A note on the properties of associated boolean functions of quadratic APN functions

Standard

A note on the properties of associated boolean functions of quadratic APN functions. / Gorodilova, A. A.

In: Прикладная дискретная математика, No. 47, 01.01.2020, p. 16-21.

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

Harvard

Gorodilova, AA 2020, 'A note on the properties of associated boolean functions of quadratic APN functions', Прикладная дискретная математика, no. 47, pp. 16-21. https://doi.org/10.17223/20710410/47/2

APA

Gorodilova, A. A. (2020). A note on the properties of associated boolean functions of quadratic APN functions. Прикладная дискретная математика, (47), 16-21. https://doi.org/10.17223/20710410/47/2

Vancouver

Gorodilova AA. A note on the properties of associated boolean functions of quadratic APN functions. Прикладная дискретная математика. 2020 Jan 1;(47):16-21. doi: 10.17223/20710410/47/2

Author

Gorodilova, A. A. / A note on the properties of associated boolean functions of quadratic APN functions. In: Прикладная дискретная математика. 2020 ; No. 47. pp. 16-21.

BibTeX

@article{f92601288b9845cda2765d9c3ec8bcaa,

title = "A note on the properties of associated boolean functions of quadratic APN functions",

abstract = "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.",

keywords = "A quadratic APN function, Degree of a function, The associated Boolean function, degree of a function, the associated Boolean function, a quadratic APN function",

author = "Gorodilova, {A. A.}",

year = "2020",

month = jan,

day = "1",

doi = "10.17223/20710410/47/2",

language = "English",

pages = "16--21",

journal = "Прикладная дискретная математика",

issn = "2071-0410",

publisher = "Tomsk State University",

number = "47",

}

RIS

TY - JOUR

T1 - A note on the properties of associated boolean functions of quadratic APN functions

AU - Gorodilova, A. A.

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