Cryptographic Properties Of Cyclotomic Sequences Of Order Three

The autocorrelation value and linear complexity of cyclotomic sequences are two very importantcryptography index. Cyclotomic sequences with a few correlation values and large linear complexityhave wide applications in communication systems and cryptography.In this paper, we do some research on the autocorrelation value and linear complexity ofcyclotomic sequences over GF(3) and construct some new sequences over GF(3). These sequenceshave a nice autocorrelation value and linear complexity. Meanwhile, we also construct someunbalanced sequences of order3over GF(2) and calculate the linear complexity by some convenientmethods.In this paper, we mainly construct some related sequences over GF(3) by the method of cyclotomicnumbers, then we calculate the autocorrelation value and linear complexity. Moreover, we calculatethe linear complexity of some unbalanced sequence over GF(2) by the method of Gauss sums. Themain research contents and the results are as follows:Firstly, we shall give a brief introduction about the research history and related conclusions,moreover, some concepts and theories will be described.Secondly, let’s denote a class of unbalanced cyclotomic sequences with period of p1mod3over GF(3). Then we give a conclusion about autocorrelation value by the cyclotomic numbers oforder three.Next we define a class of cyclotomic sequences and we calculate the linear complexity for theapplication.Last we also define another unbalanced cyclotomic sequence over GF(2). We calculate the linearcomplexity of related sequences.