An Efficient Characterization of a Family of Hyperbent Functions
Petr Lisoněk · IEEE Transactions on Information Theory · 2011
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.