Perfect nonlinear S-boxes
From MaRDI portal
Publication:4037482
DOI10.1007/3-540-46416-6_32zbMath0766.94012OpenAlexW1498892963WikidataQ21884115 ScholiaQ21884115MaRDI QIDQ4037482
Publication date: 18 May 1993
Published in: Advances in Cryptology — EUROCRYPT ’91 (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/3-540-46416-6_32
differential cryptoanalysisDillon's construction of difference setsMaiorana-McFarland construction of bent functionsnonbalanced directional derivativesperfect nonlinear S-box
Cryptography (94A60) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)
Related Items
Characteristics of nonlinearity of vectorial functions over finite fields ⋮ P℘N functions, complete mappings and quasigroup difference sets ⋮ Truncated differential properties of the diagonal set of inputs for 5-round AES ⋮ Vectorial Boolean functions with the maximum number of bent components beyond the Nyberg's bound ⋮ Revisiting some results on APN and algebraic immune functions ⋮ Construction of nonlinear component based on bent Boolean functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Perfect nonlinear S-boxes on the real-line ⋮ CS-Cipher ⋮ Статистическая оценка множества существенных аргументов двоичной вектор-функции с искаженными значениями ⋮ Construction of bent functions of 2kvariables from a basis of ⋮ Some Results on the Known Classes of Quadratic APN Functions ⋮ О примарных функциях, минимально близких к линейным ⋮ О приближении дискретных функций линейными функциями ⋮ Спектрально-линейный и спектрально-дифференциальный методы построения S-бокcов с близкими к оптимальным значениями криптографических параметров ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Improved Bounds on Sizes of Generalized Caps in $AG(n,q)$ ⋮ A Search Strategy to Optimize the Affine Variant Properties of S-Boxes ⋮ К вопросу о приближении векторных функций над конечными полями аффинными аналогами ⋮ Algorithm 959 ⋮ Bent partitions ⋮ Spectra of a class of quadratic functions: average behaviour and counting functions ⋮ Reversed genetic algorithms for generation of bijective s-boxes with good cryptographic properties ⋮ Enhanced criteria on differential uniformity and nonlinearity of cryptographically significant functions ⋮ Investigation of some cryptographic properties of the \(8 \times 8\) S-boxes created by quasigroups ⋮ Generalized Rothaus construction and non-weakly regular bent functions ⋮ Walsh transforms and cryptographic applications in bias computing ⋮ Bent and vectorial bent functions, partial difference sets, and strongly regular graphs ⋮ Constructions of (vectorial) bent functions outside the completed Maiorana-McFarland class ⋮ An analysis of a class of algorithms for \(S\)-box construction ⋮ Algebraic nonlinearity and its applications to cryptography ⋮ Towards tight security of cascaded LRW2 ⋮ A method to calculate differential uniformity for permutations ⋮ A family of skew Hadamard difference sets ⋮ A survey on \(p\)-ary and generalized bent functions ⋮ Componentwise APNness, Walsh uniformity of APN functions, and cyclic-additive difference sets ⋮ On cross-correlation indicators of an S-box ⋮ Nonlinearities of S-boxes ⋮ Design of new \(4\times 4\) S-box from finite commutative chain rings ⋮ Substitution-permutation networks resistant to differential and linear cryptanalysis ⋮ Differential cryptanalysis of Lucifer ⋮ A direct proof of APN-ness of the Kasami functions ⋮ On the algebraic immunity of multiplexer Boolean functions ⋮ Partial spread and vectorial generalized bent functions ⋮ Binary linear codes from vectorial Boolean functions and their weight distribution ⋮ Optimal FHSs and DSSs via near zero-difference balanced functions ⋮ Changing APN functions at two points ⋮ Generalized bent functions into \(\mathbb{Z}_{p^k}\) from the partial spread and the Maiorana-McFarland class ⋮ A New Criterion for Avoiding the Propagation of Linear Relations Through an Sbox ⋮ On the Properties of Vectorial Functions with Plateaued Components and Their Consequences on APN Functions ⋮ On the relationships between perfect nonlinear functions and universal hash families ⋮ Open Questions on Nonlinearity and on APN Functions ⋮ Constructing infinite families of low differential uniformity (\(n,m\))-functions with \(m>n/2\) ⋮ Further results on complete permutation monomials over finite fields ⋮ A new construction of differentially 4-uniform \((n,n-1)\)-functions ⋮ A construction of bent