A5088687711- Coding theory and cryptography
- Cryptographic Implementations and Security
- graph theory and CDMA systems
- Chaos-based Image/Signal Encryption
- Cellular Automata and Applications
- Cancer Mechanisms and Therapy
- Finite Group Theory Research
- Error Correcting Code Techniques
- Cooperative Communication and Network Coding
- Physical Unclonable Functions (PUFs) and Hardware Security
- Polynomial and algebraic computation
- semigroups and automata theory
- Advanced Malware Detection Techniques
- Advanced Algebra and Logic
- Peptidase Inhibition and Analysis
- DNA and Biological Computing
- Metaheuristic Optimization Algorithms Research
- Cryptography and Residue Arithmetic
- Computability, Logic, AI Algorithms
- Advanced Wireless Communication Techniques
- Intelligence, Security, War Strategy
- Algebraic structures and combinatorial models
- Cryptography and Data Security
- Advanced Combinatorial Mathematics
- Evolutionary Algorithms and Applications
University of Bergen
2016-2024
Université Paris 8
2015-2024
Laboratoire Analyse, Géométrie et Applications
2014-2023
Centre National de la Recherche Scientifique
2011-2023
Université Sorbonne Paris Nord
2013-2023
Université Paris Cité
2014-2023
Novosibirsk State University
2020-2021
Delft University of Technology
2021
Laboratoire de Mathématiques d'Orsay
2008-2020
Université Paris-Sud
2010-2018
In this paper, error-correcting codes from perfect nonlinear mappings are constructed, and then employed to construct secret sharing schemes. The obtained in paper very good general, many of them optimal or almost optimal. schemes have two types access structures. first type is democratic the sense that every participant involved same number minimal-access sets. second structures, there a few dictators who minimal set, while each remaining participants
Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of cryptography coding covers the whole domain all important results, building on author's influential articles with additional topics recent results. A useful resource researchers graduate students, book balances detailed discussions properties parameters examples various types cryptographic attacks that motivate consideration these parameters. It provides necessary background...
We recall why linear codes with complementary duals (LCD codes) play a role in counter-measures to passive and active side-channel analyses on embedded cryptosystems. The rate the minimum distance of such LCD must be as large possible. known primary construction cyclic codes, investigate other constructions, expanded Reed-Solomon generalized residue for which we study idempotents. These constructions do not allow reach all desired parameters. then those secondary preserve property,...
The hull $H(C)$ of a linear code $C$ is defined by $H(C)=C \cap C^\perp$. A with complementary dual (LCD) $H(C)=\{0\}$. dimension the an invariant under permutation equivalence. For binary and ternary codes also monomial equivalence we show that this determined extended weight enumerator code.\\ not if $q\geq 4$. We every ${\mathbb F}_q $-linear equivalent LCD in case $q \geq proof uses techniques from Gr\"obner basis theory. conclude there exists parameters $[n,k,d]_q$ 4$, then same...
Recently, algebraic attacks have received a lot of attention in the cryptographic literature. It has been observed that Boolean function f used as primitive, and interpreted multivariate polynomial over F/sub 2/, should not low degree multiples obtained by multiplication with nonzero functions. In this paper, we show having nonlinearity is (also) weak against attacks, extend result to higher order nonlinearities. Next, present enumeration results on linearly independent annihilators. We also...
New infinite classes of almost bent and perfect nonlinear polynomials are constructed. It is shown that they affine inequivalent to any sum a power function an
This paper introduces the first found infinite classes of almost perfect nonlinear (APN) polynomials which are not Carlet-Charpin-Zinoviev (CCZ)-equivalent to power functions (at least for some values number variables). These two APN binomials from F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2n</sub> (for n divisible by 3, resp., 4). We prove that these extended affine (EA)-inequivalent any function and they CCZ-inequivalent Gold, Kasami,...
In this correspondence, the weight distribution of a class linear codes based on perfect nonlinear functions (also called planar functions) is determined. The under study are either optimal or among best known, and have nice applications in cryptography.
We introduce a generalization to Z/sub 2/k of the Gray map and generalized versions Kerdock Delsarte-Goethals codes.