Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions


Autoria(s): Pieprzyk, Josef; Wang, Huaxiong; Zhang, Xian-Mo
Data(s)

01/05/2011

Resumo

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

Identificador

http://eprints.qut.edu.au/69351/

Publicador

Taylor & Francis

Relação

DOI:10.1080/00207160.2010.509428

Pieprzyk, Josef, Wang, Huaxiong, & Zhang, Xian-Mo (2011) Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions. International Journal of Computer Mathematics, 88(7), pp. 1398-1416.

Direitos

© 2011 Taylor & Francis

Fonte

School of Electrical Engineering & Computer Science; Science & Engineering Faculty

Palavras-Chave #anti-coincident functions #Boolean functions #h-non-coincident functions #coincident functions #Non-coincident weight #Möbius transform
Tipo

Journal Article