Construction and count of resilient rotation symmetric Boolean functions with prime number variables

The characteristic matrix of the resilient rotation symmetric Boolean functions(RSBF) with prime number va-riables were explored. Some properties about character ic matrix of them were given. A necessary and sufficient condi-tion on the construction of resilient RSBF with prime number variables was derived. So construction and count formula of all the resilient RSBF with prime number variables were determined by this way. At last, all the resilient RSBF with 3, 5 or 7 variables were given.