Analysis On Costruction And Autocorrelation Of Pseudorandom Sequeces

Pseudorandom sequences have wide applications in real life, such as spreadspectrum communication systems, radar navigation systems, stream cipher systemsand code division multiple access systems, and so on. This thesis investigates theconstruction and pseudorandom properties of the Legendre-Sidel’nikov sequence, thetwo-prime Sidel’nikov sequence and two–prime powers Sidel’nikov sequence. Theauthor obtains main results as follows:(1)With the Legendre symbol in number theory and the exponential sums infinite field, we investigate the autocorrelation of the two-prime Sidel’nikov sequencewith d=gcd (p, q)=2. We get three theorems about the autocorrelation functions. By adetailed comparison, we obtain that the bounds O(q1/2) and O(p1/2) on theautocorrelation function are sharper than the Brandst tter’s bound O((p+q)/2) whenl≡0mod(p-1) and l≡0mod(q-1). Besides, the bound O((p q)1/2) are sharper than theBrandst tter’s bound O((p+q)/2+(p q)1/2) when l≡0mod(p-1) and l≡0mod(q-1), p>>q or q>>p.(2)By generalizing the odd prime field to the power of the prime field and usingthe quadratic multiplication characteristics instead of Legendre symbol, we redefine thetwo-prime Sidel’nikov sequences and get a new two–prime powers Sidel’nikovsequence. We give a detailed analysis on balances, autocorrelation functions andaperiodic autocorrelation functions and present five theorems.This thesis investigates the autocorrelation of the two-prime Sidel’nikov sequencewith d=2and gets an upper bound, for d>2needs further study. We construct a newtwo–prime powers Sidel’nikov sequence and analyze the balances, autocorrelationfunctions and aperiodic autocorrelation functions. We can study on the correlation oforder and the linear complexity profile. We can also use other characteristics instead ofLegendre symbol.