FPGA Implementation of High-Rate Randomness Extraction for Quantum Random Number Generators

Random number generators are fundamental in several real-world applications, like cryptography and simulation. This need for randomness is commonly bridged using pseudo-random number generators, which rely on deterministic mathematical algorithms to produce uniform random sequences. It is not rare to find situations in which the deterministic aspect of these objects is not acceptable. To make up for this need, true random number generators can be used, in particular Quantum Random Number Generators (QRNGs), that exploit the inherently random nature of quantum mechanical phenomena to generate numbers. Several paradigms of QRNGs are possible, regarding the elements of the system that can be considered as trusted. Semi-device-independent schemes offer a trade-off between the speed of trusted-devices and the security assurances of device-independent generators. Multiple possibilities are available also concerning the physical phenomenon exploited to produce the numbers. Optical QRNGs, that use continuous variables of the electromagnetic field, have proven to be cost-efficient solutions that support very high generation rates. Real implementations of QRNGs are always affected by noise, because of the imperfections that characterize the experimental apparata. This aspect reduces the quality of the randomness in the numbers produced, therefore post-processing and in particular randomness extraction, is needed to eliminate the unwanted correlations. Multiple strategies are possible for this kind of post-processing in real time, including Central Processing Unit (CPU) and Graphics Processing Unit (GPU) implementations. With these, the generation rate does not meet the demand set by real high-speed systems, such as those for encryption of communication links. A possibility that has proven to be fast enough is a hardware-based approach with a Field Programmable Gate Array (FPGA). This device combines the flexibility of a re-programmable component with the efficiency of the hardware and its concurrent computation capabilities. This work reports on the randomness extraction from two QRNG implementations: a trusted QRNG, based on the fluctuations of the phase of a laser diode and a source device-independent QRNG, based on the fluctuations of the vacuum state. The post-processing is realized on a System on Chip (SoC), including a CPU and a FPGA. The circuit on the programmable logic has been designed to efficiently execute randomness extraction, based on Toeplitz hashing. It consists in a three-stage pipeline, instantiated multiple times, to allow for parallel computation of multiple data blocks. Both an online and an offline design have been implemented. The former demonstrates the possibility of high-rate randomness extraction, by processing the data coming from the QRNG in real time. The latter has been implemented to conveniently read raw data batches from an SD card and save the processed numbers on this same storage device. The bit strings obtained from randomness extraction have been tested using the autocorrelation function and the NIST test suite, that certify the quality of the randomness of the produced numbers. The analysis has been carried for both the QRNGs and the results satisfy the NIST requirements, showing uniformly distributed P−values and an acceptable proportion of successful sequences. These results reinforce the applicability of programmable logic to quantum communication applications, representing a powerful and convenient solution to high-rate data processing.