Recommendations and illustrations for the evaluation of photonic random number generators

TL;DR

This paper reviews current methods for evaluating optical random number generators, advocates for a new entropy-focused evaluation paradigm, and demonstrates its application on various optical sources to improve security assessments.

Contribution

It introduces a new evaluation framework emphasizing physical entropy measurement and applies it to compare different optical entropy sources.

Findings

Cohen-Procaccia estimate effectively quantifies entropy rate.

Evaluation highlights differences among optical sources.

Proposes separating physical entropy from post-processing.

Abstract

The never-ending quest to improve the security of digital information combined with recent improvements in hardware technology has caused the field of random number generation to undergo a fundamental shift from relying solely on pseudo-random algorithms to employing optical entropy sources. Despite these significant advances on the hardware side, commonly used statistical measures and evaluation practices remain ill-suited to understand or quantify the optical entropy that underlies physical random number generation. We review the state of the art in the evaluation of optical random number generation and recommend a new paradigm: quantifying entropy generation and understanding the physical limits of the optical sources of randomness. In order to do this, we advocate for the separation of the physical entropy source from deterministic post-processing in the evaluation of random number generators and for the explicit consideration of the impact of the measurement and digitization process on the rate of entropy production. We present the Cohen-Procaccia estimate of the entropy rate $h(\epsilon,\tau)$ as one way to do this. In order to provide an illustration of our recommendations, we apply the Cohen-Procaccia estimate as well as the entropy estimates from the new NIST draft standards for physical random number generators to evaluate and compare three common optical entropy sources: single photon time-of-arrival detection, chaotic lasers, and amplified spontaneous emission.