Solving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo linebreak="badbreak" linebreakstyle="after">−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo linebreak="badbreak" linebreakstyle="after">−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mi>b</mml:mi></mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:math> and an alternative proof of a conjecture on the differential spectrum of the related monomial functions-Reference-Cited by-同舟云学术

Solving X23n+22n+2n−1+(X+1)23n+22n+2n−1=b in F24n and an alternative proof of a conjecture on the differential spectrum of the related monomial functions

Published:2022-10 Issue: Volume:83 Page:102086
ISSN:1071-5797
Container-title:Finite Fields and Their Applications
language:en
Short-container-title:Finite Fields and Their Applications

Author:

Kim Kwang Ho,Mesnager Sihem^ORCID

Publisher

Elsevier BV

Subject

Applied Mathematics,General Engineering,Algebra and Number Theory,Theoretical Computer Science

Reference12 articles.

1. Differential cryptanalysis of DES-like cryptosystems;Biham;J. Cryptol.,1991

2. On two fundamental problems on APN power functions;Budaghyan;IEEE Trans. Inf. Theory,2022

3. Boolean Functions for Cryptography and Coding Theory;Carlet,2021

4. A direct proof of APN-ness of the Kasami functions;Carlet;Des. Codes Cryptogr.,2021

5. Another proof of Kasami's Theorem;Dobbertin;Des. Codes Cryptogr.,1999

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1. In-depth analysis of S-boxes over binary finite fields concerning their differential and Feistel boomerang differential uniformities;Discrete Mathematics;2024-12

2. A new method for solving the equation x + (x+1)  = b in Fq4 where d = q3 + q2 + q − 1;Discrete Mathematics;2024-07

3. Corrigendum to “Solving X23n+22n+2n−1+(X+1)23n+22n+2n−1=b in F24n and an alternative proof of a conjecture on the differential spectrum of the related monomial functions” [Finite Fields Appl. 83 (2022) 102086];Finite Fields and Their Applications;2023-03