Pseudo-random Sequence Design And Its Randomness Analysis

Pseudo-random sequences are widely used in communications,radar,ranging,cryptography and other fields.The M sequence,also known as the de Bruijn sequence,is an important class of pseudo-random sequences.It has the characteristics of large number of sequences,high linear complexity and excellent correlation characteristics.The construction of the M sequence is a difficulty in cryptography.The M-sequence can be generated by a nonlinear feedback shift register,but the construction of the nonlinear feedback shift register and its property analysis are progressing slowly.A typical method for constructing M sequences is the circle joining method.In this paper,a new M-sequence construction method is proposed based on the parallel method,and the random properties of the generated M sequence and its modified M sequence are analyzed.The specific research work is as follows:?1?The construction method of the existing M sequence is summarized.The construction idea of M sequence is mainly divided into two types.The new M sequence is constructed based on the existing M sequence and the M sequence is constructed based on the feedback shift register.The steps of constructing the sequence by the two methods are summarized.?2?Based on the circle joining method,a new M-sequence construction method is proposed,and the M-sequence and its linear complexity and autocorrelation properties are analyzed.The new M sequence construction method can analyze the circle structure with the initial characteristic polynomial of the feedback shift register.The main steps are as follows:Firstly,a special kind of exchange ring is constructed according to the initial feedback polynomial.Second,the elements of ringG_qnl are divided into N sets E?7???8?,according to the distribution of zero elements on different components of the elements.Isomorphic mapping??7???8?is established.Each circle and each set in the cycle structure of the initial polynomial of the feedback shift register are associated.The adjacency map is determined by calculating the conjugate state between any two circles,and the M sequence is constructed by the circle joining method.And using computer simulation,the random sequence analysis of the sequence generated by the new method was carried out.?3?The n-order modified M sequence is a sequence obtained by removing a 0 from the n-length all-zero run in the original M-sequence.The random nature of the modified M-sequence obtained in?2?is studied.The simulation results show that the linear complexity of the modified M sequence is close to its corresponding M sequence,and the autocorrelation property is better than the corresponding M sequence.?4?A tighter bound on modifying the linear complexity of the M-sequence is given and the mathematical proof is given.