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All-Silicon-Based Photonic Quantum Random Number Generators

Zahra Bisadi

Published Jan 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.15168/11572_368875

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Randomness occurs in every kind of application in which random events should be experienced such as gambling, statistical calculations, computer simulations, information security and encryption. The quality of randomness is very important for the events using randomness. In particular, the need for random numbers used in the field of cryptology to be unpredictable increases the importance of random number generators. \n \nRandom Number Generators (RNGs) are software or hardware components that can be used to generate numbers that cannot be predicted in any pattern or relationship. Software-based RNGs are deterministic applications, while hardware-based RNGs are the devices that can be integrated into the system. \n \nEncryption using numbers generated by software-based RNG can be broken in varying times depending on the strength of the encryption because it was developed in deterministic ways. It is expected that the decoding time will be shortened considerably by the quantum computers which are tried to be developed today besides classic computers that takes a long time to analyze. The hardware RNGs are more powerful in randomness quality than software-based generators, but cost-effective and use-limited generators. \n \nQuantum Random Number Generators (QRNGs) is a kind of generator based on quantum physics laws instead of classical physics. In photonic based QRNGs are produced the random numbers after various software and hardware operations by taking advantage of the uncertainty of photons. These generated numbers are unpredictably strong random numbers. \n \nIn this study, a QRNG was obtained by using the RGB (Red-Green-Blue) values of the images taken from a white-single LED light source and the randomness tests of the produced numbers were carried out with the tests provided by NIST (National Institute of Standards and Technology). As a result, the numbers derived from the images successfully passed NIST tests and true random number sequences were obtained.

