Boolean functions as points on the hypersphere in the Euclidean space
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Oleg A. Logachev
,
Sergey N. Fedorov
Abstract
A new approach to the study of algebraic, combinatorial, and cryptographic properties of Boolean functions is proposed. New relations between functions have been revealed by consideration of an injective mapping of the set of Boolean functions onto the sphere in a Euclidean space. Moreover, under this mapping some classes of functions have extremely regular localizations on the sphere. We introduce the concept of curvature of a Boolean function, which characterizes its proximity (in some sense) to maximally nonlinear functions.
Note: Originally published in Diskretnaya Matematika (2018) 30, №1, 39–55 (in Russian).
Acknowledgement
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00226-a).
References
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Articles in the same Issue
- Frontmatter
- Generalization of one method of a filter generator key recovery
- Boolean functions as points on the hypersphere in the Euclidean space
- Artinian bimodule with quasi-Frobenius bimodule of translations
- Asymptotic behavior of functions Ω(k; n) and ω(k; n) related to the number of prime divisors
- On some properties of vector functions of Boolean algebra
- Modules over strongly semiprime rings
Articles in the same Issue
- Frontmatter
- Generalization of one method of a filter generator key recovery
- Boolean functions as points on the hypersphere in the Euclidean space
- Artinian bimodule with quasi-Frobenius bimodule of translations
- Asymptotic behavior of functions Ω(k; n) and ω(k; n) related to the number of prime divisors
- On some properties of vector functions of Boolean algebra
- Modules over strongly semiprime rings
