On the nonlinearity of exponential welch costas functions

Authors:
Konstantinos Drakakis;Verónica Requena;Gary McGuire
Affiliations:
School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland and Claude Shannon Institute and UCD, CASL, Ireland;Departament de Ciència de la Computació i Intelligencia Artificial, Universitat d' Alacant, Alacant, Spain;School of Mathematical Sciences, University College, Dublin, Belfield, Dublin 4, Ireland and UCD, CASL, Ireland
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 17
Cited 1

Linear cryptanalysis method for DES cipher

EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Adapted diameters and the efficient computation of Fourier transforms on finite groups

Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Handbook of Applied Cryptography

Handbook of Applied Cryptography
Handbook of Coding Theory

Handbook of Coding Theory
Differential Cryptanalysis of DES-like Cryptosystems

CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
A Known Plaintext Attack of FEAL-4 and FEAL-6

CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Generalization of Siegenthaler Inequality and Schnorr-Vaudenay Multipermutations

CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
SAFER K-64: A Byte-Oriented Block-Ciphering Algorithm

Fast Software Encryption, Cambridge Security Workshop
Nonlinear functions in abelian groups and relative difference sets

Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Highly nonlinear mappings

Journal of Complexity - Special issue on coding and cryptography
Note: APN permutations on Zn and Costas arrays

Discrete Applied Mathematics
Determining the nonlinearity of a new family of APN functions

AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Linear cryptanalysis of non binary ciphers

SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Differential cryptanalysis for multivariate schemes

EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
A New Family of Ternary Almost Perfect Nonlinear Mappings

IEEE Transactions on Information Theory
The Status of Costas Arrays

IEEE Transactions on Information Theory
Results of the Enumeration of Costas Arrays of Order

IEEE Transactions on Information Theory

Permutations of finite fields with prescribed properties

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	754.84

Visualization

Abstract

We study the nonlinearity of the Exponential Welch Costas functions, using the Fourier Transform on Zm. These functions have been proposed for use in nonbinary cryptosystems. High nonlinearity is required to ensure resistance to linear cryptanalysis. We prove some properties of the nonlinearity of these functions, and we suggest a plausible connection of the nonlinearity to the class number of a quadratic field.