Constructing new APN functions from known ones

L. Budaghyan; C. Carlet; Gregor Leander

doi:10.1016/j.ffa.2008.10.001

Constructing new APN functions from known ones

L. Budaghyan, C. Carlet, Gregor Leander

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x(3) + tr(x(9)) over F2(n). It is proven that for n >= 7 this function is CCZ-inequivalent to the Gold functions, and in the case n = 7 it is CCZ-inequivalent to any power mapping (and, therefore, to any APN function belonging to one of the families of APN functions known so far).

Original language	English
Journal	Finite Fields and Their Applications
Volume	15
Issue number	2
Pages (from-to)	150-159
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2008.10.001
Publication status	Published - 2009

Keywords

S-box
Almost perfect nonlinear
Almost bent
Differential uniformity
CCZ-equivalence
Nonlinearity
Vectorial Boolean function

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title = "Constructing new APN functions from known ones",

abstract = "We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x(3) + tr(x(9)) over F2(n). It is proven that for n >= 7 this function is CCZ-inequivalent to the Gold functions, and in the case n = 7 it is CCZ-inequivalent to any power mapping (and, therefore, to any APN function belonging to one of the families of APN functions known so far).",

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T1 - Constructing new APN functions from known ones

AU - Budaghyan, L.

AU - Carlet, C.

AU - Leander, Gregor

PY - 2009

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N2 - We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x(3) + tr(x(9)) over F2(n). It is proven that for n >= 7 this function is CCZ-inequivalent to the Gold functions, and in the case n = 7 it is CCZ-inequivalent to any power mapping (and, therefore, to any APN function belonging to one of the families of APN functions known so far).

AB - We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x(3) + tr(x(9)) over F2(n). It is proven that for n >= 7 this function is CCZ-inequivalent to the Gold functions, and in the case n = 7 it is CCZ-inequivalent to any power mapping (and, therefore, to any APN function belonging to one of the families of APN functions known so far).

KW - S-box

KW - Almost perfect nonlinear

KW - Almost bent

KW - Differential uniformity

KW - CCZ-equivalence

KW - Nonlinearity

KW - Vectorial Boolean function

U2 - 10.1016/j.ffa.2008.10.001

DO - 10.1016/j.ffa.2008.10.001

M3 - Journal article

SN - 1071-5797

VL - 15

SP - 150

EP - 159

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

IS - 2

ER -

Constructing new APN functions from known ones

Abstract

Keywords

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