Research On The Interleaved Structure Of Sequences With Low Autocorrelation

Pseudorandom sequences have important applications in stream cipher cryptolo-gy.The sequences,which are employed in stream cipher encryptions as key stream generators,have low autocorrelation.The interleaved structure provides new ideas and methods to acquire the structure of sequences,compute the autocorrelation values of se-quences and construct new ideal autocorrelation sequences.Therefore it is significative to study the interleaved structure of sequences with low autocorrelation.Most of the ideal 2-level autocorrelation sequences with composite period have the interleaved structure,which is determined by a base sequence and a shift sequence.Twin prime sequences are the special modified Jacobi sequences and they have ideal 2-level autocorrelation,but do not have the interleaved structure.For the modified Jacobi sequences with period pq,p,q prime,the autocorrelation values of them are only dependent on the difference between p and q.Therefore,we can construct more sequences with low autocorrelation by modified Jacobi sequences.Based on the array form of modified Jacobi sequences,we derive that modified Jacobi sequences have interleaved-like structure,which is determined by two base se-quences and a shift sequence.By the structure,the relation between the Jacobi se-quence and modified Jacobi sequence is clearly,and the autocorrelation of modified Jacobi sequences can be obtained easily.Moreover,we investigate r-ary interleaved-like sequences and construct new low autocorrelation sequences with composite period.