An efficient characterization of a family of hyperbent functions.

IEEE Transactions on Information Theory 57 (2011), 6010-6014.

Charpin and Gong recently characterized a large class
of hyperbent functions defined on fields
of order 2^{n}, which include
the well known monomial functions
with the Dillon exponent as a special case. We give a reformulation
of the Charpin-Gong criterion in terms of the number of rational
points on certain hyperelliptic curves. We present two applications
of our result: The time needed to check the hyperbentness
of a specific function is now polynomial in *n*, and hyperbent
functions with subfield coefficients can be constructed.