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 article, we first reduce the autocorrelation distribution of the LSB sequence of a p-ary m-sequence with period p
ⁿ
-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<; 100. In addition, we give a lower bound on the 2-adic complexity of each of these LSB sequences for all primes p<; 20, which proves to be large enough to resist the analysis of RAA (Rational Approximation Algorithm) for FCSRs (Feedback with Carry Shift Registers). In particular, for a Mersenne prime p=2
^k
-1 (i.e., k is a prime such that p is also a prime), our results hold for all its bit-component sequences since they are shift equivalent to the LSB sequence.