Construction And Analysis Of Some Pseudorandom Sequences Derived From Arithmetical Functions

Pseudo-random sequences have a wide application in coding, cryptography, code division multiple access (CDMA) communication systems, radar, sonar and and so on. So it is a meaningful research topic to design a series of sequences with good randomness, including high linear complexity and low correlation.In this thesis, we will construct several classes of pseudorandom sequence based on arithmetical functions. Furthermore, we will analysis their properties and their applications. In detail, following topics will be addressed including the structure and properties of binary sequence derived from Fermat-Euler quotient, zero-difference balanced function and its application by using Fermat quotient, the improvement of the Legendre-Sidelnikov sequence and two-prime sequence, the multiplier sequence set based on d-ary generalized Legendre-Sidelnikov sequence. Our main research works are summarized as follows.1. We present a new construction of a binary sequence based on Fermat-Euler quo-tient. Which is different from the original sequence, the sequence with flexible support set, can be more free to select internal elements, and the previous se-quence is determined once its period determined. At the same time, we analysis the new sequence linear complexity, in most cases it has high linear complexity, and we give the conditions which are required to meet.2. By Fermat quotient and cyclotomic properties, the new (p2,p,p) zero-difference balance function is presented in this paper. Different from the structure of Ding, the structure can produce more functions and the limit requirements are greatly reduced. Using new functions, we construct the optimal frequency hopping sequences and optimal perfect difference system.3. First, binary Legendre-Sidelnikov sequence were improved, which has better bal-ance, then the periodic autocorrelation values of the sequence was calculated. And the results were compared with original one. Then we use d-ary general-ized Legendre-Sidelnikov sequence to constructed multiplier sequence sets, and calculates its periodic cross-correlation values. It is found that it has low corre- lation. In particular, in particular values, the conclusion can be used to compute autocorrelation of d-ary generalized Legendre-Sidelnikov sequence.4. Two-prime sidelnikov sequence was improved, which is always balanced, then the periodic autocorrelation values of the sequence was calculated and an upper bound was presented. We also compared the sequence with the original one by an example. Under some special conditions, the sequence is equivalent to Sidelnikov sequence, which also has many good pseudo-random properties.