Quantifying Randomness in Stochastic Bit Sequences

Recent advancements in the field of communications and cryptology have attracted significant research efforts in studying randomness of bit sequences. Randomised bit sequences play a vital role in sensor applications by ensuring security (i.e., protecting against brute-force, replay, and eavesdropping attacks in wireless networks) and reliable signal processing (i.e., in sensor multiplexing schemes such as code-division or time-division schemes). Such bit sequences enable spread-spectrum techniques, which allow an improved signal separation in dense networks such as structural health monitoring. Furthermore, unpredictability is essential for secure communication among sensors, as seen in fiber Bragg grating systems. The mentioned studies have led to the development of different test methodologies, such as the NIST (National Institute of Standards and Technology) test suite, whose main objectives are to verify the independence of the individual elements in the sequence and to test their distribution within the bitstream. In this article, industry-relevant use cases are discussed for the application of random bit sequences and a gap-based approach for analysing bit sequences is presented and used together with a NIST-specified test. We introduce a simplified non-IID test approach (independent and identical distribution) to indicate whether the commonly considered IID characteristics of random variables are violated. To validate the proposed approach, this study employs different polynomial and nonpolynomial sequence generation methods. Furthermore, random sequences generated by different methods in hardware are included in the verification tests. The results confirm that the proposed methods of randomness assessment effectively indicates the non-IID characteristics of randomised bit sequences.