Finite fields
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Elliptic curves and their applications to cryptography: an introduction
Elliptic curves and their applications to cryptography: an introduction
On Z_4-Linear Goethals Codes and KloostermanSums
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
On the Connection between Kloosterman Sums and Elliptic Curves
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
On certain values of Kloosterman sums
IEEE Transactions on Information Theory
On integer values of Kloosterman sums
IEEE Transactions on Information Theory
Monomial and quadratic bent functions over the finite fields of odd characteristic
IEEE Transactions on Information Theory
Hyperbent Functions, Kloosterman Sums, and Dickson Polynomials
IEEE Transactions on Information Theory
Propagation characteristics of x→ x-1 and Kloosterman sums
Finite Fields and Their Applications
On integer values of Kloosterman sums
IEEE Transactions on Information Theory
On divisibility of exponential sums of polynomials of special type over fields of characteristic 2
Designs, Codes and Cryptography
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A Kloosterman zero is a non-zero element of $${{\mathbb F}_q}$$ for which the Kloosterman sum on $${{\mathbb F}_q}$$ attains the value 0. Kloosterman zeros can be used to construct monomial hyperbent (bent) functions in even (odd) characteristic, respectively. We give an elementary proof of the fact that for characteristic 2 and 3, no Kloosterman zero in $${{\mathbb F}_q}$$ belongs to a proper subfield of $${{\mathbb F}_q}$$ with one exception that occurs at q = 16. It was recently proved that no Kloosterman zero exists in a field of characteristic greater than 3. We also characterize those binary Kloosterman sums that are divisible by 16 as well as those ternary Kloosterman sums that are divisible by 9. Hence we provide necessary conditions that Kloosterman zeros must satisfy.