Construction And Analysis On Two Pseudo-Random Sequences

Pseudo-random sequences are widely used in spread spectrum communication system,pseudo-random code ranging,delay measurement,radar navigation,signal synchronization.The construction and analysis on pseudo-random sequences is an important branch of cryptography.In practice,important indexes to measure pseudo-random sequences are balance and autocorrelation properties.In a general way,the absolute values of autocorrelation are the smaller the better in engineering.Based on the methods of number theory,this paper constructs two pseudo-random sequences,studies on their balance property and the distribution of autocorrelation values.Main results are as follows:(1)By modifying Jacobi sequences,using the Chinese Remainder Theorem,this paper constructs modified Jacobi sequences.The modified sequences are balanced in any period,with p,q not merely to the restriction of gcd(p-1,q-1)(28)2.What's more,this paper gives the distribution of autocorrelation values.(2)This paper constructs new Legendre-Sidelnikov sequences by applying the parity of the elements,which are always balanced in any period.It also gives the distribution of autocorrelation values in any period in detail.The results show that autocorrelation values are small on some specific periods.(3)This paper gives the procedure of two sequences in Magma,and gets autocorrelation values of some examples.The values we get in theoretical derivation are same as in Magma.