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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Charpin and Gong recently characterized a large class of hyperbent functions defined on fields of order 2n, 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.