Generalized rotation symmetric and dihedral symmetric boolean functions - 9 variable boolean functions with nonlinearity 242

Date

2007-12-20

Author

Kavut, Selcuk
Yucel, Melek Diker

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

238
views

0
downloads

Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and Dihedral Symmetric Boolean Functions (DSBFs). These functions do not have any zero in the Walsh spectrum values, hence they cannot be made balanced easily. This result also shows that the covering radius of the first order Reed-Muller code R(1, 9) is at least 242.

Subject Keywords

Rotation symmetric boolean functions, Dihedral symmetric boolean functions, Nonlinearity

URI

https://hdl.handle.net/11511/65557

Collections

Department of Computer Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Characterisation and enumeration of a class of semi bent quadratic Boolean functions KOÇAK, Neşe; Koçak, Onur Ozan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2015-01-01) In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2 Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28) We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
Enumeration of 9-variable rotation symmetric Boolean functions having nonlinearity > 240 Kavut, Selcuk; Maitra, Subhamoy; Sarkar, Sumanta; Yücel, Mustafa (2006-12-13) The existence of 9-variable Boolean functions having nonlinearity strictly greater than 240 has been shown very recently (May 2006) by Kavut, Maitra and Yucel; a few functions with nonlinearity 241 have been identified by a heuristic search in the class of Rotation Symmetric Boolean Functions (RSBFs). In this paper, using combinatorial results related to the Walsh spectra of RSBFs, we efficiently perform the exhaustive search to enumerate the 9-variable RSBFs having nonlinearity > 240 and found that there a...
Improvement in non-linearity of carlet-feng infinite class of boolean functions Khan, Mansoor Ahmed; Özbudak, Ferruh (2012-12-01) In this paper we present a Walsh spectrum based method derived from the genetic hill climbing algorithm to improve the non-linearity of functions belonging to Carlet-Feng infinite class of Boolean functions, without degrading other cryptographic properties they possess. We implement our modified algorithms to verify the results and also present a comparison of the resultant cryptographic properties with the original functions.
Decomposing perfect discrete Morse functions on connected sum of 3-manifolds Kosta, Neza Mramor; Pamuk, Mehmetcik; Varli, Hanife (2019-06-15) In this paper, we show that if a closed, connected, oriented 3-manifold M = M-1 # M-2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M-1 and M-2. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition.

Citation Formats

S. Kavut and M. D. Yucel, “Generalized rotation symmetric and dihedral symmetric boolean functions - 9 variable boolean functions with nonlinearity 242,” 2007, vol. 4851, p. 321, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65557.