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Charlotte, North Carolina, USA

May 2, 2010 to May 4, 2010

ISBN: 978-0-7695-4056-6

pp: 265-272

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FCCM.2010.48

ABSTRACT

We show that there is significant benefit to using a reconfigurable computer to enumerate bent Boolean functions for cryptographic applications. Bent functions are rare, and the only known way to generate all bent functions is by a sieve technique in which many prospective functions are tested. The speed-up achieved depends on the number of variables n; for n = 8, we show that the reconfigurable computer achieves better than a 60,000x speed-up over a conventional computer. Further, we introduce the transeunt triangle as a means to reduce the number of functions that must be considered. For n=6, this reduction is better than 500,000,000 to 1. Previously, the transeunt triangle had been used only in the design of exclusive OR logic circuits; it converts a truth table to the algebraic normal form. However, this fact has never been proven rigorously, and that shortcoming is removed in this paper. Our proof provides a practical benefit; it yields a new realization of the transeunt triangle that has less complexity and delay. Finally, we show computational results from a reconfigurable computer.

CITATION

J. L. Shafer,
S. W. Schneider,
J. T. Butler,
P. Stanica,
"Enumeration of Bent Boolean Functions by Reconfigurable Computer",

*FCCM*, 2010, Field-Programmable Custom Computing Machines, Annual IEEE Symposium on, Field-Programmable Custom Computing Machines, Annual IEEE Symposium on 2010, pp. 265-272, doi:10.1109/FCCM.2010.48