On decomposition of bent functions in 8 variables into the sum of two bent functions | Applied Discrete Mathematics. Supplement. 2022. № 15. DOI: 10.17223/2226308X/15/10

On decomposition of bent functions in 8 variables into the sum of two bent functions

A Boolean function in an even number of variables is called bent if it has maximal nonlinearity. We study the well-known hypothesis about the representation of arbitrary Boolean functions in n variables of degree at most n/2 as the sum of two bent functions. We prove that bent functions in 8 variables of degree at most 3 can be represented as the sum of two bent functions in 8 variables. It was shown that all quadratic Boolean functions in an even number of variables n > 4 can be represented as the sum of two bent functions of a special form.

Download file

Counter downloads: 15

Keywords

Boolean functions, bent functions, decomposition into sum of bent functions

Authors

Name	Organization	E-mail
Shaporenko Alexandr S.	Institute of Mathematics. S. L. Sobolev SB RAS; Novosibirsk State University	a.shaporenko@g.nsu.ru

Всего: 1

References

Rothaus O. S. On “bent” functions //j.Combinat. Theory. Ser. A. 1976. V. 20. No.3. P. 300-305.

Tokareva N. Bent Functions: Results and Applications to Cryptography. Acad. Press. Elsevier, 2015.

Matsui M. Linear cryptanalysis method for DES cipher // LNCS. 1994. V. 765. P. 386-397.

Adams C. Constructing symmetric ciphers using the CAST design procedure // Design, Codes, Cryptogr. 1997. V. 12. No. 3. P. 283-316.

Hell M., Johansson T., Maximov A., and Meier W. A stream cipher proposal: Grain-128 // IEEE Intern. Symp. Inform. Theory. 2006. P. 1614-1618.

Carlet C. Open questions on nonlinearity and on APN Functions // LNCS. 2015. V. 9061. P. 83-107.

Tokareva N. On the number of bent functions from iterative constructions: lower bounds and hypotheses // Adv. Math.Commun. 2011. V. 5. No. 4. P. 609-621.

Canteaut A. and Charpin P. Decomposing bent functions // IEEE Trans. Inform. Theory. 2003. V. 49. No. 8. P. 2004-2019.

Hou X. D. Cubic bent functions // Discr. Math. 1998. V. 189. Iss. 1-3. P. 149-161.

Qu L. and Li C. New results on the Boolean functions that can be expressed as the sum of two bent functions // IEICE Trans. Fundam. Electron.Commun.Comput. Sci. 2016. V. 99-A. No. 8. P. 1584-1590.