Aperiodic propagation criteria for Boolean functions

Authors:
Lars Eirik Danielsen;T. Aaron Gulliver;Matthew G. Parker
Affiliations:
The Selmer Center, Department of Informatics, University of Bergen, PB 7800, N-5020 Bergen, Norway;Depatment of Electronics and Computer Engineering, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC, Canada V8W 3P6;The Selmer Center, Department of Informatics, University of Bergen, PB 7800, N-5020 Bergen, Norway
Venue:
Information and Computation
Year:
2006

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Abstract

We characterise the aperiodic autocorrelation for a Boolean function, f, and define the Aperiodic Propagation Criteria (APC) of degree l and order q. We establish the strong similarity between APC and the Extended Propagation Criteria (EPC) as defined by Preneel et al. in 1991, although the criteria are not identical. We also show how aperiodic autocorrelation can be related to the first derivative of f. We further propose the metric APC distance and show that quantum error correcting codes (QECCs) are natural candidates for Boolean functions with favourable APC distance.