The development of technologies leads to the need of revising the methods used to obtain cryptographic keys. The randomness parameters of sequences generated by physical random sequence generators are affected by the physical parameters of the recording equipment and the environment. The requirements for the randomness of the sequence, when passing the binary test, are obtained. It is shown that as the sequence length increases, the requirements for possible deviations from the equiprobable distribution of 0 and 1 increase. The randomness stability of the sequences generated by the generator based on the study of photons is estimated. The oscillator under study consists of an LED and a compact silicon photomultiplier designed to detect low-power light radiation. Possible physical processes leading to the deterioration of the randomness of sequences are shown. The possibility of using a generator of random numerical sequences based on a small-sized silicon photomultiplier for cryptographic purposes is estimated.
The development of technologies leads to the need of revising the methods used to obtain cryptographic keys. The randomness parameters of sequences generated by physical random sequence generators are affected by the physical parameters of the recording equipment and the environment. The requirements for the randomness of the sequence, when passing the binary test, are obtained. It is shown that as the sequence length increases, the requirements for possible deviations from the equiprobable distribution of 0 and 1 increase. The randomness stability of the sequences generated by the generator based on the study of photons is estimated. The oscillator under study consists of an LED and a compact silicon photomultiplier designed to detect low-power light radiation. Possible physical processes leading to the deterioration of the randomness of sequences are shown. The possibility of using a generator of random numerical sequences based on a small-sized silicon photomultiplier for cryptographic purposes is estimated.
Methods and means for analysing, assessing and comparing properties of random sequences and random numbers are considered in the work. The article also discusses such aspects as mathematical modeling of random processes, statistical methods for estimating distribution parameters, comparative analysis of the properties of random variables. To date, random sequences (RS) and random numbers (RN), produced by physically real (PT RNG) and non-physically real (NPT RNG) generators, are widely used in practice, they essentially legislate key generation mechanisms in cryptographic systems. Depending on the cryptographic transformations, they are used to generate long-term keys and session keys of symmetric cryptographic transformations, long-term asymmetric key pairs and session key pairs, general parameters of cryptographic transformations and cryptographic protocols, specific one-time values (nonces), challenges (challenges), blinding and masking values, etc. Among the set of requirements for such generators is the provision of the maximum possible value of the initial entropy in a number of, and possibly most, cryptographic applications. The analysis of international and national legal documents regarding the requirements for PT RNG and NPT RNG sources and, accordingly, generators, carried out in the work showed that they, taking into account the significant challenges associated with expanding the possibilities of cryptanalysis based on application, in addition to classical, quantum and side channel attacks should be significantly improved and evaluated using complex methods using a system of unconditional criteria. The purpose of this article is to substantiate, develop and confirm experimentally the correct application of RS and RN generation algorithms based on PTRNG and NPTRNG, including in the application of classical and quantum microelectronics, as well as the development of recommendations for their use for generating keys and parameters for quantum stable methods and standards of cryptographic transformations.
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.
Nowadays information technologies are widespread and used in every computer-based system, hence information security tasks are quite important and their successful solution is required in business process. Cryptographic means are used in different applications, especially in cases when data confidentiality should be provided; although they can be utilized to maintain data availability and integrity, user's anonymity, author's non-repudiation and so on. Many information security tools use random numbers, but unfortunately, quality of output random numbers and speed of their generation do not satisfy modern requirements. The rate of production-run random number generators is limited by the physical processes used. One of the reasons of low random numbers generating rate is application of binary events. Many generators use analog events, e.g. noise in electronic devices, converted to binary numbers utilizing the threshold value or quantum discrete events, e.g. photon passing through the polarizer. The main idea of this work is that one can increase random number generator's rate using the non-binary sequences, e.g. non-binary quantum processes.
In our modern society random number generators are widely circulated. Numerical simulations, the gambling industry, authentication tasks like the generation of pin/tan numbers all the way to cryptographic environments are applications for random number generators. Today algorithmic or physical deterministic approaches are used, which cannot produce true random numbers. The indeterminacy and unpredictability in quantum mechanics however provide the possibility to generate true random numbers. In this work a random number generator is developed using quantum mechanical e ects. The random source is based on the light emission of a light emitting diode. The emitted photons are detected by a photomultiplier tube. The random bit values are extracted by counting the number of photons detected in a certain time interval. Both the photon emission process of the LED, the detection process and the electronical pulse recognition circuit are considered in developing the theoretical model. It turns out that the main contributions to the nal detected photon number distribution come from a coulomb blockade e ect of electrons inside the semiconductor junction of the LED, the optical attenuation of the photons and the dead time of the detection circuitry. Remarkably the e ect of the dead time modi es the photon statistics in such a way that equally distributed random bit sequences can be generated even at low mean photon numbers. In case of a Poissonian statistics this would require an in nitely high photon number. In a compact experimental setup this theoretical model can be veri ed. Random bit rates of up to 50 MBit/s can be generated. A nal analysis of bit sequences with statistical methods do not reveal any regularities in these sequences. In future this random number generator will be integrated into the quantum key distribution setup of the LMUMunich. An increase in the generation rate by scaling the setup would allow to adopt this system in modern cryptographic applications with rates of up to 1 GBit/s.
One key requirement for many cryptograhic schemes is the generation of random numbers.Sequences of random numbers are used at several stages of a standard cryptographic protocol.One simple example is a Vernam cipher, where a string of random numbers is added to message string to generate encrypted code.C = M ⊕ K.It has been mathematically shown that this simple scheme is unbreakable if key K is as long as M and is used only once.The security of a cryptosystem shall not be based on keeping the algorithm secret but solely on keeping the key secret.The security of a random number generator (RNG) is related to the difficulty of predicting its future sequence values from past values.The quality and unpredictability of secret data is critical to securing communication by modern cryptographic techniques.The generation of such data for cryptographic purposes typically requires an unpredictable physical source of random data.We studied a chaotic circuit which consisted of an inductor, capacitance, diode and thus used for the BB84 protocol.We have studied both pseudo random and true random number generators and evaluated them through various tests like frequency, correlation, NIST etc.
This work is dedicated to the construction and evaluation of random number generators used in cryptography. The critical element on which the security of information is based is the cryptographic key (usually a binary sequence). In order to be resistant to brute force attacks it is necessary that it be made up of random variables with a certain degree of randomness and independence. Formally, this comes back to generate the cryptographic key through the systems which ensures a certain minimum level of entropy. The observer has access to a sample, of a certain size, and based on it he will estimate the minimum value of the entropy, in the situations in which the variables resulting from the measurement process are independent. In the situation where these variables are not independent, complex mathematical procedures also allow estimation of the minimum entropy. This article is a review of how mathematical entropy can be estimated and evaluated, of the construction mode (from technologies based on analogue procedures: thermal noise in a transistor to modern procedures: quantum devices), as well as to evaluate the security of binary sequence generators used for generating cryptographic keys or critical security parameters related to new technologies based on quantum principles. The techniques and methods used to generate binary random values as well as the methods of statistical and informational validation (Shannon entropy) are exemplified in this paper.