Recommendations and illustrations for the evaluation of photonic random number generators

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( , τ ) 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. arXiv:1612.04415v3 [physics.optics]

Multiplexed Quantum Random Number Generation

“…This extractor is designed to minimise the effect of the classical noise on the output signal. The total bit rate of this construction is given by the product of the sample rate (55MSPS), extracted bits per sample (8), and number of channels (7), and is 3.08 Gbit/s. We sample at least 27.5 MHz of the homodyne detector bandwidth as allowed by the Shannon-Hartley limit [8].…”

“…The randomness properties of the source have a profound effect on the security of the encryption, with several examples of compromised security from an attack on the random number generator [3][4][5]. In this area, quantum optics has provided advantages over previous methods, enabling random number generation with high speeds and enhanced security [6][7][8].…”

“…Multiplexed quantum random number generation has previously been theoretically proposed as a solution to post-processing bottlenecks in the real-time rate of QRNGs [7,8]. Previous demonstrations of a parallel nature remain focused on increasing single-channel data rates.…”

Evaluating entropy rate of laser chaos and shot noise

“…A key challenge arises from the difficulty of quantifying physical process randomness from the raw data. To quantify the randomness of laser chaos, entropy in its many forms, such as Shannon entropy [14,15], Kolmogorov-Sinai (KS) entropy [16][17][18][19] and permutation entropy (PE) [20][21][22][23][24][25], provides a way to measure temporal randomness of a physical process. The positivity of the entropy per unit time or entropy rate is an evidence for randomness in time series, which characterizes the production of new and random information of high-dimensional and noisy dynamical systems.…”

“…Meanwhile, laser chaos rapidly and nonlinearly amplifies the uncertainty of intrinsic quantum noise and the chaotic amplification of the intrinsic noise is completely different from output fluctuation caused by deterministic chaos [8]. It is important to understand the origins of the stochastic properties and assess the randomness of the physical process [14,18,19]. Shot noise is an intrinsic noise of chaotic system and a fundamental quantum noise limit of optical source, which represents quantum vacuum state or zero-point fluctuations allowed by the minimum uncertainty product of quantum mechanics [26][27][28].…”