The Cryptological Properties Of FCSR Sequences

The binary sequences generated with feedback with carry shift registers (FCSR) are a new class of stream ciphers. Feedback shift registers with carry operation are analyzed with respect to memory requirements,initial loading,period,graph of states, complexity and distributional properties of their output sequences. Many parallels with the theory of linear feedback shift registers(LFSR's) are presented. This paper is based on the background of the intrinsic relationship among FCSR sequences, 2-adic numbers and rational numbers with odd prime numbers as denominators. Some new cryptological properties of the FCSR sequences are proved. A new sufficient and necessary condition under which a FCSR sequence is a periodic sequence is presented. The graph of states of periodic sequences, the properties of the summation cipher and some properties of d-FCSR sequences are also analyzed in the paper and we get some new results.