Abstract Quantum realizations have opened a new ways for computer science. The new characteristics and phenomenons allow us to create new algorithms for general proposes. An interesting topic is random number generation. There are two perspectives for this proposes. True random numbers generator (TRN) and pseudo random numbers generator (PRNG). True Random Number Generators has four significant characteristics: randomness, long Period, insensitivity to seeds, repeatability. Additionally, Pseudo Random Number Generators is a fascinating topic that leverages the principles of computer science to craft deterministic algorithms, enabling the creation of a sequence of pseudo-random numbers. A crucial element in this process is the 'seed', which serves as the initial value to generate the entire sequence. This document proposes a algorithm based on a quantum system and the quasi-probability of its possible states to generate a long set of numbers which has pseudo random properties. The quantum system is compound by n qubits, its initial conditions and a small set of rotation gates with a fixed angle. The tests were realized using the battery test called NIST SP800-22, and alpha=0.01 as a threshold to ensures 99\% of precision. The results demonstrate that it is possible generate a long set of pseudo numbers with random characteristics using a quantum simple operation. However, the experiments reveal that a real world implementation require a quantum system with at least 10-9 precision order.
Abstract Quantum realizations have opened a new ways for computer science. The new characteristics and phenomenons allow us to create new algorithms for general proposes. An interesting topic is random number generation. There are two perspectives for this proposes. True random numbers generator (TRN) and pseudo random numbers generator (PRNG). True Random Number Generators has four significant characteristics: randomness, long Period, insensitivity to seeds, repeatability. Additionally, Pseudo Random Number Generators is a fascinating topic that leverages the principles of computer science to craft deterministic algorithms, enabling the creation of a sequence of pseudo-random numbers. A crucial element in this process is the 'seed', which serves as the initial value to generate the entire sequence. This document proposes a algorithm based on a quantum system and the quasi-probability of its possible states to generate a long set of numbers which has pseudo random properties. The quantum system is compound by n qubits, its initial conditions and a small set of rotation gates with a fixed angle. The tests were realized using the battery test called NIST SP800-22, and alpha=0.01 as a threshold to ensures 99% of precision. The results demonstrate that it is possible generate a long set of pseudo numbers with random characteristics using a quantum simple operation. However, the experiments reveal that a real world implementation require a quantum system with at least 10-9 precision order.
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.
ABSTRACT Quantum random number generator (QRNG) platforms use principles of quantum mechanics to create truly random numbers. Traditional pseudo-random number generators (PRNGs) generate numbers based on deterministic formulas. QRNG's use of the principles of superposition and measurement can provide numbers that cannot be predicted or replicated; therefore, they have been used as a source of randomness in various fields. In this research project, an experimental QRNG was designed and built using Qiskit simulations. Each experiment consisted of a series of two-qubit circuits. The circuits were created to place both qubits into an equal probability state. This was done by applying a pair of Hadamard gates (Hadamard gate applies a rotation operator of π/2 radians). Then each circuit was measured. For each measurement, there would be one output from each qubit. Since the Hadamard gate creates an equal-probability superposition, the combination of each qubit will either add up to 1 or subtract from -1. These combinations will be recorded and processed through several methods to evaluate their quality. Those methods include: Shannon Entropy Analysis, Frequency Distribution Analysis and Chi-Square Uniformity Testing. Keywords: Quantum Random Number Generator, Quantum Computing, Quantum Measurement, Cryptography, Secure Randomness, Qiskit Simulation
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.
The generation of true randomness remains a significant challenge in computer science, particularly when relying solely on classical algorithms. Many current approaches employ pseudo-random number generators (PRNGs), which, despite their computational efficiency, are inherently predictable and lack genuine randomness. This paper proposes a novel method for algorithmic randomness generation leveraging the principles of quantum walks. We demonstrate that the inherent uncertainty and superposition properties of quantum systems provide a robust mechanism for generating truly random numbers. Specifically, we outline a framework for designing quantum walks on graphs, where the evolution of the walker's state is fundamentally probabilistic and unpredictable. The core of our approach resides in exploiting the quantum walk's non-deterministic nature to produce sequences of numbers that exhibit statistical properties consistent with true randomness. The theoretical framework is presented, including a detailed description of the mathematical formalism underlying the quantum walk and the probability distribution of the walker's positions. We highlight the potential advantages of this approach, particularly in scenarios demanding high-quality randomness for cryptographic applications or simulations. The key concept is to translate a classical problem into a quantum one, where the inherent probabilistic nature of quantum mechanics offers a superior solution to the problem of generating genuine randomness.
Abstract In the process of quantum key distribution (QKD), the communicating parties need to randomly determine quantum states and measurement bases. To ensure the security of key distribution, we aim to use true random sequences generated by true random number generators as the source of randomness. In practical systems, due to the difficulty of obtaining true random numbers, pseudo-random number generators are used instead. Although the random numbers generated by pseudo-random number generators are statistically random, meeting the requirements of uniform distribution and independence, they rely on an initial seed to generate corresponding pseudo-random sequences. Attackers may predict future elements from the initial elements of the random sequence, posing a security risk to quantum key distribution. This paper analyzes the problems existing in current pseudo-random number generators and proposes corresponding attack methods and applicable scenarios based on the vulnerabilities in the pseudo-random sequence generation process. Under certain conditions, it is possible to obtain the keys of the communicating parties with very low error rates, thus effectively attacking the quantum key system. This paper presents new requirements for the use of random numbers in quantum key systems, which can effectively guide the security evaluation of quantum key distribution protocols.
This paper explores the design of cryptographic algorithms leveraging the inherent randomness of quantum random number generators (QRNGs). Traditional cryptographic algorithms often rely on pseudo-random number generators (PRNGs), which are deterministic and therefore vulnerable to attacks if their internal state is compromised. QRNGs, on the other hand, derive their randomness from quantum mechanical phenomena, offering a fundamentally unpredictable source of numbers. This research investigates the application of QRNGs to enhance cryptographic security, focusing on constructing algorithms that exploit this unique property. The core claim is that utilizing QRNG characteristics allows for the design of more secure cryptographic algorithms. The proposed mechanism involves capitalizing on the non-deterministic nature of QRNGs to build algorithms with heightened security levels. This approach presents a novel security guarantee method by incorporating true randomness into cryptographic processes. We examine specific algorithm designs and analyze their security implications compared to traditional PRNG-based approaches. The paper concludes with a discussion on the challenges and future directions of utilizing QRNGs in cryptography.