Nonlinearly balanced Boolean functions and their propagation characteristics
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On Propagation Characteristics of Resilient Functions
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Construction of Cryptographically Important Boolean Functions
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
New Constructions of Resilient Boolean Functions with Maximal Nonlinearity
FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
Minimum Distance between Bent and Resilient Boolean Functions
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
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In this paper we present a strategy to construct 1-resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1-resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise in this context are “at least how many bits and which bits in the output of a bent function need to be changed to construct a 1-resilient Boolean function”. We present an algorithm which determines a minimum number of bits of a bent function that need to be changed to construct a 1-resilient Boolean function. We also present a technique to compute points whose output in the bent function need to be modified to get a 1-resilient function. In particular, the technique is applied upto 14-variable functions and we show that the construction provides 1-resilient functions reaching currently best known nonlinearity and achieving very low autocorrelation absolute indicator values which were not known earlier.