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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. 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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.
Different electronic devices nowadays exploit random number generators either to create the seed for simulations, for gaming or to encrypt the communications. Particularly for cryptography applications, there is an increasing effort to realize a truly random number generator, based not on mathematical algorithms but exploiting randomness of physical processes. Among them quantum processes, provide intrinsic unpredictability, for example exploiting the arrival time, the number or the properties of photons. In this work we focus on photonic quantum random number generator (QRNG), and we analyze different approaches and entropy extraction methods to realize a fully integrated, CMOS compatible, QRNG with photon-emitter realized on the same chip and very close to the detectors of single photons. Non-idealities of the emitter and the detector have to be studied and depends on the structure. They can be mitigated with robust extraction methods which however should not introduce complex algorithms or secondary entropy sources that can make the device no longer quantum based. The ultimate goal is to realize a CMOS building block that can be implemented as building block, with low power consumption and robust to environmental conditions.
Random numbers find applications in a range of different fields, from quantum key distribution and classical cryptography to fundamental science.They also find extensive use in gambling and lotteries.By exploiting the probabilistic nature of Quantum Mechanics, quantum random number generators (QRNGs) provide a secure and efficient means to produce random numbers.Most of the quantum random number generators demonstrated so far have been built in bulk optics, either using free space or fibre-optic components.While showing good performance, most of these demonstrations are strongly limited in real life applications, due to issues such as size, costs and the manufacturing process.In this thesis I report the demonstration of three different QRNGs based on integrated photonics.First, I demonstrated a QRNG based on homodyne measurement of optical vacuum states on a Silicon-on-insulator (SOI) chip.Second, I developed a SOI QRNG based on phase fluctuations from a laser diode.In these two schemes all the optical and opto-electronic components, excluding the laser, were integrated onto a silicon-on-insulator device.These schemes, being built on a silicon-on-insulator chip are potentially CMOS compatible and pave the way for being integrated onto other more complex systems.These QRNGs showed Gbps generation rates and passed the statistical tests provided by NIST.Third, I report the preliminary study of a QRNG based on homodyne measurement of optical vacuum states onto a Indium Phosphide (InP) chip.In this third experiment, all the components, including a laser diode, were monolithically integrated in the same chip, which provide a great advantage in terms of the overall size of the optics of the device.First, I would like to thank Jonathan, for the opportunity to pursue my PhD and for guiding my research in these four years.Thank you for giving me the chance to follow my curiosity and for pushing me to get the best out of my research.Thank you, Dylan, for being so helpful, always ready to answer my questions.I would like to thank Giacomo for sharing a big part of my research in these years
Random Number Generators (RNGs) are used in various applications, including cryptography, scientific simulations, gaming, and virtual reality. The quality of these random numbers is crucial, especially for computational approaches that rely on unpredictability to produce accurate results. In this thesis, we perform a comprehensive assessment of the quality of a novel Quantum Random Number Generator (QRNG) based on single photon. QRNGs leverage quantum mechanical properties to produce truly random numbers. This ensures high entropy, unpredictability, and security, making QRNGs particularly useful in fields that require high-quality randomness.We evaluate the statistical properties of strings generated by our QRNG and then its practical application by comparing it to traditional Pseudo-Random Number Generators (PRNGs) in Monte Carlo Integration (MCI), a technique that estimates integrals using random sampling. In particular, we use two statistical randomness test suits, namely NIST and Dieharder, to assess the statistical properties of our QRNG. All tests within these tests were passed, confirming that the corresponding QRNG achieves true randomness with sufficient high entropy. Next, we use our QRNG-generated numbers to seed Monte Carlo Integration (MCI) and compare it against results obtained using classical PRNG. The QRNG-based MCI demonstrated more accurate and stable numerical estimates, showing lower error rates and improved convergence compared to PRNG-based simulations.These findings highlight the advantages of QRNGs in enhancing numerical accuracy and computational security. While QRNGs may have slower generation rates than PRNGs, their superior randomness quality allows for more reliable Monte Carlo-based simulations, suggesting that fewer samples may be needed to achieve the same level of accuracy compared to classical PRNGs. This research underscores the potential of QRNG-powered numerical methods, paving the way for their integration into more advanced applications, including scientific computing, financial modeling, and cryptographic security.
For globally connected devices like smart phones, personal computers and Internet-of-things devices, the ability to generate random numbers is essential for execution of cryptographic protocols responsible for information security. Generally, a random number generator should be small, robust, utilize as few hardware and energy resources as possible, yet provide excellent randomness at a high enough speed (bitrate) for a given purpose. In this work we present a quantum random number generator (QRNG) which makes use of a photoelectric effect in single-photon avalanche diodes (SPADs) as a source of randomness and is scalable to any desired bitrate. We use the random flip-flop method in which random bits are obtained by periodic sampling of a randomly toggling flip-flop. For the first time we investigate this method in detail and find that, out of two main imperfections, bias is due only to hardware imperfections while autocorrelation predominantly resides with the method itself. SPADs are integrated on a silicon chip together with passive quenching and digital pulse-shaping circuitry, using a standard 180 nm CMOS process. A separate FPGA chip derives random numbers from the detection signals. The basic QRNG cell, made of only two SPADs and a few logic circuits, can generate up to 20 Mbit/s that pass NIST statistical tests without any further postprocessing. This technology allows integration of a QRNG on a single silicon chip using readily available industrial processes.
A small-sized photonic quantum random number generator, easy to be implemented in small electronic devices for secure data encryption and other applications, is highly demanding nowadays. Here, we propose a compact configuration with Silicon nanocrystals large area light emitting device (LED) coupled to a Silicon photomultiplier to generate random numbers. The random number generation methodology is based on the photon arrival time and is robust against the non-idealities of the detector and the source of quantum entropy. The raw data show high quality of randomness and pass all the statistical tests in national institute of standards and technology tests (NIST) suite without a post-processing algorithm. The highest bit rate is 0.5 Mbps with the efficiency of 4 bits per detected photon.
Randomness occurs in every kind of application in which random events should be experienced such as gambling, statistical calculations, computer simulations, information security and encryption. The quality of randomness is very important for the events using randomness. In particular, the need for random numbers used in the field of cryptology to be unpredictable increases the importance of random number generators. \n \nRandom Number Generators (RNGs) are software or hardware components that can be used to generate numbers that cannot be predicted in any pattern or relationship. Software-based RNGs are deterministic applications, while hardware-based RNGs are the devices that can be integrated into the system. \n \nEncryption using numbers generated by software-based RNG can be broken in varying times depending on the strength of the encryption because it was developed in deterministic ways. It is expected that the decoding time will be shortened considerably by the quantum computers which are tried to be developed today besides classic computers that takes a long time to analyze. The hardware RNGs are more powerful in randomness quality than software-based generators, but cost-effective and use-limited generators. \n \nQuantum Random Number Generators (QRNGs) is a kind of generator based on quantum physics laws instead of classical physics. In photonic based QRNGs are produced the random numbers after various software and hardware operations by taking advantage of the uncertainty of photons. These generated numbers are unpredictably strong random numbers. \n \nIn this study, a QRNG was obtained by using the RGB (Red-Green-Blue) values of the images taken from a white-single LED light source and the randomness tests of the produced numbers were carried out with the tests provided by NIST (National Institute of Standards and Technology). As a result, the numbers derived from the images successfully passed NIST tests and true random number sequences were obtained.