Towards the Structure of a Class of Permutation Matrices Associated With Bent Functions

Radomir S. Stankovic; Milena Stankovic; Jaakko Astola; Claudio Moraga

doi:10.1007/978-3-030-20323-8_4

Towards the Structure of a Class of Permutation Matrices Associated With Bent Functions

Radomir S. Stankovic
, Milena Stankovic
, Jaakko Astola
, Claudio Moraga

Computing Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

Abstract

Bent functions, that are useful in cryptographic applications, can be characterized in different ways. A recently formulated characterization is in terms of the Gibbs dyadic derivative. This characterization can be interpreted through permutation matrices associated with bent functions by this differential operator. We point out that these permutation matrices express some characteristic block structure and discuss a possible determination of it as a set of rules that should be satisfied by the corresponding submatrices. We believe that a further study of this structure can bring interesting results providing a deeper insight into features of bent functions.

Original language	English
Title of host publication	Proceedings of the 13 International Workshop on Boolean Problems
Publisher	Springer
Pages	83-105
ISBN (Electronic)	978-3-030-20323-8
ISBN (Print)	978-3-030-20322-1
DOIs	https://doi.org/10.1007/978-3-030-20323-8_4
Publication status	Published - 2018
Publication type	A4 Article in conference proceedings
Event	INTERNATIONAL WORKSHOP ON BOOLEAN PROBLEMS - Duration: 1 Jan 1900 → …

Conference

Conference	INTERNATIONAL WORKSHOP ON BOOLEAN PROBLEMS
Period	1/01/00 → …

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10.1007/978-3-030-20323-8_4

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@inproceedings{e095f56b67f4425687b5f68e31b28065,

title = "Towards the Structure of a Class of Permutation Matrices Associated With Bent Functions",

abstract = "Bent functions, that are useful in cryptographic applications, can be characterized in different ways. A recently formulated characterization is in terms of the Gibbs dyadic derivative. This characterization can be interpreted through permutation matrices associated with bent functions by this differential operator. We point out that these permutation matrices express some characteristic block structure and discuss a possible determination of it as a set of rules that should be satisfied by the corresponding submatrices. We believe that a further study of this structure can bring interesting results providing a deeper insight into features of bent functions.",

author = "Stankovic, \{Radomir S.\} and Milena Stankovic and Jaakko Astola and Claudio Moraga",

note = "EXT={"}Stankovic, Radomir S.{"}; INTERNATIONAL WORKSHOP ON BOOLEAN PROBLEMS ; Conference date: 01-01-1900",

year = "2018",

doi = "10.1007/978-3-030-20323-8\_4",

language = "English",

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T1 - Towards the Structure of a Class of Permutation Matrices Associated With Bent Functions

AU - Stankovic, Radomir S.

AU - Stankovic, Milena

AU - Astola, Jaakko

AU - Moraga, Claudio

N1 - EXT="Stankovic, Radomir S."

PY - 2018

Y1 - 2018

N2 - Bent functions, that are useful in cryptographic applications, can be characterized in different ways. A recently formulated characterization is in terms of the Gibbs dyadic derivative. This characterization can be interpreted through permutation matrices associated with bent functions by this differential operator. We point out that these permutation matrices express some characteristic block structure and discuss a possible determination of it as a set of rules that should be satisfied by the corresponding submatrices. We believe that a further study of this structure can bring interesting results providing a deeper insight into features of bent functions.

AB - Bent functions, that are useful in cryptographic applications, can be characterized in different ways. A recently formulated characterization is in terms of the Gibbs dyadic derivative. This characterization can be interpreted through permutation matrices associated with bent functions by this differential operator. We point out that these permutation matrices express some characteristic block structure and discuss a possible determination of it as a set of rules that should be satisfied by the corresponding submatrices. We believe that a further study of this structure can bring interesting results providing a deeper insight into features of bent functions.

U2 - 10.1007/978-3-030-20323-8_4

DO - 10.1007/978-3-030-20323-8_4

M3 - Conference contribution

SN - 978-3-030-20322-1

SP - 83

EP - 105

BT - Proceedings of the 13 International Workshop on Boolean Problems

PB - Springer

T2 - INTERNATIONAL WORKSHOP ON BOOLEAN PROBLEMS

Y2 - 1 January 1900

ER -

Towards the Structure of a Class of Permutation Matrices Associated With Bent Functions

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