Kwang Ho Kim

collaborators

3 papers

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.IT2021

Complete solution over $\GF{p^n}$ of the equation $X^{p^{k} + 1} + X + a = 0$

Kwang Ho Kim, Jong Hyok Choe, Sihem Mesnager

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

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 $\GF{2^{4k}}$

Complete solution over $\GF{p^n}$ of the equation Xpk+1+X+a=0

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 $\GF{2^{4k}}$

Complete solution over $\GF{p^n}$ of the equation $X^{p^{k} + 1} + X + a = 0$