Several new infinite families of bent functions via second order derivatives

DOI10.1007/s12095-020-00436-0zbMath1468.94979OpenAlexW3025611388MaRDI QIDQ2040322

Yanjun Li, Jie Peng, Haibin Kan, Lijing Zheng

Publication date: 13 July 2021

Published in: Cryptography and Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12095-020-00436-0

zbMATH Keywords

dualWalsh spectrumbent functionsalgebraic degreesecond order derivative

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50) Boolean functions (94D10)

Related Items (9)

A complete characterization of \(\mathcal{D}_0 \cap\mathcal{M}^\#\) and a general framework for specifying bent functions in \(\mathcal{C}\) outside \(\mathcal{M}^\#\) ⋮ Explicit infinite families of bent functions outside the completed Maiorana-McFarland class ⋮ Cryptographic functions with interesting properties from CCZ-equivalence ⋮ Generic construction of Boolean functions with a few Walsh transform values of any possible algebraic degree ⋮ Constructions of several special classes of cubic bent functions outside the completed Maiorana-McFarland class ⋮ New classes of bent functions via the switching method ⋮ Bent functions constructed from finite pre-quasifield spreads ⋮ Several classes of bent functions over finite fields ⋮ Constructing vectorial bent functions via second-order derivatives

Cites Work

• Four decades of research on bent functions
• Note on cubics over \(GF(2^n)\) and \(GF(3^n)\)
• On ``bent functions
• New quadratic bent functions in polynomial forms with coefficients in extension fields
• A new class of monomial bent functions
• Finding nonnormal bent functions
• Several New Infinite Families of Bent Functions and Their Duals
• Monomial bent functions
• Explicit evaluation of certain exponential sums.
• Generic Construction of Bent Functions and Bent Idempotents With Any Possible Algebraic Degrees
• Comments on "Monomial Bent Functions" [Feb 2006 738-743]
• Bent Functions
• Constructing Bent Functions Outside the Maiorana–McFarland Class Using a General Form of Rothaus
• Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

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