Kwang Ho Kim

activity

20182023

x^{2^{k} + 1} + x + a = 0

F_{2^{n}}

with

g cd (n, k) = 1

4 citations · 9 across the 10 of their papers we have counts for

collaborators

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12 papers · 1 filter

cs.IT2023

On the Boomerang Spectrum of Power Permutation $X^{2^{3 n} + 2^{2 n} + 2^{n} - 1}$ over $\GF{2^{4n}}$ and Extraction of Optimal Uniformity Boomerang Functions

Kwang Ho Kim, Sihem Mesnager, Ye Bong Kim

A substitution box (S-box) in a symmetric primitive is a mapping $F$ that takes $k$ binary inputs and whose image is a binary $m$ -tuple for some positive integers $k$ and $m$ , whic…

cs.IT2023

Solving $X^{2^{2 k} + 2^{k} + 1} + (X + 1)^{2^{2 k} + 2^{k} + 1} = b$ over $\GF{2^{4k}}$

Kwang Ho Kim, Sihem Mesnager, Chung Hyok Kim

Let $F (X) = X^{2^{2 k} + 2^{k} + 1}$ be the power function over the finite field $\GF{2^{4k}}$ which is known as the Bracken-Leander function. In \cite{BCC10,BL10,CV20,Fu22,XY17}, it was pr…

cs.IT2022

Solving $X^{2^{3 n} + 2^{2 n} + 2^{n} - 1} + (X + 1)^{2^{3 n} + 2^{2 n} + 2^{n} - 1} = b$ in $GF 2^{4 n}$

Kwang Ho Kim, Sihem Mesnager

This article determines all the solutions in the finite field $GF 2^{4 n}$ of the equation $x^{2^{3 n} + 2^{2 n} + 2^{n} - 1} + (x + 1)^{2^{3 n} + 2^{2 n} + 2^{n} - 1} = b$ . Specifically, we explicitly…

cs.IT2020

Preimages of $p -$ Linearized Polynomials over $\GF{p}$

Kwang Ho Kim, Sihem Mesnager, Jong Hyok Choe +1

Linearized polynomials over finite fields have been intensively studied over the last several decades. Interesting new applications of linearized polynomials to coding theory and f…

cs.IT2020

Solving Some Affine Equations over Finite Fields

Sihem Mesnager, Kwang Ho Kim, Jong Hyok Choe +1

Let $l$ and $k$ be two integers such that $l ∣ k$ . Define $T_{l}^{k} (X) := X + X^{p^{l}} + \dots + X^{p^{l (k / l - 2)}} + X^{p^{l (k / l - 1)}}$ and $S_l^k(X):=X-X^{p^l}+\cdots+(-1)^{(k/l-1)}X^{p^{l(k/l-1)}…

cs.IT2020

A direct proof of APN-ness of the Kasami functions

Claude Carlet, Kwang Ho Kim, Sihem Mesnager

Using recent results on solving the equation $X^{2^{k} + 1} + X + a = 0$ over a finite field $F_{2^{n}}$ , we address an open question raised by the first author in WAIFI 2014 concerni…

cs.IT2019★ 2 cited

Solving $X^{q + 1} + X + a = 0$ over Finite Fields

Kwang Ho Kim, Junyop Choe, Sihem Mesnager

Solving the equation $P_{a} (X) := X^{q + 1} + X + a = 0$ over finite field $\GF{Q}$, where $Q = p^{n}, q = p^{k}$ and $p$ is a prime, arises in many different contexts including finite geometry, the i…

cs.IT2019★ 2 cited

Solutions of $x^{q^{k}} + \dots + x^{q} + x = a$ in $GF 2^{n}$

Kwang Ho Kim, Jong Hyok Choe, Dok Nam Lee +2

Though it is well known that the roots of any affine polynomial over a finite field can be computed by a system of linear equations by using a normal base of the field, such solvin…

cs.IT2019★ 4 cited

Solving $x^{2^{k} + 1} + x + a = 0$ in $F_{2^{n}}$ with $g cd (n, k) = 1$

Kwang Ho Kim, Sihem Mesnager

Let $N_{a}$ be the number of solutions to the equation $x^{2^{k} + 1} + x + a = 0$ in $\GF {n}$ where $g cd (k, n) = 1$ . In 2004, by Bluher \cite{BLUHER2004} it was known that possible values of $…

cs.IT2018★ 1 cited

A Proof of the Beierle-Kranz-Leander Conjecture related to Lightweight Multiplication in $\mathds{F}_{2^n}$

Sihem Mesnager, Kwang Ho Kim, Dujin Jo +3

Lightweight cryptography is a key tool for building strong security solutions for pervasive devices with limited resources. Due to the stringent cost constraints inherent in extrem…

cs.IT2018

Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions

Sihem Mesnager, Kwang Ho Kim, Myong Song Jo

To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystem…

cs.IT2018

On the Menezes-Teske-Weng's conjecture

Sihem Mesnager, Kwang Ho Kim, Junyop Choe +1

In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conjecture on properties of the solutions of a type of quadratic equation over the binary extension fields, which…

On the Boomerang Spectrum of Power Permutation X23n+22n+2n−1 over $\GF{2^{4n}}$ and Extraction of Optimal Uniformity Boomerang Functions

Solving X22k+2k+1+(X+1)22k+2k+1=b over $\GF{2^{4k}}$

Solving X23n+22n+2n−1+(X+1)23n+22n+2n−1=b in GF24n

Preimages of p−Linearized Polynomials over $\GF{p}$

Solving Some Affine Equations over Finite Fields

A direct proof of APN-ness of the Kasami functions

Solving Xq+1+X+a=0 over Finite Fields

Solutions of xqk+⋯+xq+x=a in GF2n

Solving x2k+1+x+a=0 in F2n​ with gcd(n,k)=1

A Proof of the Beierle-Kranz-Leander Conjecture related to Lightweight Multiplication in $\mathds{F}_{2^n}$

Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions

On the Menezes-Teske-Weng's conjecture

On the Boomerang Spectrum of Power Permutation $X^{2^{3 n} + 2^{2 n} + 2^{n} - 1}$ over $\GF{2^{4n}}$ and Extraction of Optimal Uniformity Boomerang Functions

Solving $X^{2^{2 k} + 2^{k} + 1} + (X + 1)^{2^{2 k} + 2^{k} + 1} = b$ over $\GF{2^{4k}}$

Solving $X^{2^{3 n} + 2^{2 n} + 2^{n} - 1} + (X + 1)^{2^{3 n} + 2^{2 n} + 2^{n} - 1} = b$ in $GF 2^{4 n}$

Preimages of $p -$ Linearized Polynomials over $\GF{p}$

Solving $X^{q + 1} + X + a = 0$ over Finite Fields

Solutions of $x^{q^{k}} + \dots + x^{q} + x = a$ in $GF 2^{n}$

Solving $x^{2^{k} + 1} + x + a = 0$ in $F_{2^{n}}$ with $g cd (n, k) = 1$