Entropy Measurement and On-line Quality Control of Bit Streams by a True Random Bit Generator

Cesare Caratozzolo^1*Valeria Rossi¹Kamil Witek^1,2Alberto Trombetta³Mateusz Baszczyk²Piotr Dorosz²Wojciech Kucewicz²Massimo Caccia¹

• ¹Department of Science and High Technology, University of Insubria, Como, Italy
• ²Akademia Gorniczo-Hutnicza im Stanislawa Staszica w Krakowie, Kraków, Poland
• ³Universita degli Studi dell'Insubria, Varese, Italy

Abstract—Generating random bit streams is required in various applications, most notably cyber-security essential for Internet of Everything applications to enable secure communication between interconnected devices. Ensuring high-quality and robust randomness is crucial to mitigate risks associated with predictability and system compromise. True random numbers provide the highest unpredictability levels. However, known systematic biases that can emerge from physical imperfections, environmental variations, and device aging in the processes exploited for the random number generation must be carefully monitored. This paper reports the implementation and characterization of an on-line procedure for the detection of anomalies in a true random bit stream. It is based on the NIST Adaptive Proportion and Repetition Count tests, complemented by statistical analysis relying on the Monobit and RUNS. The procedure is firmware im-plemented through dedicated hardware accelerators processing configurable-length sequences, with automated anomaly detection triggering alerts after three consecutive threshold violations. The implementation is performed simultaneously with the bit stream generation, and provides as well an estimate of the entropy of the source. A statistical analysis of the results coming from the NIST procedure to evaluate the symbols of the bit-stream as Independently and Identically Distributed is also performed and leads to a computation of the minimum entropy of the source that cross-checks the previously mentioned estimate. The experimental validation of the approach is performed upon the bit streams generated by a quantum, silicon-based entropy source.