functions of \(n+2\) variables from a bent function of \(n\) variables and its cyclic shifts ⋮ On the construction of hardware-friendly \(4\times4\) and \(5\times5\) S-boxes ⋮ CCZ-equivalence of bent vectorial functions and related constructions ⋮ Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions ⋮ A note on the minimal binary linear code ⋮ Four decades of research on bent functions ⋮ Almost perfect and planar functions ⋮ Constructions with high algebraic degree of differentially 4-uniform \((n, n - 1)\)-functions and differentially 8-uniform \((n, n - 2)\)-functions ⋮ Divisible designs and semi-regular relative difference sets from additive Hadamard cocycles ⋮ Sets of zero-difference balanced functions and their applications ⋮ More constructions of APN and differentially 4-uniform functions by concatenation ⋮ Literature survey on nonlinear components and chaotic nonlinear components of block ciphers ⋮ On multiple output bent functions ⋮ A note on vectorial bent functions ⋮ Revisiting iterated attacks in the context of decorrelation theory ⋮ On generalized bent functions with Dillon's exponents ⋮ The shift action on 2-cocycles. ⋮ Nonlinear functions in abelian groups and relative difference sets. ⋮ Bent and \(\mathbb{Z}_{2^k}\)-bent functions from spread-like partitions ⋮ On APN exponents, characterizations of differentially uniform functions by the Walsh transform, and related cyclic-difference-set-like structures ⋮ A note on nonexistence of vectorial bent functions with binomial trace representation in the \(\mathcal{PS}^-\) class ⋮ A new construction of highly nonlinear S-boxes ⋮ Intersection of Hamming codes avoiding Hamming subcodes ⋮ A practical-time related-key attack on the \texttt{KASUMI} cryptosystem used in GSM and 3G telephony ⋮ New links between nonlinearity and differential uniformity ⋮ Vectorial bent functions and partial difference sets ⋮ On perfect nonlinear functions \((\Pi)\) ⋮ Highly nonlinear balanced S-boxes with improved bound on unrestricted and generalized nonlinearity ⋮ A new method for secondary constructions of vectorial bent functions ⋮ Bent vectorial functions and linear codes from o-polynomials ⋮ Doubly perfect nonlinear boolean permutations ⋮ On the nonlinearity of S-boxes and linear codes ⋮ Fast Correlation Attacks: Methods and Countermeasures ⋮ Vectorial bent functions and their duals ⋮ Compositional inverses and complete mappings over finite fields ⋮ Almost perfect nonlinear families which are not equivalent to permutations ⋮ A secondary construction of bent functions, octal gbent functions and their duals ⋮ On constructions and properties of \((n,m)\)-functions with maximal number of bent components ⋮ Determining the Walsh spectra of Taniguchi's and related APN-functions ⋮ A new characterization of semi-bent and bent functions on finite fields ⋮ Asymptotic nonlinearity of vectorial Boolean functions ⋮ Construction of bent functions via Niho power functions ⋮ Constructing vectorial bent functions via second-order derivatives ⋮ Bent functions on partial spreads ⋮ Perfect nonlinear functions and cryptography ⋮ On the linear structures of balanced functions and quadratic APN functions ⋮ Vectorial bent functions in odd characteristic and their components ⋮ Cryptographic properties of small bijective S-boxes with respect to modular addition ⋮ Recent results and problems on constructions of linear codes from cryptographic functions ⋮ Algebraic manipulation detection codes via highly nonlinear functions ⋮ Construction of Lightweight S-Boxes Using Feistel and MISTY Structures ⋮ G-perfect nonlinear functions ⋮ Три подхода к понятию функций, максимально отличающихся от гомоморфизмов ⋮ \(C\)-differential bent functions and perfect nonlinearity ⋮ A new characterization of group action-based perfect nonlinearity ⋮ Highly nonlinear mappings ⋮ Zero-difference balanced functions with applications ⋮ A new construction of zero-difference balanced functions and two applications ⋮ Further study on the maximum number of bent components of vectorial functions ⋮ On certain diagonal equations over finite fields ⋮ Provable security against a differential attack ⋮ Symbolic dynamics and rotation symmetric Boolean functions ⋮ Linear codes and incidence structures of bent functions and their generalizations ⋮ Permutations of finite fields with prescribed properties ⋮ Quadratic zero-difference balanced functions, APN functions and strongly regular graphs
