Short cycle rotation Boolean functions: generators and count
by Jose E. Calderon-Gomez, Luis A. Medina and Carlos Molina-Salazar
Rotation symmetric Boolean functions were introduced by Pieprzyk and Qu in late 1990's. These functions are useful, among other things, in the design of fast hashing algorithms with strong cryptographic properties. A monomial rotation Boolean function is called long cycle if the number of terms in its algebraic normal form coincides with the number of variables and short cycle if the number of terms is less than the number of variables. In this article, we characterize a family of generators of short cycles. We then use such family to count the number of short cycles.
