On the Algebraic Immunity of Symmetric Boolean Functions

From MaRDI portal
Publication:5450975

DOI10.1007/11596219_4zbMath1153.94353OpenAlexW1821279578WikidataQ62045623 ScholiaQ62045623MaRDI QIDQ5450975

Bart Preneel, An Braeken

Publication date: 17 March 2008

Published in: Progress in Cryptology - INDOCRYPT 2005 (Search for Journal in Brave)

Full work available at URL: https://www.cosic.esat.kuleuven.be/publications/article-577.pdf




Related Items

On the fast algebraic immunity of threshold functionsOn various nonlinearity measures for Boolean functionsA construction of 1-resilient Boolean functions with good cryptographic propertiesHamming weights of symmetric Boolean functionsBasic theory in construction of Boolean functions with maximum possible annihilator immunityBoolean functions of an odd number of variables with maximum algebraic immunitySecondary constructions of Boolean functions with maximum algebraic immunityOn the algebraic immunity of direct sum constructionsA characterization of balanced Boolean functions with optimal algebraic immunityProperties of a Family of Cryptographic Boolean FunctionsCryptographic properties of the hidden weighted bit functionWeightwise perfectly balanced functions and nonlinearityCharacterization of robust immune symmetric Boolean functionsOn the algebraic immunity -- resiliency trade-off, implications for Goldreich's pseudorandom generatorWeightwise almost perfectly balanced functions: secondary constructions for all \(n\) and better weightwise nonlinearitiesOn the affine equivalence relation between two classes of Boolean functions with optimal algebraic immunityBalanced Boolean functions with optimum algebraic degree, optimum algebraic immunity and very high nonlinearityOn extended algebraic immunityOn the security of the Feng-Liao-Yang Boolean functions with optimal algebraic immunity against fast algebraic attacksA new method to construct Boolean functions with good cryptographic propertiesBoolean Functions for Homomorphic-Friendly Stream CiphersAlgebraic immunity for cryptographically significant Boolean functions: analysis and constructionA design of Boolean functions resistant to (fast) algebraic cryptanalysis with efficient implementationTwo constructions of balanced Boolean functions with optimal algebraic immunity, high nonlinearity and good behavior against fast algebraic attacksA trigonometric sum sharp estimate and new bounds on the nonlinearity of some cryptographic Boolean functionsOn the \(2^{m}\)-variable symmetric Boolean functions with maximum algebraic immunityConstruction and enumeration of Boolean functions with maximum algebraic immunityEfficient Computation of Algebraic Immunity for Algebraic and Fast Algebraic AttacksSimpler proof for nonlinearity of majority functionWeight Support Technique and the Symmetric Boolean Functions with Maximum Algebraic Immunity on Even Number of VariablesAn Infinite Class of Balanced Functions with Optimal Algebraic Immunity, Good Immunity to Fast Algebraic Attacks and Good NonlinearityOn the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their GeneralizationsHybrid classes of balanced Boolean functions with good cryptographic propertiesSome lower bounds on the algebraic immunity of functions given by their trace formsFurther properties of several classes of Boolean functions with optimum algebraic immunityOn second-order nonlinearity and maximum algebraic immunity of some bent functions in \(\mathcal{PS}^{+}\)Improved lower bound on the number of balanced symmetric functions over \(\text{GF}(p)\)Enumeration of balanced symmetric functions over \(GF(p)\)On \((2^{m}+1)\)-variable symmetric Boolean functions with submaximum algebraic immunity \(2^{m - 1}\)Construction of balanced rotation symmetric Boolean functions with optimal algebraic immunityOn the weightwise nonlinearity of weightwise perfectly balanced functionsA construction of Boolean functions with good cryptographic properties