Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871397 | Discrete Applied Mathematics | 2018 | 10 Pages |
Abstract
Generalized bent (gbent) functions is a class of functions f:Z2nâZq, where qâ¥2 is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot of research has recently been devoted towards derivation of the necessary and sufficient conditions when f is represented as a collection of Boolean functions. Nevertheless, apart from the necessary conditions that these component functions are bent when n is even (respectively semi-bent when n is odd), no general construction method has been proposed yet for n odd case. In this article, based on the use of the well-known Maiorana-McFarland (MM) class of functions, we give an explicit construction method of gbent functions, for any even q>2 when n is even and for any q of the form q=2r (for r>1) when n is odd. Thus, a long-term open problem of providing a general construction method of gbent functions, for odd n, has been solved. The method for odd n employs a large class of disjoint spectra semi-bent functions with certain additional properties which may be useful in other cryptographic applications.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
S. HodžiÄ, E. Pasalic,