On cross-correlation properties of Boolean functions

Abstract

The relationship among cross-correlation of arbitrary four Boolean functions is presented. Several known cross-correlation properties of Boolean functions are generalized. Based on them, a lower bound for the maximal cross-correlation (in absolute value) of two Boolean functions (if one of the functions is bent) is obtained.

Keywords:

• Boolean function
• strict avalanche criterion
• correlation function
• propagation characteristics
• global avalanche characteristics

2000 AMS Subject Classifications :

• 94A60
• 06E30

Acknowledgements

This work is supported in part by the Natural Science Foundation of China under Grant 60773003, 60970120 and 61003299. The author would like to thank the anonymous reviewers who, by numerous and suggestions, have contributed to improve the manuscript.