Scalable ultrafast random bit generation using wideband chaos-based entropy sources

TL;DR

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.

Abstract

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.

Figures (8)

• Figure 1: Generation of the wideband chaos-based entropy source (WCBES).a, Schematic of the experimental setup. OSA, optical spectrum analyzer; OSC, real-time digital oscilloscope; PM, phase modulator; PD, photodetector; SG, signal generator. b, Intensity fluctuations of the emission from the chaotic laser (upper blue trace) and the WCBES (lower black trace), showing substantially faster temporal oscillations in the WCBES. c, Electrical spectra of the emission from the chaotic laser (upper blue trace) and the WCBES (lower black trace). The chaotic laser exhibits a standard bandwidth of 40 GHz, an effective bandwidth of 38 GHz, and a spectral flatness of 0.96, whereas the WCBES has a standard bandwidth of 104 GHz, an effective bandwidth of 73 GHz, and a spectral flatness of 0.91. d, Optical spectrum of the combined output from the chaotic laser and the comb laser. e, Autocorrelation functions of the emission from the chaotic laser (upper blue trace) and the WCBES (lower black trace), showing a reduction in the time-delay signature from 0.346 to 0.075, indicating enhanced temporal randomness in the WCBES.
• Figure 1: Detailed schematic of the experimental setup. ATT, variable optical attenuator; EDFA, erbium-doped fiber amplifier; FC, fiber coupler; LC, laser controller; OSA, optical spectrum analyzer; OSC, real-time digital oscilloscope; PC, polarization controller; PD, photodetector; PM, power meter; PS, power supply; SG, signal generator; VOA, voltage-controlled variable optical attenuator.
• Figure 2: Entropy rate assessment and random bit generation.a, Schematic of the data acquisition and bit-extraction pipeline. ADC, analog-to-digital converter; LSB, least significant bit. b, Estimated entropy rate $H_{\rm NIST}$ as a function of the number of digitized bits $n$ (black symbols), evaluated using the NIST SP 800-90B entropy estimation suite. The red line denotes the Shannon–Hartley theoretical limit $H_{\rm SH}$. c, Autocorrelation of the 6-LSB bitstream (black) with statistical bounds of $\pm3\sigma_{\rm c}$ (red), where $\sigma_{\rm c}=1/\sqrt{N}$ and $N=10^7$ bits. d, Bias $|P_{1} - 0.5|$ as a function of $N$ (black), where $P_{1}$ is the probability of observing “1” in the sequence. The bias remains below the statistical threshold $3\sigma_{\rm B}$ (red), where $\sigma_{\rm B}=1/(2\sqrt{N})$, demonstrating long-term binary balance. e, Number of passed NIST SP 800-22 tests as a function of the number of extracted LSBs $k$. A value of “15” indicates that all NIST tests are passed. For each $k$, eleven 1-Gbit sequences are evaluated; the median number of passed tests is plotted, with error bars showing the minimum and maximum values. The results indicate that LSBs with $k\le6$ can be reliably extracted from each digitized data sample for random bit generation. f, Representative NIST SP 800-22 results for $k=6$, taken from one of the passed trials in e. All 15 pass proportions fall within the expected interval $0.99 \pm 0.0094$ (red) at a significance level of 0.01, and all $P$-values exceed 0.0001, confirming the statistical randomness of the 6-LSB bitstream.
• Figure 2: Spectral characteristics of chaos induced by delayed optical self-feedback.a, Chaos spectra for different optical feedback strengths $\xi_{\rm f}$. b, Standard bandwidth and c, spectral flatness as a function of $\xi_{\rm f}$. d, Chaos spectra for different bias currents. e, Standard bandwidth and f, spectral flatness as a function of bias current.
• Figure 3: Parallel RBG using multiple independent WCBES channels.a, Schematic of the scalable parallel RBG architecture. The output from a comb laser is split into $M$ optical paths, each combined with chaotic emission from an independent semiconductor laser. This generates $M$ physically distinct WCBESs, each detected by a high-speed PD and digitized by a 10-bit ADC at 256 GS/s. The present demonstration is limited to $M=4$ by currently available hardware. b, Electrical spectral analysis of the four WCBES channels, each exhibiting a standard bandwidth exceeding 100 GHz (black symbols), an effective bandwidth over 72 GHz (green symbols), and a spectral flatness of approximately 0.9 (red symbols). c, $H_{\mathrm{NIST}}$ for Channel 1 to 4 under 10-bit digitization. All values exceed 1.8 Tb/s, demonstrating consistent entropy generation across the four channels. d, Cross-correlation coefficients between all channel pairs. Off-diagonal values lie within statistical bounds of $\pm3\sigma_{\mathrm{c}}$ with $N=10^{7}$ bits, indicating negligible inter-channel correlation. e, Maximum bias across the four channels as a function of $N$ bits (black). Bias remains below the statistical threshold $3\sigma_{\mathrm{B}}$ (red), confirming long-term binary balance of the bitstreams from all channels. f, Median value of the minimum pass proportion across eleven NIST SP 800-22 trials for each channel, all within the statistical acceptance range of $0.99 \pm 0.0094$ (red). g, Median value of the lowest $P$-values across eleven NIST SP 800-22 trials for each channel, all exceeding 0.0001. Together, the results in f and g confirm that the bitstreams from all four channels satisfy the statistical randomness criteria.