This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
2010 18th IEEE Annual International Symposium on Field-Programmable Custom Computing Machines
Enumeration of Bent Boolean Functions by Reconfigurable Computer
Charlotte, North Carolina, USA
May 02-May 04
ISBN: 978-0-7695-4056-6
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, pp.265-272, 2010 18th IEEE Annual International Symposium on Field-Programmable Custom Computing Machines, 2010
Usage of this product signifies your acceptance of the Terms of Use.