Propagation characteristics of \(x\mapsto x^{-1}\) and Kloosterman sums

DOI10.1016/j.ffa.2005.08.007zbMath1148.11041OpenAlexW2069017437MaRDI QIDQ946890

Tor Helleseth, Pascale Charpin, Victor A. Zinoviev

Publication date: 25 September 2008

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.08.007

zbMATH Keywords

Boolean functionsKloosterman sumcryptographic criteriaMelas codesinverse permutationvectorial mapping

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05)

Related Items (16)

Enhanced criteria on differential uniformity and nonlinearity of cryptographically significant functions ⋮ On classical Kloosterman sums ⋮ A note on the moments of Kloosterman sums ⋮ Autocorrelations of vectorial Boolean functions ⋮ New differentially 4-uniform permutations from modifications of the inverse function ⋮ Vectorial Boolean functions with very low differential-linear uniformity using Maiorana-McFarland type construction ⋮ On divisibility of exponential sums of polynomials of special type over fields of characteristic 2 ⋮ On zeros of Kloosterman sums ⋮ Permutation polynomials EA-equivalent to the inverse function over \(\mathrm{GF}(2^n)\) ⋮ On subspaces of Kloosterman zeros and permutations of the form \(L_1(x^{-1})+L_2(x)\) ⋮ Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros ⋮ On ternary Kloosterman sums modulo 12 ⋮ On the Connection between Kloosterman Sums and Elliptic Curves ⋮ On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations ⋮ CONSTRUCTION OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMS: O + (2n, 2 r ) CASE ⋮ An efficient deterministic test for Kloosterman sum zeros

Cites Work

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• Some results about the cross-correlation function between two maximal linear sequences
• Codes, bent functions and permutations suitable for DES-like cryptosystems
• On cosets of weight 4 of binary BCH codes with minimum distance 8 and exponential sums
• The weights of the orthogonals of the extended quadratic binary Goppa codes
• Niho type cross-correlation functions via dickson polynomials and Kloosterman sums
• On cryptographic properties of the cosets of R(1, m)
• Modifications of Patterson-Wiedemann functions for cryptographic applications

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