Sequences, Bent functions and Jacobsthal sums

Authors:
Tor Helleseth;Alexander Kholosha
Affiliations:
The Selmer Center, Department of Informatics, University of Bergen, Bergen, Norway;The Selmer Center, Department of Informatics, University of Bergen, Bergen, Norway
Venue:
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Year:
2010

Citing 5
Cited 1

Finite fields

Finite fields
Strongly regular graphs associated with ternary bent functions

Journal of Combinatorial Theory Series A
New binomial bent functions over the finite fields of odd characteristic

IEEE Transactions on Information Theory
Monomial and quadratic bent functions over the finite fields of odd characteristic

IEEE Transactions on Information Theory
p-Ary and q-ary versions of certain results about bent functions and resilient functions

Finite Fields and Their Applications

Crosscorrelation of m-sequences, exponential sums, bent functions and Jacobsthal sums

Cryptography and Communications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The p-ary function f(x) mapping GF(p4k) to GF(p) and given by f(x) = Tr4k(axd + bx2) with a, b ∈ GF(pp4k) and d = pp3k + p2k - pk + 1 is studied with the respect to its exponential sum. In the case when either apk(pk+1) ≠ apk+1: or a2 = bd with b ≠ 0, this sum is shown to be three-valued and the values are determined. For the remaining cases, the value of the exponential sum is expressed using Jacobsthal sums of order pk + 1. Finding the values and the distribution of those sums is a long-lasting open problem.