Spectral and Nonlinear Properties of the Sum of Boolean Functions
Keywords:
Boolean function, Walsh-Hadamard Transform, Distance of Nonlinearity, Cryptography,Abstract
Boolean functions are the mathematical basis of modern cryptographic algorithms. However, in practice, a set of interrelated Boolean functions is often used to construct a cryptographic algorithm. This circumstance makes the task of research of cryptographic quality, in particular, the distance of the nonlinearity of the sum of few Boolean functions important. The nonlinearity distance of a Boolean function is determined by the maximum value of its Walsh-Hadamard transform coefficients. In this paper, we proposed a formula that is the equivalent of the summation of Boolean functions in the Walsh-Hadamard transform domain. The application of this formula, as well as the Walsh-Hadamard spectral classification made it possible to determine the structure of WalshHadamard transform coefficients, and the distance of the nonlinearity when summing the Boolean functions lengths N 8 and N 16 , indicating valuable practical application for information protection.Downloads
Published
How to Cite
Issue
Section
License
TRANSFER OF COPYRIGHT AGREEMENT
The manuscript is herewith submitted for publication in the Journal of Telecommunication, Electronic and Computer Engineering (JTEC). It has not been published before, and it is not under consideration for publication in any other journals. It contains no material that is scandalous, obscene, libelous or otherwise contrary to law. When the manuscript is accepted for publication, I, as the author, hereby agree to transfer to JTEC, all rights including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the author(s) specifically retain(s):
- All proprietary right other than copyright, such as patent rights
- The right to make further copies of all or part of the published article for my use in classroom teaching
- The right to reuse all or part of this manuscript in a compilation of my own works or in a textbook of which I am the author; and
- The right to make copies of the published work for internal distribution within the institution that employs me
I agree that copies made under these circumstances will continue to carry the copyright notice that appears in the original published work. I agree to inform my co-authors, if any, of the above terms. I certify that I have obtained written permission for the use of text, tables, and/or illustrations from any copyrighted source(s), and I agree to supply such written permission(s) to JTEC upon request.