Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of p-Ary m-Sequence

LSB (Least Significant Bit) sequences are widely used as the initial inputs in some modern stream ciphers, such as the ZUC algorithm-the core of the 3GPP LTE International Encryption Standard. Therefore, analyzing the statistical properties (for example, autocorrelation, linear complexity and 2-adic complexity) of these sequences becomes an important research topic. In this paper, we first reduce the autocorrelation distribution of the LSB sequence of a p-ary m-sequence with period pn - 1 for any order n≥2 to the autocorrelation distribution of a corresponding Costas sequence with period p - 1, and from the computing of which by computer, we obtain the explicit autocorrelation distribution of the LSB sequence for each prime p