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Scientific Reports

On multiplexing in physical random number generation, and conserved total entropy content

Frédéric Monet, Raman Kashyap

Published May 16, 2023• 3 citations
Publisher

Abstract

In the current article, we use a random supercontinuum based on a random Raman distributed feedback laser to investigate the generation of random numbers by spectrally demultiplexing the broad supercontinuum spectrum in parallel channels. By tuning the spectral separation between two independent channels, we test the most typically used statistical tests' abilities to identify the required minimum spectral separation between channels, especially after the use of post-processing steps. Out of all the tests that were investigated, the cross-correlation across channels using the raw data appears to be the most robust. We also demonstrate that the use of post-processing steps, either least significant bits extraction or exclusive-OR operations, hinders the ability of these tests to detect the existing correlations. As such, performing these tests on post-processed data, often reported in literature, is insufficient to properly establish the independence of two parallel channels. We therefore present a methodology, which may be used to confirm the true randomness of parallel random number generation schemes. Finally, we demonstrate that, while tuning a single channel's bandwidth can modify its potential randomness output, it also affects the number of available channels, such that the total random number generation bitrate is conserved.

DOI
10.1038/s41598-023-35130-7

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In the current article, we use a random supercontinuum based on a random Raman distributed feedback laser to investigate the generation of random numbers by spectrally demultiplexing the broad supercontinuum spectrum in parallel channels. By tuning the spectral separation between two independent channels, we test the most typically used statistical tests' abilities to identify the required minimum spectral separation between channels, especially after the use of post-processing steps. Out of all the tests that were investigated, the cross-correlation across channels using the raw data appears to be the most robust. We also demonstrate that the use of post-processing steps, either least significant bits extraction or exclusive-OR operations, hinders the ability of these tests to detect the existing correlations. As such, performing these tests on post-processed data, often reported in literature, is insufficient to properly establish the independence of two parallel channels. We therefore present a methodology, which may be used to confirm the true randomness of parallel random number generation schemes. Finally, we demonstrate that, while tuning a single channel's bandwidth can modify its potential randomness output, it also affects the number of available channels, such that the total random number generation bitrate is conserved.
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A simple novel method for random number generation is presented, based on a random Raman fiber laser. This laser is built in a half-open cavity scheme, closed on one side by a narrow-linewidth 100 mm fiber Bragg grating. The interaction between the randomly excited lasing modes of this laser, in addition to nonlinear effects such as modulation instability, allow the generation of random bits at rates of up to 540 Gbps with minimal post processing. Evaluation of the resulting bit streams' randomness by the NIST statistical test suite highlights the importance of evaluating the physical entropy content, as bit sequences generated by this random laser pass all the statistical tests with a significance level of 0.01, despite being generated at more than twice the theoretical entropy generation speed.
The exponential growth of data transmission and processing speeds in modern digital infrastructure requires entropy sources capable of producing large volumes of true randomness for information security. Chaotic emissions from semiconductor lasers are attractive in this context because of their fast dynamics and nonrepetitive behavior. Their spectral bandwidth, however, is typically limited to several tens of gigahertz, which constrains the achievable entropy rate and makes ultrafast random bit generation difficult without substantial post-processing. Here, we demonstrate a chaos-based entropy source that employs optical heterodyning between the chaotic emission from a semiconductor laser and an optical frequency comb, yielding a bandwidth exceeding 100 GHz and an experimentally verified single-channel entropy rate of 1.86 Tb/s. By directly extracting multiple bits from the digitized output of the entropy source, we achieve a single-channel random bit generation rate of 1.536 Tb/s, while four-channel parallelization reaches 6.144 Tb/s with no observable interchannel correlation. This linear scalability suggests that aggregate throughput could reach hundreds of terabits per second with additional parallel channels. The broadband, low-overhead photonic architecture presented here provides a viable route to real-time, ultrafast random bit generation with broad implications for secure communications, high-performance AI computing, and large-scale data analytics.
True random numbers occupy a core role in the field of encryption and security by virtue of their properties such as unpredictability and independence. In this paper, we propose a high-speed physical random number generator based on a dual-emission random fiber laser. The system improves the spectral bandwidth characteristics of the output signals by adjusting the pump power and the feedback length of the single mode fiber. This study effectively suppresses the autocorrelation feature by performing exclusive-OR operations on the forward and backward random laser signals, and obtain the random number sequence with a generation rate of 20 Gbps by post-processing with high-order finite difference and least significant bit extraction. In order to verify the practical application performance, we apply the random sequence as encryption key to digital image encryption, and the experimental results show that the generator has both theoretical security and practical application value.
We present an optical approach for high-speed parallel random bit generation based on stochastic pulse-to-pulse fluctuation in the supercontinuum (SC). Through spectrally demultiplexing the SC pulse sequence into different wavelength channels, we simultaneously extract multiple independent fast random bit streams from each SC pulse subsequence via associated comparators in parallel. Proof-of-concept experiments demonstrate that using our method, four 10 Gb/s random bit streams are obtained from a SC pulse source with verified randomness. Moreover, this method also provides a promising strategy to fabricate ultrafast random bit generators with Tb/s throughput capacity just by increasing additional wavelength channels.
True random number generation is a critical capability for fault-tolerant quantum computing at millikelvin temperatures. Yet existing Josephson-junction-based TRNGs all rest on a widely accepted but untested assumption: that reliable entropy extraction requires precisely controlled device parameters. Here we show that this assumption does not always hold. We demonstrate a counterintuitive finding: a single current-biased Josephson junction, regardless of its parameter quality, can serve as a cryptographic-grade true random number generator. To establish the universality of this conclusion, we deliberately selected the most extremely deviated devices from fabrication, with critical currents three orders of magnitude away from theoretical predictions and IcRI_cRIc​R products an order of magnitude above conventional values, as the ultimate stress test. Even under these extreme conditions, the raw Shannon entropy reaches 0.9981~bit (99.8\% of the theoretical maximum), with a min-entropy of 0.9271~bit. Using a square-wave pulsed-bias scheme, we tune the switching probability to P≈0.5P\approx0.5P≈0.5. After SHA-256 post-processing, the bitstreams pass all 15 NIST SP 800-22 tests under a conservative m=3m=3m=3 criterion that is more demanding than the standard recommendation, and this certification holds across the entire 100-700~mK operating window of a dilution refrigerator.