Simulation of physical processes and Monte Carlo solutions to numerical problems on digital computers require sources of random numbers that follow specified density functions. In our experiments, the spatial coordinates of detected photoevents are used as a fast source of true random numbers to solve numerical problems by the Monte Carlo method. The probability density function for the location of a photoevent on the detector surface is proportional to the irradiance. We have constructed an optical random number generator using a microchannel plate detector with a resistive anode. It can produce bivariate random deviates with any probability density and any correlation between the two variables. The numbers pass the standard tests for randomness and fit to the given distributions (chi-square, correlation, sequence tests). Nonuniform distributions can be obtained with no loss of speed by manipulating the irradiance distribution across the detector, e.g., by imaging a transparency onto it. In particular, we have produced uniformly distributed random numbers and normally distributed random numbers with various correlations between the variables. We have also used the optical random number generator to find approximate solutions to systems of large linear algebraic equations and approximations to the inverses of large matrices, with a maximum error of <5%.
Simulation of physical processes and Monte Carlo solutions to numerical problems on digital computers require sources of random numbers that follow specified density functions. In our experiments, the spatial coordinates of detected photoevents are used as a fast source of true random numbers to solve numerical problems by the Monte Carlo method. The probability density function for the location of a photoevent on the detector surface is proportional to the irradiance. We have constructed an optical random number generator using a microchannel plate detector with a resistive anode. It can produce bivariate random deviates with any probability density and any correlation between the two variables. The numbers pass the standard tests for randomness and fit to the given distributions (chi-square, correlation, sequence tests). Nonuniform distributions can be obtained with no loss of speed by manipulating the irradiance distribution across the detector, e.g., by imaging a transparency onto it. In particular, we have produced uniformly distributed random numbers and normally distributed random numbers with various correlations between the variables. We have also used the optical random number generator to find approximate solutions to systems of large linear algebraic equations and approximations to the inverses of large matrices, with a maximum error of <5%.
A 2-D position-sensitive photon-counting detector is used in an optical random number generator in which the locations of detected photoevents provide the random numbers. The spatial distribution of photoevent locations is dictated by imaging a control object onto the detector. An iterative calibration procedure is used to determine the brightness distribution of the control object. Two control objects were examined-film and a video monitor. With both control objects, the performance of the optical random number generator approached that of pseudorandom number generators.
Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.
Random numbers sequences (RNSs) play a vital role in various scientific and engineering applications. They are critical to the integrity of classical and quantum cryptography, the accuracy of mathematical modeling and Monte Carlo simulations, and the core mechanics of applications in fields as diverse as gambling and statistical sampling. While the primary criteria for RNSs sources are their quality and generation rate, their integration into experimental designs is equally significant for many fundamental physical tests and applications. This work presents a comparative analysis of optical random number generation architectures, which can be seamlessly included into various advanced classical and quantum optical experimental schemes. In particular, we evaluate the trade-off between the high generation rate of an attenuated laser (a quasi-single-photon source) and the superior statistical quality of a heralded single-photon source operating at a much lower frequency. To overcome the limitations of each individual source, we propose and examine a novel hybrid architecture that utilizes their mixed radiation, enabling the generation of highquality RNSs at an enhanced rate. Furthermore, we demonstrate that the raw sequences generated by such a source can not only exhibit but, in some cases, even surpass the degree of randomness achieved by sequences processed through powerful randomness extractors.
A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device, which minimizes the impact of the photon counters ’ noise, dead-time and after pulses. Random numbers are employed today as well for numerical simulations as for cryptography. Unfortunately computers are not able to generate true random numbers, as they are deterministic systems. Numerical pseudo-random generators rely on complexity [1]. Although such pseudo-random numbers can generally be employed for numerical computation, such as Monte-Carlo simulations, their use in cryptography, for example to generate keys, is more critical. The only way to get true random numbers, hence true security for crypto-systems, is to build a generator based on a random physical phenomenon [2,3,4]. As quantum theory is intrinsically random, a quantum process is an ideal base for a physical random number generator. The randomness of a sequence of numbers can be extensively tested, though not proven. It is thus of interest to thoroughly understand the behavior of the random process, so as to gain
Abstract Quantum random number generators give the opportunity to, in theory, obtain completely unpredictable numbers only perturbed by the noise in the measurement. The obtained data can be digitalized and processed so that it gives as a result a uniform sequence of binary random numbers without any relation with the classical noise in the system. In this work we analyze the performance of optical QRNGs with three different arrangements: a homodyne detector measuring vacuum fluctuations, a homodyne detector measuring amplified spontaneous emission from an EDFA and a spontaneous emission phase noise-based generator. The raw data from the experiments is processed using a Toeplitz extractor, giving as a result sequences of binary numbers capable of passing the NIST Statistical Test Suite.
Random number generators are essential for applications in information security and numerical simulations. Most optical-chaos-based random number generators produce random bit sequences by offline post-processing with large optical components. We demonstrate a real-time hardware implementation of a fast physical random number generator with a photonic integrated circuit and a field programmable gate array (FPGA) electronic board. We generate 1-Tbit random bit sequences and evaluate their statistical randomness using NIST Special Publication 800-22 and TestU01. All of the BigCrush tests in TestU01 are passed using 410-Gbit random bit sequences. A maximum real-time generation rate of 21.1 Gb/s is achieved for random bit sequences in binary format stored in a computer, which can be directly used for applications involving secret keys in cryptography and random seeds in large-scale numerical simulations.