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Quantifying Randomness in Stochastic Bit Sequences
Christoph Lange1, Andreas Ahrens2, Yadu Krishnan Krishnakumar2,3
1School of Engineering-Energy and Information, Hochschule für Technik und Wirtschaft Berlin (University of Applied Sciences), Wilhelminenhofstraße 75 A, 12459 Berlin, Germany.
Sensors (Basel, Switzerland)
|August 13, 2026
Summary
This study presents a new method to assess the randomness of bit sequences, crucial for secure sensor communications. The approach effectively identifies sequences that violate independent and identical distribution (IID) properties, enhancing communication security.
Area of Science:
- Communications and Cryptology
- Information Theory
- Sensor Networks
Background:
- Random bit sequences are essential for security and signal processing in sensor applications, protecting against attacks and enabling reliable data transmission.
- Existing methodologies like the NIST test suite verify sequence randomness, focusing on element independence and distribution.
- Unpredictability is critical for secure sensor communication, particularly in systems like fiber Bragg grating networks.
Purpose of the Study:
- To discuss industry-relevant use cases for random bit sequences in communications and cryptology.
- To introduce and validate a novel gap-based approach for analyzing bit sequences, including a simplified non-IID test.
- To assess the effectiveness of the proposed method in identifying non-independent and identically distributed (non-IID) characteristics.
Main Methods:
- A gap-based analysis approach combined with a NIST-specified test was employed.
- A simplified non-IID test was introduced to detect violations of independent and identical distribution properties.
- Various polynomial and non-polynomial sequence generation methods, including hardware-generated sequences, were used for validation.
Main Results:
- The proposed randomness assessment methods successfully identified non-IID characteristics in randomized bit sequences.
- The simplified non-IID test effectively indicated deviations from the expected IID properties.
- Validation across different generation methods confirmed the robustness of the proposed assessment approach.
Conclusions:
- The developed gap-based and simplified non-IID testing approach provides an effective means for assessing the randomness of bit sequences.
- This method enhances the security and reliability of sensor communications by ensuring the quality of random bit sequences.
- The findings contribute to the development of more robust security protocols and signal processing techniques in communications and cryptology.
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