Securing NB-IoT Uplink Using Chaotic Phase-Transformed Sequences

In this work, chaotic phase transformed sequences are explored, where only the phases of modulated symbols are modified according to specific chaotic maps. Alongside conventional chaotic maps like Chebyshev and Bernoulli maps, Poincaré maps derived from the dynamics of a Duffing oscillator are proposed to generate chaotic phase transformed sequences. A detailed evaluation of chaotic properties and a mathematical analysis of the distribution of the magnitude of cross-correlation between sequences are also presented. Since the receiver determines the transmitted chaotic phase transformed sequence using hypothesis testing, it is essential to select a subset of sequences where the maximum cross-correlation between any pair of sequences is minimized. To selectKsuch sequences from a larger pool ofNsequences, Row-Column Elimination, Genetic and Greedy-Search algorithms are proposed, with Poincaré map based sequences providing the best results for largerK.Considering the narrowband Internet of things (NB-IoT) standard, it is shown that data decoding is successful only when the initial conditions of Poincaré map are estimated accurately to the 15thdecimal place. Alternatively, it is computationally infeasible for a malicious node/user to decode data even if the initial condition is estimated accurately to the 14thdecimal place, thereby making it highly secure.