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High-Meets-Low: Construction of Strictly Almost Optimal Resilient Boolean Functions via Fragmentary Walsh Spectra.
- Source :
- IEEE Transactions on Information Theory; Sep2019, Vol. 65 Issue 9, p5856-5864, 9p
- Publication Year :
- 2019
-
Abstract
- This paper considers the construction of resilient Boolean functions on an odd number of variables with strictly almost optimal (SAO) nonlinearity. Through introducing the fragmentary Walsh transform, a construction technique called “High-Meets-Low” is proposed. The detailed design procedures of a 39-variable 3-resilient Boolean function with SAO nonlinearity $2^{38}-2^{19}+2^{16}+2^{14}$ are given. It is shown that the nonlinearity of an $n$ -variable $t$ -resilient Boolean function can reach $2^{n-1}-2^{(n-1)/2}+5\cdot 2^{(n-11)/2}$ or $2^{n-1}-2^{(n-1)/2}+2^{(n-7)/2}$ , which are the largest known values for the corresponding $n$ and $t$ values. Finally, by constructing a 29-variable balanced Boolean function with SAO nonlinearity $2^{28}-2^{14}+2^{10}+2^{9}$ , we show an alternative method to realize the High-Meets-Low construction technique. [ABSTRACT FROM AUTHOR]
- Subjects :
- BOOLEAN functions
ODD numbers
STREAM ciphers
CONSTRUCTION
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 138144581
- Full Text :
- https://doi.org/10.1109/TIT.2019.2899397