinfeng Chong,Ruirui Yu, Mingsheng Ren
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Mingsheng Ren
description TP918.1; 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., f1‖f2 and f1‖f2‖f3‖f4. Firstly, for the function f = f1‖f2 , the cross?correlation function of f1 , f2 in the special condition are studied. In this case, f, f1 , f2 must be in desired form. By computing their sum?of?squares indicators, the cross?correlation function between f1 , f2 is obtained. Secondly, for the function g = f1‖f2‖f3‖f4 , 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 f1 , f2 , f3 , f4 are good.
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Firstly, for the function f = f1‖f2 , the cross?correlation function of f1 , f2 in the special condition are studied. In this case, f, f1 , f2 must be in desired form. By computing their sum?of?squares indicators, the cross?correlation function between f1 , f2 is obtained. Secondly, for the function g = f1‖f2‖f3‖f4 , 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 f1 , f2 , f3 , f4 are good.</description><identifier>ISSN: 1005-9113</identifier><identifier>DOI: 10.11916/j.issn.1005-9113.2016.03.011</identifier><language>eng</language><publisher>School of Mathematical Science, Huaibei Normal University, Huaibei 235000, China</publisher><ispartof>哈尔滨工业大学学报（英文版）, 2016-06, Vol.23 (3), p.91-96</ispartof><rights>Copyright © Wanfang Data Co. Ltd. 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In this case, f, f1 , f2 must be in desired form. By computing their sum?of?squares indicators, the cross?correlation function between f1 , f2 is obtained. Secondly, for the function g = f1‖f2‖f3‖f4 , 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. 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