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It has been conjectured that there are no homogeneous rotation symmetric bentBoolean functions of degree greater than two. In this paper we begin by provingthat sums of short-cycle rotation symmetric bent Boolean functions must containa specific degree two monomial rotation symmetric Boolean function. We thenprove most cases of the conjecture in n=2p, p>2 prime, variables and extendthis work to the nonhomogeneous case.

Rotation Symmetric Bent Boolean Functions for n = 2p