2005 Has erratum 2005**Abstract:** Abstract:We give the equivalence between perfect nonlinear functions and appropriate splitting semi-regular relative difference sets, construct a class of splitting relative difference sets by using Galois rings and bent functions, and prove that there exists a 4-phase perfect nonlinear function if and only if the number of input variables is at least twice the number of output variables. # 2005 Wiley Periodicals, Inc. J Combin Designs 13: [349][350][351][352][353][354][355][356][357][358][359][360][361][362] …

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“…An alternative construction by means of coordinate functions is suggested in e.g. [11,13]. Much work on an efficient P-box has been done by designers of AES [5].…”

confidence: 99%

“…An alternative construction by means of coordinate functions is suggested in e.g. [11,13]. Much work on an efficient P-box has been done by designers of AES [5].…”

confidence: 99%