A random number generator produces a periodic sequence of numbers on a computer. The starting point can be random, but after it is chosen, everything else is deterministic. A random number generator produces a periodic sequence of numbers on a computer. The starting point can be random, but after it is chosen, everything else is deterministic. This paper presents the entropy and p-value tests performed on classical and quantum random number generators, in order to check the randomness of the generated output data. Both generators have been integrated in software applications reproducing asymmetrical cryptosystems, their results contributing to the generation of key material within Diffie-Hellman protocol. Can regard these tests as a first step in determining if a generator is suitable for a particular cryptographic application. At the same time, the statistical tests cannot serve as a substitute for cryptanalysis.
A random number generator produces a periodic sequence of numbers on a computer. The starting point can be random, but after it is chosen, everything else is deterministic. A random number generator produces a periodic sequence of numbers on a computer. The starting point can be random, but after it is chosen, everything else is deterministic. This paper presents the entropy and p-value tests performed on classical and quantum random number generators, in order to check the randomness of the generated output data. Both generators have been integrated in software applications reproducing asymmetrical cryptosystems, their results contributing to the generation of key material within Diffie-Hellman protocol. Can regard these tests as a first step in determining if a generator is suitable for a particular cryptographic application. At the same time, the statistical tests cannot serve as a substitute for cryptanalysis.
This paper presents a few aspects regarding the testing of two random number generators. The importance of the quality of a generator is according to the type of application used. The outputs of these generators may be used in cryptographic applications to generate encryption keys. Random number generators used in cryptographic applications must meet certain requirements, and the most important is that their outputs must be unpredictable in the absence of knowledge of the inputs. This paper presents the analysis of a few statistical tests performed on two random number generators: a classic-software, and a quantum-hardware. These tests may be considered to determine if a generator is adequate to be used in particular cryptographic applications.
Random numbers play a central role in cryptography, cyber security, and gaming applications. Extracting bits from some random natural activity is one of the primitive ways to generate random numbers. True random number generator(TRNG) and quantum random number generator(QRNG) are examples of this random number sequence. The development of quantum technology made it possible to extract random sequences from quantum entropy sources. This sequence is called quantum random numbers and the whole setup is named a quantum random number generator. A suitable sampling and a physical device for the entropy source are the building blocks for a TRNG. Here we present a comparative analysis of two random number generators. Apart from the conventional statistical test for randomness, here we introduce a straightforward coefficient based on the concept of non-linearity of the Boolean function to determine the availability of any linearity in a chosen random binary sequence. It reveals the cryptographic suitability of the generated sequence w.r.t any correlation attack. A comparison of the nonlinearity of two Boolean sequences generated from two different random sources is presented.
Topicality. Reliable random number generation is one of the key requirements for modern cryptographic systems and cybersecurity applications. Traditional pseudo-random number generators are based on deterministic algorithms and may exhibit limited entropy and predictability, which can negatively affect information security. The subject of study in the article is methods of quantum random number generation and approaches to evaluating the quality of generated random sequences. The purpose of the article is to analyze modern methods of quantum random number generation, develop a software tool for obtaining quantum random numbers based on the ANU Quantum Random Number Generator service, perform statistical testing of the generated sequences, and analyze the obtained results. The following results were obtained. Modern quantum random number generation systems were analyzed and compared. A software tool was implemented in Python for automatic retrieval of quantum random numbers through the ANU QRNG API. The generated binary sequences were evaluated using Frequency Test and Block Frequency Test from the NIST SP 800-22 statistical test suite. The obtained p-values were 0.977181 and 0.200659 respectively, confirming successful completion of both tests. Additionally, visual analysis of the generated sequences revealed no noticeable patterns or repetitive structures. Conclusion. The obtained results confirm the high quality of quantum random sequences generated using ANU QRNG and demonstrate the applicability of the developed software tool for cryptographic and cybersecurity applications requiring high-quality randomness.
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.
The development of information society, which led to an impressive increase of the volume of information, mostly economic, which was circulated in computer networks, accelerated the development and especially the use of modern cryptography tools. The role of modern cryptography is to assure by specific mathematical means, both theoretically and practically, the four basic characteristics of information: confidentiality, integrity, authenticity, and nonrepudiation. This paper presents a series of results obtained within an ample project, whose purpose is to integrate devices based on quantum properties, in order to gradually replace the current classical equipment which becomes vulnerable, and also to develop software applications. The results were obtained as a result of performance and testing of an experimental model which implements an architecture of client-server type, and which integrates a quantum random number generator in the mechanism of obtaining the cryptographic key.
Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.