Interleaved Sequences Over Finite Fields

We study cryptographic properties such as correlation, correlation measure and linear complexity profile of the sequences defined by characters with interleaved structure. Families of pseudorandom sequences with low cross correlation have important applications in communications and cryptography. Among several known constructions of sequences with low cross correlation, interleaved constructions proposed by Gong use two sequences of the same period with two-level autocorrelation. We generalize the interleaved algorithm and construct some families of interleaved sequences. We study the balance property and the cross correlation of the interleaved sequences. Then we interleave two m-ary sequences of integer periods. We study the power correlation measure of order k (with bound B) of the interleaved m-ary sequences. A relation between the linear complexity profile and the power correlation measure of order $ with bound $ is also provided. For applications in communications sequences with a small alphabet size are often required. We define a new class of sequences over the set of complex numbers with unit magnitude (and 0) which have small alphabet size, long period and almost perfect autocorrelation. Sequences with low correlation property or zero correlation property around the origin can be used in such systems for reducing multiple-access interference. Such sequence sets are called low correlation zone (LCZ) or zero correlation zone (ZCZ) sequence sets (families), respectively. A new family of interleaved polyphase sequences is constructed using the newly defined sequences as the base sequences and the shift sequence being a Costas sequence. We find the ZCZ of this constructed family of interleaved polyphase sequences. A family of sequences constructed by shift-adding one two-prime generator of order 2 sequence, is also studied.