EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Hyper-bent functions and cyclic codes
Journal of Combinatorial Theory Series A
Construction of bent functions via Niho power functions
Journal of Combinatorial Theory Series A
A New Class of Bent Functions*
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
The divisibility modulo 24 of Kloosterman sums on GF(2m), m odd
Journal of Combinatorial Theory Series A
Cubic Monomial Bent Functions: A Subclass of $\mathcal{M}$
SIAM Journal on Discrete Mathematics
New families of binary sequences with low correlation
IEEE Transactions on Information Theory
On bent and semi-bent quadratic Boolean functions
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Constructions of quadratic bent functions in polynomial forms
IEEE Transactions on Information Theory
Bent Functions With Niho Exponents
IEEE Transactions on Information Theory
On Quadratic Bent Functions in Polynomial Forms
IEEE Transactions on Information Theory
Hyperbent Functions, Kloosterman Sums, and Dickson Polynomials
IEEE Transactions on Information Theory
A new class of monomial bent functions
Finite Fields and Their Applications
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
Hyper-bent Boolean functions with multiple trace terms
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Binary kloosterman sums with value 4
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Dickson polynomials, hyperelliptic curves and hyper-bent functions
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Semi-bent functions with multiple trace terms and hyperelliptic curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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Bent functions are maximally nonlinear Boolean functions and exist only for functions with even number of inputs. This paper is a contribution to the construction of bent functions over $${\mathbb{F}_{2^{n}}}$$ (n = 2m) having the form $${f(x) = tr_{o(s_1)} (a x^ {s_1}) + tr_{o(s_2)} (b x^{s_2})}$$ where o(s i ) denotes the cardinality of the cyclotomic class of 2 modulo 2 n 驴 1 which contains s i and whose coefficients a and b are, respectively in $${F_{2^{o(s_1)}}}$$ and $${F_{2^{o(s_2)}}}$$ . Many constructions of monomial bent functions are presented in the literature but very few are known even in the binomial case. We prove that the exponents s 1 = 2 m 驴 1 and $${s_2={\frac {2^n-1}3}}$$ , where $${a\in\mathbb{F}_{2^{n}}}$$ (a 驴 0) and $${b\in\mathbb{F}_{4}}$$ provide a construction of bent functions over $${\mathbb{F}_{2^{n}}}$$ with optimum algebraic degree. For m odd, we give an explicit characterization of the bentness of these functions, in terms of the Kloosterman sums. We generalize the result for functions whose exponent s 1 is of the form r(2 m 驴 1) where r is co-prime with 2 m + 1. The corresponding bent functions are also hyper-bent. For m even, we give a necessary condition of bentness in terms of these Kloosterman sums.