On the Connection between Kloosterman Sums and Elliptic Curves
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
On the values of Kloosterman sums
IEEE Transactions on Information Theory
On certain values of Kloosterman sums
IEEE Transactions on Information Theory
A New Family of Hyper-Bent Boolean Functions in Polynomial Form
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Some results concerning cryptographically significant mappings over GF(2n)
Designs, Codes and Cryptography
On integer values of Kloosterman sums
IEEE Transactions on Information Theory
Hyper-bent Boolean functions with multiple trace terms
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
A new class of bent and hyper-bent Boolean functions in polynomial forms
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Permutation polynomials EA-equivalent to the inverse function over GF (2n)
Cryptography and Communications
Binary kloosterman sums with value 4
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On multiple output bent functions
Information Processing Letters
Dickson polynomials, hyperelliptic curves and hyper-bent functions
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
On divisibility of exponential sums of polynomials of special type over fields of characteristic 2
Designs, Codes and Cryptography
On generalized bent functions with Dillon's exponents
Information Processing Letters
| Hi-index | 755.02 |
This paper is devoted to the study of hyperbent functions in n variables, i.e., bent functions which are bent up to a change of primitive roots in the finite field GF(2n). Our main purpose is to obtain an explicit trace representation for some classes of hyperbent functions. We first exhibit an infinite class of monomial functions which is not hyperbent. This result indicates that Kloosterman sums on F2 m cannot be zero at some points. For functions with multiple trace terms, we express their spectra by means of Dickson polynomials. We then introduce a new tool to describe these hyperbent functions. The effectiveness of this new method can be seen from the characterization of a new class of binomial hyperbent functions.