Abstract
In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analyzed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent functions having some additional properties that enable the construction of strongly regular graphs are formed, and explicit expressions for bent functions with maximal degree are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carlet C., Dobbertin H., Leander G.: Normal extensions of bent functions. IEEE Trans. Inf. Theory 50, 2880–2885 (2004)
Chee Y.M., Tan Y., Zhang X.D.: Strongly regular graphs constructed from p-ary bent functions. J. Algebr. Comb. 34, 251–266 (2011)
Çeşmelioğlu A., McGuire G., Meidl W.: A construction of weakly and non-weakly regular bent functions. J. Comb. Theory Ser. A 119, 420–429 (2012)
Çeşmelioğlu A., Meidl W.: Bent functions of maximal degree. IEEE Trans. Inf. Theory 58(2) (2012).
Charpin P., Pasalic E., Tavernier C.: On bent and semi-bent quadratic Boolean functions. IEEE Trans. Inf. Theory 51, 4286–4298 (2005)
Feng T., Wen B., Xiang Q., Yin J.: Partial difference sets from p-ary weakly regular bent functions and quadratic forms. Arxiv 1002.2797.pdf (2011).
Helleseth T., Kholosha A.: Monomial and quadratic bent functions over the finite field of odd characteristic. IEEE Trans. Inf. Theory 52, 2018–2032 (2006)
Hou X.D.: p-ary and q-ary versions of certain results about bent functions and resilient functions. Finite Fields Appl. 10, 566–582 (2004)
Leander G., McGuire G.: Construction of bent functions from near-bent functions. J. Comb. Theory Ser. A 116, 960–970 (2009)
Lidl R., Niederreiter H.: Finite Fields, 2nd ed., Encyclopedia Math. Appl., vol. 20. Cambridge University Press, Cambridge (1997).
Tan Y., Pott A., Feng T.: Strongly regular graphs associated with ternary bent functions. J. Comb. Theory Ser. A 117, 668–682 (2010)
Tan Y., Yang J., Zhang X.: A recursive approach to construct p-ary bent functions which are not weakly regular. In: Proceedings of IEEE International Conference on Information Theory and Information Security, pp. 156–159. Beijing (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
Rights and permissions
About this article
Cite this article
Çeşmelioğlu, A., Meidl, W. A construction of bent functions from plateaued functions. Des. Codes Cryptogr. 66, 231–242 (2013). https://doi.org/10.1007/s10623-012-9686-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-012-9686-2