|| On Galois NFSRs with Terminal Bits
||Yingyin Pan, Institute of Information Engineering, Chinese Academy of Sciences; School of Cyber Security, University of Chinese Academy of Sciences, China; Jianghua Zhong, Dongdai Lin, Institute of Information Engineering, Chinese Academy of Sciences, China|
||D7-S2-T4: Topics in Privacy & Cryptography I
||Tuesday, 20 July, 22:20 - 22:40
||Tuesday, 20 July, 22:40 - 23:00
This paper considers the Galois nonlinear feedback shift registers (NFSRs) with terminal bits, which have the first several bits involved only shifts and have been used in many stream ciphers such as Grain and Trivium. First, the paper gives a special class of such Galois NFSRs and reveals its relation with Fibonacci ones with respect to their sets of output sequences. Then, it presents a necessary and sufficient condition for an n-stage Galois NFSR with terminal bit equivalent to an n-stage Fibonacci NFSR. Based on this condition, the paper enumerates those n-stage Galois NFSRs with the same terminal bit that are equivalent to a given n-stage Fibonacci NFSR. Finally, the paper gives a necessary/sufficient condition for the nonsingularity of the Galois NFSRs with terminal bits.