Algebraic Construction of Near-Bent and APN Functions

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

doi:10.1007/s00006-019-1012-x

Algebraic Construction of Near-Bent and APN Functions

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 language	English
Article number	93
Journal	Advances in Applied Clifford Algebras
Volume	29
Issue number	5
DOIs	https://doi.org/10.1007/s00006-019-1012-x
Publication status	Published - 01-11-2019

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1007/s00006-019-1012-x

Cite this

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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.\}",

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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).

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Algebraic Construction of Near-Bent and APN Functions

Abstract

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