Low differentially uniform permutations from Dobbertin APN function over 𝔽_2^n

03/19/2021
by   Yan-Ping Wang, et al.
0

Block ciphers use S-boxes to create confusion in the cryptosystems. Such S-boxes are functions over 𝔽_2^n. These functions should have low differential uniformity, high nonlinearity, and high algebraic degree in order to resist differential attacks, linear attacks, and higher order differential attacks, respectively. In this paper, we construct new classes of differentially 4 and 6-uniform permutations by modifying the image of the Dobbertin APN function x^d with d=2^4k+2^3k+2^2k+2^k-1 over a subfield of 𝔽_2^n. Furthermore, the algebraic degree and the lower bound of the nonlinearity of the constructed functions are given.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/31/2019

Differentially low uniform permutations from known 4-uniform functions

Functions with low differential uniformity can be used in a block cipher...
research
11/08/2021

Higher Order c-Differentials

EFRST20, the notion of c-differentials was introduced as a potential exp...
research
12/08/2020

On the differential spectrum of a class of power functions over finite fields

Differential uniformity is a significant concept in cryptography as it q...
research
01/26/2021

On -1-differential uniformity of ternary APN power functions

Very recently, a new concept called multiplicative differential and the ...
research
02/08/2020

Invariant Hopping Attacks on Block Ciphers

Block ciphers are in widespread use since the 1970s. Their iterated stru...
research
12/09/2022

On the Evolution of Boomerang Uniformity in Cryptographic S-boxes

S-boxes are an important primitive that help cryptographic algorithms to...
research
05/12/2019

Lack of Unique Factorization as a Tool in Block Cipher Cryptanalysis

Linear (or differential) cryptanalysis may seem dull topics for a mathem...

Please sign up or login with your details

Forgot password? Click here to reset