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arXiv:2107.14177

Parallel and real-time post-processing for quantum random number generators

Xiaomin Guo, Ming-Chuan Wu, Jiangjiang Zhang, Ziqing Wang, Yu Wang, Yanqiang Guo

Published Jul 29, 2021• 2 citations
arXivHTMLPDF

Abstract

Quantum random number generators (QRNG) based on continuous variable (CV) quantum fluctuations offer great potential for their advantages in measurement bandwidth, stability and integrability. More importantly, it provides an efficient and extensible path for significant promotion of QRNG generation rate. During this process, real-time randomness extraction using information theoretically secure randomness extractors is vital, because it plays critical role in the limit of throughput rate and implementation cost of QRNGs. In this work, we investigate parallel and real-time realization of several Toeplitz-hashing extractors within one field-programmable gate array (FPGA) for parallel QRNG. Elaborate layout of Toeplitz matrixes and efficient utilization of hardware computing resource in the FPGA are emphatically studied. Logic source occupation for different scale and quantity of Toeplitz matrices is analyzed and two-layer parallel pipeline algorithm is delicately designed to fully exploit the parallel algorithm advantage and hardware source of the FPGA. This work finally achieves a real-time post-processing rate of QRNG above 8 Gbps. Matching up with integrated circuit for parallel extraction of multiple quantum sideband modes of vacuum state, our demonstration shows an important step towards chip-based parallel QRNG, which could effectively improve the practicality of CV QRNGs, including device trusted, device-independent, and semi-device-independent schemes.

DOI
10.48550/arxiv.2107.14177

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As a universal-hashing function, Toeplitz hashing is migrated in QRNG from privacy amplification of QKD to execute information-theoretically provable true randomness extraction. Though random seed needed for constructing a Toeplitz matrix is longer than the output string, Toeplitz-hashing extractor is still much more favored in practical implementation of QRNG because its relative simple structure and parallel operation property compared to the other universal-hashing strong extractor, Trevisan's extractor, especially in the booming integration realization of randomness extractor via FPGA. But two origin issues have been put off for long in the random number post-processing in FPGA besides chasing speed: collision probability threaten owing to small matrix and security parameter growth due to seed reuse. In this work, seed update and collision probability are both paid close attention when realize real-time parallel post-processing of CV-QRNG, who has a pretty practical prospect as well as greatest demand on post-processing both because of whose wide detection bandwidth and multibit discretization. We propose a sub-seed generation scheme based on reading and writing between two levels of memories in FPGA, which effectively avoid the consumption of logic resources. One seeds pool is built in storage element of the FPGA and distinct random seed is chosen for each post-processing instance by a random selection process. And the seeds pool is swiftly updated via PCIe interface once security parameter reaches a pre-set threshold. Furthermore, by elaborate layout of Toeplitz matrixes and two-layer parallel pipeline algorithm with TDM designed delicately, four-channel parallel seed renewable Toeplitz post-processing with matrix of about1700 × 2500{\mathbf{1700}\mathbf {\, \times \, }\mathbf{2500}}1700×2500is realized with a real-time random number yield of 11.3 Gbps in one medium-configuration FPGA. In order to guarantee the robustness of the hardware-based parallel Toeplitz post-processing, timing is optimized by register replication, global clock buffers and data cache. This investigation fills an obvious hole in randomness extraction and provides a referential technique for privacy amplification.
The quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. The real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here we use a multiplexing scheme to create a fast real-time quantum random number generator based on continuous variable vacuum fluctuations. Multiple sideband frequency modes of a quantum vacuum state within a homodyne detection bandwidth are concurrently extracted as the randomness source. Parallel postprocessing of raw data from three subentropy sources is realized in one field-programmable gate array (FPGA) based on Toeplitz-hashing extractors. A cumulative generation rate of 8.25 Gbps in real time is achieved. The system relies on optoelectronic components and circuits that could be integrated in a compact, economical package.
We present a real-time and fully integrated quantum random number generator (QRNG) by measuring laser phase fluctuations. The QRNG scheme based on laser phase fluctuations is featured for its capability of generating ultra-high-speed random numbers. However, the speed bottleneck of a practical QRNG lies on the limited speed of randomness extraction. To close the gap between the fast randomness generation and the slow post-processing, we propose a pipeline extraction algorithm based on Toeplitz matrix hashing and implement it in a high-speed field-programmable gate array. Further, all the QRNG components are integrated into a module, including a compact and actively stabilized interferometer, high-speed data acquisition, and real-time data post-processing and transmission. The final generation rate of the QRNG module with real-time extraction can reach 3.2 Gbps.
Continuous-variable quantum random number generator (cv-QRNG) has attracted much attention due to its convenient state preparation and high measurement bandwidth. Chip-size integration of this type of QRNG is expectable because all components involved have been integrated on a single chip recently. Most of the existing schemes, including all existing commercial schemes, usually use a once-and-for-all approach to evaluate quantum entropy. In this work, we propose a double-level parallel cv-QRNG scheme that integrates real-time phase-space monitoring and entropy evaluation. By using dynamic threshold monitoring and self-adapting scaling of Toeplitz matrix, the security and generation rate of QRNG can be enhanced simultaneously. Experimentally, a parallel extraction system of vacuum state double quadratures and multiple sideband modes is constructed based on heterodyne, providing sufficient raw data for high-precision and high-speed tomography reconstruction of quantum entropy source and parallel extraction of QRNG. Based on the statistical analysis of data under long-term stable operation of the system, dynamic KLD-sensitive security threshold for statistical distribution of Husimi-Q function of the entropy source is established. When a weak chaotic field is injected to simulate a thermal state attack, the KLD value jumps and quickly deviates from the steady state baseline, manifesting a sensitive identification of the attack. It is worth pointing out that the threshold parameter can be dynamically optimized according to the security requirements of actual application scenarios. An FPGA-based real-time feedback Toeplitz-hash extractor employs a maximum matrix bit-width truncation method to dynamically adjust Toeplitz matrix parameters. This optimization reduces the maximum extraction ratio interval from 6% to 1.8%, with all intervals below 1% for extraction ratios ≤76%, significantly mitigating entropy losses caused by discrete adjustment of the Toeplitz matrix, and achieving a minimum extraction ratio of 16.9%. This flexibility enables the system to accurately control the response sensitivity of abnormal signals while maintaining the real-time generation of quantum random bits. Finally, real-time generation rate of 17.512 Gbit/s is attained with security parameters at the level of 10–50 and the generated random numbers passed NIST SP 800-22, Diehard, and TestU01 standard tests. This research provides a technical path for real-time assessment of entropy source security in QRNG. The proposed scheme has good integrability and scalability, presenting a feasible solution for QRNG to enter the application stage.
Abstract We present a high-speed continuous-variable quantum random number generator (QRNG) based on heterodyne detection of vacuum fluctuations. The scheme follows a source-device-independent security model in which the entropy originates from quantum measurement uncertainty and no model of the source is required; security depends only on the trusted measurement device and the calibrated discretization, and thus remains valid even under adversarial state preparation. The optical field is split by a 90 ∘ optical hybrid and measured by two balanced photodiodes to obtain both quadratures of the vacuum state simultaneously. The analog outputs are digitized using a dual-channel 12-bit analog-to-digital converter operating at a sampling rate of 3.2 GS s −1 per channel, and processed in real time by an field-programmable gate array (FPGA) implementing Toeplitz hashing for randomness extraction. The quantum-to-classical noise ratio was verified through calibrated power spectral density measurements and cross-checked in the time domain, confirming vacuum-noise dominance within the 1.6 GHz detection bandwidth. After extraction, the system achieves a sustained generation rate of R net = 33.92 Gbit s − 1 of uniformly distributed random bits, which pass all NIST and Dieharder statistical tests. The demonstrated platform provides a compact, FPGA-based realization of a practical heterodyne continuous-variable source-independent QRNG suitable for high-rate quantum communication and secure key distribution systems.