A Note on Semi-Bent Functions With Multiple Trace Terms and Hyperelliptic Curves

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Executive Summary

Semi-bent functions with even number of variables are a class of important Boolean functions whose Hadamard transform takes three values. The authors subsequently give a connection between the property of semi-bentness and the number of rational points on some associated hyperelliptic curves. They use the hyperelliptic curve formalism to reduce the computational complexity in order to provide a polynomial time and space test leading to an efficient characterization of semi-bentness of such functions (which includes an efficient characterization of the hyper-bent functions proposed by Wang et al.).

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