On the covering radius of Reed-Muller codes
Discrete Mathematics - A collection of contributions in honour of Jack van Lint
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
GL(m,2) acting on R(r,m)/R(r−1,m)
Discrete Mathematics
Handbook of Applied Cryptography
Handbook of Applied Cryptography
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Probabilistic Higher Order Differential Attack and Higher Order Bent Functions
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Journal of Complexity - Special issue on coding and cryptography
Journal of Complexity - Special issue on coding and cryptography
Piecewise Constructions of Bent and Almost Optimal Boolean Functions
Designs, Codes and Cryptography
Finding nonnormal bent functions
Discrete Applied Mathematics - Special issue: Coding and cryptography
Non-linear approximations in linear cryptanalysis
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Efficient computation of the best quadratic approximations of cubic boolean functions
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
A new class of single cycle t-functions
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
On the higher order nonlinearities of algebraic immune functions
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
IEEE Transactions on Information Theory
New covering radius of Reed-Muller codes for t-resilient functions
IEEE Transactions on Information Theory
On bent and semi-bent quadratic Boolean functions
IEEE Transactions on Information Theory
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes
IEEE Transactions on Information Theory
Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Identifying Codes and Covering Problems
IEEE Transactions on Information Theory
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
On the second-order nonlinearities of some bent functions
Information Sciences: an International Journal
| Hi-index | 754.84 |
In this paper, we consider the problem of computing best low-order approximations of Boolean functions; we focus on the best quadratic approximations of a subclass of cubic functions with arbitrary number of variables and we provide formulas for their efficient calculation. Our methodology is developed upon properties of the best affine approximations of quadratic functions, for which formulas for their direct computation (not by means of the Walsh-Hadamard transform) are given. We determine the cubic functions in the above subclass that achieve the maximum second-order nonlinearity, thus yielding a lower bound for the covering radius of the second order Reed-Muller code RM(2, n) in RM(3, n). Simple extensions of these results to some special cases of higher degree functions, are seen to hold. Furthermore, a preliminary analysis of well-known constructions for bent functions, in terms of their second-order nonlinearity, is performed that indicates potential weaknesses if construction parameters are not properly chosen.