The Linear Complexity Of A Class Of Binary Sequences With Period 2~l_n

With the improvement of the information in our society,information security has become a crucial problem.Cryptography permeates the whole process of information security,stream cipher is an important cryptosystem in secure communications.The security of stream cipher is depend on the key stream sequence.The linear complexity is an important indicator that measures a given sequence.According to the B-M algo-rithm,we can easily recover the sequence if it has 2L consecutive digits of a sequence with linear complexity L.In order to resist the plaintext attack and enhance the security of data,the linear complexity of a sequence must be not less than the half of its period.Thus,the key questions of the research of sequence are how to construct a sequence of large linear complexity,and how to calculate the linear complexity of sequence.Based on the isomorphism of residue class rings and the Chinese Remainder The-orem,we construct a binary sequence with period 2~ln by a binary sequence with period n(n is odd).Further,we investigate the correlation of minimal polynomial between original sequence and the new sequence,and then get the relationship of their linear complexity.In particular,let original sequence be the Legendre sequence,Hall's sextic residue sequence,biquadratic residue sequence or generalized cyclotomic sequence of order 2,respectively.The minimal polynomial and linear complexity of new sequence can be determined in field F2 and F_p(p is an odd prime),and the linear complexity can reach the maximum in F_p in some cases.