International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Soumen Maity

Publications

Year
Venue
Title
2004
FSE
2003
EPRINT
Minimum Distance between Bent and 1-resilient Boolean Functions
Soumen Maity Subhamoy Maitra
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.

Coauthors

Subhamoy Maitra (2)