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09/05/2023
In-depth analysis of S-boxes over binary finite fields concerning their differential and Feistel boomerang differential uniformities
Substitution boxes (S-boxes) play a significant role in ensuring the res...
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05/23/2023
Constructions of Constant Dimension Subspace Codes
Subspace codes have important applications in random network coding. It ...
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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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05/09/2023
On differential properties of a class of Niho-type power function
This paper deals with Niho functions which are one of the most important...
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03/16/2023
Characterizations of a Class of Planar Functions over Finite Fields
Planar functions, introduced by Dembowski and Ostrom, have attracted muc...
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03/16/2023
Binomials and Trinomials as Planar Functions on Cubic Extensions of Finite Fields
Planar functions, introduced by Dembowski and Ostrom, are functions from...
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12/09/2022
The Subfield Codes of Some Few-Weight Linear Codes
Subfield codes of linear codes over finite fields have recently received...
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12/09/2022
On the Evolution of Boomerang Uniformity in Cryptographic S-boxes
S-boxes are an important primitive that help cryptographic algorithms to...
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10/21/2022
Cyclic codes from low differentially uniform functions
Cyclic codes have many applications in consumer electronics, communicati...
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10/19/2022
On the differential spectrum of a class of APN power functions over odd characteristic finite fields and their c-differential properties
Only three classes of Almost Perfect Nonlinear (for short, APN) power fu...
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10/18/2022
Two low differentially uniform power permutations over odd characteristic finite fields: APN and differentially 4-uniform functions
Permutation polynomials over finite fields are fundamental objects as th...
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08/04/2022
On the Niho type locally-APN power functions and their boomerang spectrum
In this article, we focus on the concept of locally-APN-ness (“APN" is t...
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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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12/05/2021
Optimal quaternary (r,δ)-Locally Recoverable Codes: Their Structures and Complete Classification
Aiming to recover the data from several concurrent node failures, linear...
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09/19/2021
On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and their Consequences
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass o...
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09/10/2021
Constructions of Binary Cross Z-Complementary Pairs With Large CZC Ratio
Cross Z-complementary pairs (CZCPs) are a special kind of Z-complementar...
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07/24/2021
New constructions of q-Ary 2-D Z-Complementary Array Pairs
This paper is devoted to sequences and focuses on designing new two-dime...
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03/29/2021
A function field approach toward good polynomials for optimal LRC codes
Because of the recent applications to distributed storage systems, resea...
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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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10/19/2020
Investigations on c-(almost) perfect nonlinear functions
In a prior paper <cit.>, two of us, along with P. Ellingsen, P. Felke an...
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06/15/2020
Fast algebraic immunity of Boolean functions and LCD codes
Nowadays, the resistance against algebraic attacks and fast algebraic at...
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04/10/2020
A Novel Application of Boolean Functions with High Algebraic Immunity in Minimal Codes
Boolean functions with high algebraic immunity are important cryptograph...
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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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10/15/2019
Further study of 2-to-1 mappings over F_2^n
2-to-1 mappings over finite fields play an important role in symmetric c...
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08/05/2019
Minimal linear codes from characteristic functions
Minimal linear codes have interesting applications in secret sharing sch...
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06/27/2019
On two-to-one mappings over finite fields
Two-to-one (2-to-1) mappings over finite fields play an important role i...
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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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05/21/2019
Codebooks from generalized bent Z_4-valued quadratic forms
Codebooks with small inner-product correlation have application in unita...
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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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03/15/2019
A class of narrow-sense BCH codes over F_q of length q^m-1/2
BCH codes with efficient encoding and decoding algorithms have many appl...
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03/01/2019
On the boomerang uniformity of (quadratic) permutations over F_2^n
At Eurocrypt'18, Cid, Huang, Peyrin, Sasaki, and Song introduced a new t...
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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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11/19/2018
Cyclic bent functions and their applications in codes, codebooks, designs, MUBs and sequences
Let m be an even positive integer. A Boolean bent function f on m-1× is ...
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09/10/2018
Strongly regular graphs from weakly regular plateaued functions
The paper provides the first constructions of strongly regular graphs an...
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08/14/2018
Two constructions of optimal pairs of linear codes for resisting side channel and fault injection attacks
Direct sum masking (DSM) has been proposed as a counter-measure against ...
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08/11/2018
Several classes of minimal linear codes with few weights from weakly regular plateaued functions
Minimal linear codes have significant applications in secret sharing sch...
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07/05/2018
On the Menezes-Teske-Weng's conjecture
In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conje...
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01/21/2018
Further study on the maximum number of bent components of vectorial functions
In 2018, Pott, at al. have studied in [IEEE Transactions on Information ...
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12/30/2017