Cryptology ePrint Archive: Report 2003/133
Minimum Distance between Bent and 1-resilient Boolean Functions
Soumen Maity and Subhamoy Maitra
Abstract: In this paper we study the minimum distance between the set of bent functions and the set of 1-resilient Boolean functions and present a lower bound on that. The bound is proved to be tight for functions up to $10$ input variables. As a consequence, we present a strategy to modify the bent functions, by toggling some of its outputs, in getting a large class of $1$-resilient functions with very good nonlinearity and autocorrelation. In particular, the technique is applied upto $12$-variable functions and we show that the construction provides a large class of $1$-resilient functions reaching currently best known nonlinearity and achieving very low autocorrelation values which were not known earlier. The technique is sound enough to theoretically solve some of the mysteries of $8$-variable, $1$-resilient functions with maximum possible nonlinearity. However, the situation becomes complicated from $10$ variables and above, where
we need to go for complicated combinatorial analysis with trial and error using computational facility.
Category / Keywords: secret-key cryptography / Boolean Functions
Publication Info: Accepted in FSE 2004
Date: received 12 Jul 2003, last revised 24 Jan 2004
Contact author: subho at isical ac in
Available formats: Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation
Note: Some proofs are now written more carefully after getting the review comments from FSE 2004.
Version: 20040124:101614 (All versions of this report)
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