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A note on the properties of associated boolean functions of quadratic APN functions. / Gorodilova, A. A.
в: Прикладная дискретная математика, № 47, 01.01.2020, стр. 16-21.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - A note on the properties of associated boolean functions of quadratic APN functions
AU - Gorodilova, A. A.
N1 - Publisher Copyright: © 2020 Tomsk State University. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - Let F be a quadratic APN function in n variables. The associated Boolean function γF in 2n variables (γF (a, b) = 1 if a ≠ 0 and equation F(x)+F(x+a) = b has solutions) has the form γF (a, b) = ΦF (a) · b+φF (a)+1 for appropriate functions ΦF : Fn 2 → Fn 2 and φF : Fn 2 → F2. We summarize the known results and prove new ones regarding properties of ΦF and φF. For instance, we prove that degree of ΦF is either n or less or equal to n-2. Based on computation experiments, we formulate a conjecture that degree of any component function of ΦF is n -2. We show that this conjecture is based on two other conjectures of independent interest.
AB - Let F be a quadratic APN function in n variables. The associated Boolean function γF in 2n variables (γF (a, b) = 1 if a ≠ 0 and equation F(x)+F(x+a) = b has solutions) has the form γF (a, b) = ΦF (a) · b+φF (a)+1 for appropriate functions ΦF : Fn 2 → Fn 2 and φF : Fn 2 → F2. We summarize the known results and prove new ones regarding properties of ΦF and φF. For instance, we prove that degree of ΦF is either n or less or equal to n-2. Based on computation experiments, we formulate a conjecture that degree of any component function of ΦF is n -2. We show that this conjecture is based on two other conjectures of independent interest.
KW - A quadratic APN function
KW - Degree of a function
KW - The associated Boolean function
KW - degree of a function
KW - the associated Boolean function
KW - a quadratic APN function
UR - http://www.scopus.com/inward/record.url?scp=85085996962&partnerID=8YFLogxK
UR - https://www.elibrary.ru/item.asp?id=42525641
U2 - 10.17223/20710410/47/2
DO - 10.17223/20710410/47/2
M3 - Article
AN - SCOPUS:85085996962
SP - 16
EP - 21
JO - Прикладная дискретная математика
JF - Прикладная дискретная математика
SN - 2071-0410
IS - 47
ER -
ID: 24470226