With increasing one-time costs for the production of integrated circuits, the drive to integration of configurable circuits together with standard processor cores and interface will increase. So far, either established FPGA fabrics (e.g. Xilinx ZYNQ family) have been used or the configurable units were custom designed for a very specific function (e.g. PowerEN EFSM - TBD). It is therefore of interest to investigate the structures and algorithms for configurable circuits for a well-defined set of functions. As a first step, this paper investigates the class of functions which are invariant under cyclic shifts of their input vectors.