| Stream ciphers are widely used in practice because of their easy hardware and software implement,fast encryotion and decryption features,especially in the govern-ment,military and diplomatic service.The security of stream cipher depends largely on the characteristics of the key stream,and pseudo-random sequences are usually utilized for key streams in stream cipher.Usually,some properties such as randomness,long period,balance,low correlation of a key-stream are requried.In general,the nonlinear complexity is one of the important criteria used to measure the randomness of a se-quence.In the European eSTREAM project,the design of stream ciphers has become increasingly diversified,and a large number of algorithms based on nonlinear feedback shift registers have been proposed,which greatly promotes the development of stream ciphers.This shows that nonlinear feedback shift registers have become an important design component of the key stream generator and the nonlinear feedback shift register corresponds to the nonlinear complexity.So it is great practical significance to study the nonlinear complexity of sequences.An important issue in the study of nonlinear complexity is to construct a sequence of large nonlinear complexity.In this paper,a p-ray sequence with length n and nonlin-ear complexity n-5 is constructed.Specifically,it is divided into two parts,on the one hand,when the nonlinear complexity is less than half the length,the last element of the sequence is changed,and the nonlinear complexity jumps;then the relationship be?tween the value of the nonlinear complexity and the number of different subsequences with a given length of 5 is studied.On the other hand,when the nonlinear complexity is greater than half of the length,the sequence structure is determined by extending the characteristic that the nonlinear complexity of any one element remains unchanged.Combine the two to explore the length of n and the nonlinear complexity n-5,and obtain its number. |
PDF Full Text Request