Introduction to finite fields and their applications
Introduction to finite fields and their applications
Construction of bent functions via Niho power functions
Journal of Combinatorial Theory Series A
An improved list decoding algorithm for the second order Reed---Muller codes and its applications
Designs, Codes and Cryptography
Information Sciences: an International Journal
On the lower bounds of the second order nonlinearities of some Boolean functions
Information Sciences: an International Journal
Non-linear approximations in linear cryptanalysis
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Applicable Algebra in Engineering, Communication and Computing
International Journal of Computer Mathematics
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
A new class of monomial bent functions
Finite Fields and Their Applications
On the second-order nonlinearities of some bent functions
Information Sciences: an International Journal
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In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form ${\rm f}({\rm x}) = {\rm Tr}_{1}^{{\rm n}}(\rmalpha_{1}{\rm x}^{{\rm d}_{1}} + \rmalpha_{2}{\rm x}^{{\rm d}_{2}})$, where d 1 and d 2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a recent result of Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is shown in Section 3, by a direct computation, that for large values of n, the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao.