Randomness extraction algorithms play an essential role in Quantum Random Number Generators (QRNGs), where they are used to suppress unwanted classical noise and distill true randomness from their biased output. By employing the SHA-512 hash function and Toeplitz matrix multiplication, we analyse two suitable constructions based on different principles and reach postprocessing rates of 8.69 Mbps and 3.68 Mbps, respectively. Finally, we develop a length-compatible Toeplitz-hashing algorithm able to achieve rates of 143.29 Mbps in a parallelized GPU implementation.
Randomness extraction algorithms play an essential role in Quantum Random Number Generators (QRNGs), where they are used to suppress unwanted classical noise and distill true randomness from their biased output. By employing the SHA-512 hash function and Toeplitz matrix multiplication, we analyse two suitable constructions based on different principles and reach postprocessing rates of 8.69 Mbps and 3.68 Mbps, respectively. Finally, we develop a length-compatible Toeplitz-hashing algorithm able to achieve rates of 143.29 Mbps in a parallelized GPU implementation.
Abstract Random Number Generators (RNGs) are devices whose utility spans from cryptography to gambling. Depending on the source of the random seed, RNGs are classified as Pseudo-Random Number Generators (PRNGs), which are based on mathematical algorithms, True Random Number Generators (TRNGs) sourced through seemingly random physical processes, and finally, Quantum Random Number Generators (QRNGs) which harness the intrinsic randomness of measured outcomes of quantum states. To ensure that the output of a QRNG is private and nearly uniform, the raw data undergoes a strong extraction process such as Toeplitz or Trevisan Hashing. The extraction process needs to be extremely efficient to achieve high-speed random number generation. The present work demonstrates state-of-the-art methods for performing information-theoretically provable randomness extraction using variations of the Toeplitz Hashing algorithm. These algorithms are implemented on various hardware for comprehensive analysis. Subsequently, these methods are applied to two raw data sets from a PRNG source and a quantum source. A new benchmark of 19.5 Gbps for Randomness Extraction using the Fast Fourier Transform-based Toeplitz Strong Extractor is demonstrated in this work. The implementation of the algorithm on a GPU-based system demonstrates notably enhanced speed, marking a significant leap beyond the existing state-of-the-art implementations.
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.
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.
Theoretically, Quantum random number generators (QRNGs) can produce truly random numbers that cannot be predicted in advance and have numerous uses. But in practice, it cannot escape the problem of unwanted classical noise, which reduces the quality of the random bits they produce. Therefore, we need to post-process data from a QRNG’s entropy source to improve the statistical quality of the classical output sequence generated from the quantum entropy source. In this work, we implement and compare six extraction primitives: Von Neumann, Multi-level Peres, Toeplitz-hash, Circulant-hash, Trevisan’s construction, and SHA-256 distillation. Using a large classical random bit stream generated by an experimental QRNG, we evaluate these algorithms based on extraction efficiency (η), computational complexity, and seed-entropy requirements. The findings show that although deterministic approaches, such as Multi-level Peres, outperform von Neumann maps, algebraic approaches, especially Circulant extractors, offer higher throughput (η = 0.90) and lower seed consumption by leveraging the cyclicity of the group Zn. The Trevisan extractor provides strong theoretical security with reduced seed growth, but at the cost of higher computational complexity. In contrast, the SHA-256-based method offers fast practical post-processing but provides no information-theoretic entropy guarantees. Statistical validation via autocorrelation and inter-sequence cross-correlation confirms that all evaluated methods successfully decouple hardware-induced dependencies
As one of the applications of randomness extraction, post-processing is important for the high-speed and real-time QRNG (Quantum Random Number Generator) system. This work proposes a multi-thread and streamed-processing algorithm to optimize post-processing based on Toeplitz matrix on GPU (Graphics Processing Unit) and achieves a high speed over 6.8 Gbps. Furthermore, random tests are done to evaluate the quality of the random bits generated. The results show that both the execution speed and the randomness can satisfy the requirements of the high-speed and real-time QRNG system.
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.