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05/22/2023
On the Boomerang Spectrum of Power Permutation X^2^3n+2^2n+2^n-1 over 2^4n and Extraction of Optimal Uniformity Boomerang Functions
A substitution box (S-box) in a symmetric primitive is a mapping F that ...
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05/22/2023
Solving X^2^2k+2^k+1+(X+1)^2^2k+2^k+1=b over 2^4k
Let F(X)=X^2^2k+2^k+1 be the power function over the finite field 2^4k w...
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11/28/2022
Regional Precipitation Nowcasting Based on CycleGAN Extension
Unusually, intensive heavy rain hit the central region of Korea on Augus...
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04/08/2022
Solving X^2^3n+2^2n+2^n-1+(X+1)^2^3n+2^2n+2^n-1=b in GF2^4n
This article determines all the solutions in the finite field GF2^4n of ...
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01/04/2021
Complete solution over p^n of the equation X^p^k+1+X+a=0
The problem of solving explicitly the equation P_a(X):=X^q+1+X+a=0 over ...
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11/22/2020
Preimages of p-Linearized Polynomials over p
Linearized polynomials over finite fields have been intensively studied ...
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02/12/2020
Solving Some Affine Equations over Finite Fields
Let l and k be two integers such that l|k. Define T_l^k(X):=X+X^p^l+...+...
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01/31/2020
A direct proof of APN-ness of the Kasami functions
Using recent results on solving the equation X^2^k+1+X+a=0 over a finite...
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12/29/2019
Solving X^q+1+X+a=0 over Finite Fields
Solving the equation P_a(X):=X^q+1+X+a=0 over finite field Q, where Q=p^...
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05/25/2019
Solutions of x^q^k+...+x^q+x=a in GF2^n
Though it is well known that the roots of any affine polynomial over a f...
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03/18/2019
Solving x^2^k+1+x+a=0 in F_2^n with (n,k)=1
Let N_a be the number of solutions to the equation x^2^k+1+x+a=0 in n wh...
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12/23/2018
A Proof of the Beierle-Kranz-Leander Conjecture related to Lightweight Multiplication in F_2^n
Lightweight cryptography is a key tool for building strong security solu...
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11/27/2018
Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions
To determine the dimension of null space of any given linearized polynom...
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07/05/2018
