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- Title
On a method of derivation of lower bounds for the nonlinearity of Boolean functions.
- Authors
Lobanov, M.
- Abstract
The calculation of the exact value of the rth order nonlinearity of a Boolean function (the power of the distance between the function and the set of functions is at most r) or the derivation of a lower bound for it is a complicated problem (especially for r > 1). Lower bounds for nonlinearities of different orders in terms of the value of algebraic immunity were obtained in a number of papers. These estimates turn out to be sufficiently strong if the value of algebraic immunity is maximum or close to maximum. In the present paper, we prove a statement that allows us to obtain fairly strong lower bounds for nonlinearities of different orders and for many functions with low algebraic immunity.
- Subjects
MATHEMATICAL bounds; BOOLEAN functions; NONLINEAR theories; ALGEBRAIC immunity; POLYNOMIALS; MATHEMATICAL mappings
- Publication
Mathematical Notes, 2013, Vol 93, Issue 5/6, p727
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S000143461305009X