Algebraic Construction of Near-Bent and APN Functions

Prasanna Poojary, Harikrishnan Panackal, Vadiraja G.R. Bhatta

Research output: Contribution to journalArticle

Abstract

Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functions. If exponents are either Mersenne numbers or Fermat numbers, then the resulting functions are found to be APN (almost perfect nonlinear).

Original languageEnglish
Article number93
JournalAdvances in Applied Clifford Algebras
Volume29
Issue number5
DOIs
Publication statusPublished - 01-11-2019

Fingerprint

Boolean Functions
Nonlinear Function
Boolean functions
Mersenne number
Fermat number
Exponent
Bent Function
Power Function
Cryptosystem
Galois field
Trace
Cryptography
Form

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Poojary, Prasanna ; Panackal, Harikrishnan ; Bhatta, Vadiraja G.R. / Algebraic Construction of Near-Bent and APN Functions. In: Advances in Applied Clifford Algebras. 2019 ; Vol. 29, No. 5.
@article{e76cfbda03ac431fa134d637a4c49c65,
title = "Algebraic Construction of Near-Bent and APN Functions",
abstract = "Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functions. If exponents are either Mersenne numbers or Fermat numbers, then the resulting functions are found to be APN (almost perfect nonlinear).",
author = "Prasanna Poojary and Harikrishnan Panackal and Bhatta, {Vadiraja G.R.}",
year = "2019",
month = "11",
day = "1",
doi = "10.1007/s00006-019-1012-x",
language = "English",
volume = "29",
journal = "Advances in Applied Clifford Algebras",
issn = "0188-7009",
publisher = "Birkhauser Verlag Basel",
number = "5",

}

Algebraic Construction of Near-Bent and APN Functions. / Poojary, Prasanna; Panackal, Harikrishnan; Bhatta, Vadiraja G.R.

In: Advances in Applied Clifford Algebras, Vol. 29, No. 5, 93, 01.11.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Algebraic Construction of Near-Bent and APN Functions

AU - Poojary, Prasanna

AU - Panackal, Harikrishnan

AU - Bhatta, Vadiraja G.R.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functions. If exponents are either Mersenne numbers or Fermat numbers, then the resulting functions are found to be APN (almost perfect nonlinear).

AB - Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functions. If exponents are either Mersenne numbers or Fermat numbers, then the resulting functions are found to be APN (almost perfect nonlinear).

UR - http://www.scopus.com/inward/record.url?scp=85073224943&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073224943&partnerID=8YFLogxK

U2 - 10.1007/s00006-019-1012-x

DO - 10.1007/s00006-019-1012-x

M3 - Article

AN - SCOPUS:85073224943

VL - 29

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

SN - 0188-7009

IS - 5

M1 - 93

ER -