Minimum Distance between Bent and Resilient Boolean Functions

Authors:
Longjiang Qu;Chao Li
Affiliations:
Department of Mathematic and System Science, Science College, National University of Defense Technology, ChangSha, China 410073 and National Mobile Communications Research Laboratory, Southeast Un ...;Department of Mathematic and System Science, Science College, National University of Defense Technology, ChangSha, China 410073
Venue:
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Year:
2009

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Abstract

The minimum distance between bent and resilient functions is studied. This problem is converted into two problems. One is to construct a special matrix, which leads to a combinatorial problem; the other is the existence of bent functions with specified types. Then the relation of these two problems is studied. For the 1-resilient functions, we get a solution to the first combinatorial problem. By using this solution and the relation of the two problems, we present a formula on the lower bound of the minimum distance of bent and 1-resilient functions. For the latter problem, we point out the limitation of the usage of the Maiorana-McFarland type bent functions, and the necessity to study the existence of bent functions with special property which we call partial symmetric. At last, we give some results on the nonexistence of some partial symmetric bent functions.