Search

Your search keyword '"Martinsen, Thor"' showing total 3 results
Start Over Author "Martinsen, Thor" Topic bent functions
3 results on '"Martinsen, Thor"'

1. Correlation immunity, avalanche features, and other cryptographic properties of generalized Boolean functions

Author

Martinsen, Thor, Stǎnicǎ, Pantelimon, and Applied Mathematics

Subjects
strict avalanche criterion, information warfare, bent functions, information security, Cryptography, cyber, coding theory, Boolean functions, generalized Boolean functions, communications security, correlation immunity
Abstract

This dissertation investigates correlation immunity, avalanche features, and the bent cryptographic properties for generalized Boolean functions defined on Vn with values in Zԛ. We extend the concept of correlation immunity from the Boolean case to the generalized setting, and provide multiple construction methods for order 1 and higher correlation immune generalized Boolean functions. We establish necessary and sufficient conditions for generalized Boolean functions. Additionally, we discuss correlation immune and rotation symmetric generalized Boolean functions, introducing a construction method along the way. Using a graph-theoretic and probabilistic frame of reference, we subsequently establish several, increasingly stringent, strict avalanche criteria along with a con-struction method for generalized Boolean functions. We introduce the notion of a uniform avalanche criterion and demonstrate that generalized Boolean functions that satisfy this criterion are also order 1 correlation immune and always have Boolean function compo-nents that are both order 1 correlation immune and satisfy the strict avalanche criterion.We subsequently investigate linear structures, directional derivatives and define a unit vector gradient for generalized Boolean function. We introduce the Walsh-Hadamard trans-form of a generalized Boolean function along with the notion of generalized bent Boolean functions. We provide a construction of generalized bent Boolean functions with outputs in Z8 and establish necessary conditions for generalized bent Boolean functions. http://archive.org/details/correlationimmun1094556155 Commander, United States Navy Approved for public release; distribution is unlimited.

Published
2017

2. Decomposing Generalized Bent and Hyperbent Functions.

Author

Martinsen, Thor, Meidl, Wilfried, Mesnager, Sihem, and Stanica, Pantelimon

Subjects
*BOOLEAN functions, *HADAMARD codes, *CYCLOTOMIC fields, *MATHEMATICAL decomposition, *THEORY of distributions (Functional analysis)
Abstract

In this paper, we introduce generalized hyperbent functions from \mathbb F2^{n} to \mathbb Z2^{k} , and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions f from \mathbb F2^{n} to \mathbb Z2^{k} consist of components which are generalized (hyper)bent functions from \mathbb F2^{n} to {\mathbb Z}_{2^{k^\prime }}$ for some $k^\prime < k$ . For even $n$ , most notably we show that the g-hyperbentness of $f$ is equivalent to the hyperbentness of the components of $f$ with some conditions on the Walsh–Hadamard coefficients. For odd $n$ , we show that the Boolean functions associated to a generalized bent function form an affine space of semibent functions. This complements a recent result for even $n$ , where the associated Boolean functions are bent. [ABSTRACT FROM AUTHOR]

Published
2017
Full Text
View/download PDF

3. Partial spread and vectorial generalized bent functions.

Author

Martinsen, Thor, Meidl, Wilfried, and Stănică, Pantelimon

Subjects
BENT functions, BOOLEAN functions, DIFFERENCE sets, CRYPTOGRAPHY, GENERALIZATION
Abstract

In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from $${\mathbb {F}}_2^n$$ to $${\mathbb {Z}}_{2^t}$$ . Explicitly, we describe gbent functions from $${\mathbb {F}}_2^n$$ to $${\mathbb {Z}}_{2^t}$$ , which can be seen as a gbent version of Dillon's $$PS_{ap}$$ class. For the first time, we also introduce the concept of a vectorial gbent function from $${\mathbb {F}}_2^n$$ to $${\mathbb {Z}}_q^m$$ , and determine the maximal value which m can attain for the case $$q=2^t$$ . Finally we point to a relation between vectorial gbent functions and relative difference sets. [ABSTRACT FROM AUTHOR]

Published
2017
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results