Investigation on pseudorandom properties of FCSR sequence

Feedback with carry shift register (FCSR) proposed a new path for pseudorandom sequence design, however its properties still need to be revealed in depth. In this paper compared with LFSR, the properties of FCSR are reviewed briefly and the present conclusions about pseudorandom properties of FCSR are analyzed as well. Both full-period and half-period l-sequences generated by FCSR are tested by eight tests in the NIST (National Institute of Standardization and Technology) STS package to investigate its pseudorandom property including balance, uniformity, linear span, linear dependence, runs, compressible property and deBruijn property etc. As a result, both full-period and half-period l-sequences that present the real features of FCSR sequences, have passed all tests but the discrete Fourier transform (DFT) test when the length of tested subsequences becomes long enough. That means FCSR with excellent pseudorandom property is a good component of a stream cipher generator but cannot be used individually. It is recommended to combine LFSR with FCSR to design stream ciphers in the future, which have passed all eight tests in this paper.