Enumeration of Bent Boolean Functions by Reconfigurable Computer

• Published in: 2010 18th IEEE Annual International Symposium on Field-Programmable Custom Computing Machines pp. 265 - 272
• Main Authors: Shafer, J L, Schneider, S W, Butler, J T, Stănică, P
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.05.2010
• Subjects: Application software; Autocorrelation; Boolean functions; Cryptography; Delay; Gold; Linear systems; Logic circuits; Spread spectrum communication; Testing
• ISBN: 9781424471423; 0769540562; 9780769540566; 1424471427
• DOI: 10.1109/FCCM.2010.48

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 60,000× 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.