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

Josef Pieprzyk, Huaxiong Wang*, Xian Mo Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1398-1416
Number of pages19
JournalInternational Journal of Computer Mathematics
Volume88
Issue number7
DOIs
Publication statusPublished - May 2011

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