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.
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.
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.
In recent decades, quantum cryptography has made its way from scientific researches to practical implementations and commercial use. The absolute advantage of using quantum methods of information protection is independence from the computing capabilities of an attacker. In addition, due to the use of unique properties of quantum methods, it becomes possible to achieve an unprecedented level of security with the possibility of detecting the violator during the operation of some protocols in online mode. However, although many questions and problems in quantum cryptography have already been solved, there are still many unresolved ones. The use of ternary pseudorandom sequences raised the question of the statistical reliability of these sequences. And although today there are a large number of different methods for evaluating the randomness of a sequence, however, they are mostly aimed at evaluating standard binary sequences. This work is devoted to the method of evaluating ternary sequences, one of the stages and an experimental study are presented.
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.
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.
Random numbers play a crucial role in cryptography since the security of cryptographic protocols relies on the assumption of the availability of uniformly distributed and unpredictable random numbers to generate secret keys, passwords, initialization vectors, nonces, salt, etc. True Random Number Generators (TRNGs) extract random numbers from physical processes (such as radioactive decay, thermal noise, and atmospheric noise) that are inherently unpredictable. However, real-world random number generators sometimes fail and produce outputs with low entropy, leading to security vulnerabilities. It is commonly observed that the TRNG outputs have statistical biases and dependencies that make them unsuitable to be directly used for cryptographic purposes. There are some standards and guidelines on generating and testing random numbers that are suitable for cryptographic applications. The National Institute of Standards and Technology (NIST) Special Publication (SP) 800-90 series provide guidelines and recommendations for generating random numbers for cryptographic applications and describes statistical randomness testing, estimating min-entropy with 10 black-box entropy estimation methods. In this thesis, we evaluate the effectiveness and limitations of the SP 800-90B methods by exploring the accuracy of these estimators using simulated random numbers with known entropy, investigating the correlation between entropy estimates, and studying the impacts of deterministic transformations on the estimators. To understand the unpredictability of the outputs, it is important to estimate their entropy accurately. The National Institute of Standards and Technology (NIST) Special Publication (SP) 800-90B specifies ten min-entropy estimators ranging from simple frequency-based estimators to more advanced approaches. Each estimator has specific assumptions, making them suitable for different types of sources. The minimum of these estimates is assumed to be the min-entropy of the TRNG. We propose a new entropy estimator (estimates min-entropy and also Shannon entropy) called index-value coincidence estimate that is suitable for outputs that might include some dependencies and we also provide some experimental results that demonstrate the effectiveness of the estimator. Additionally, TRNGs may be affected by outside conditions such as temperature, humidity, etc. Health tests are an integral part of the noise source of TRNG, defined to detect unexpected changes in the working process and dramatic changes in the amount of entropy generated by the noise source. Existing health test suites are examined, and a health test suite for cryptographic TRNGs is introduced by using random variables weight, run, runs of length 1 and overlapping templates. Some suggested parameters and experimental results are given.
Generating random bit streams is required in various applications, most notably in cyber-security, which is essential for Internet of Everything applications to enable secure communication between interconnected devices. Ensuring high-quality and robust randomness is crucial to mitigate risks associated with predictability and system compromise. True random numbers provide the highest levels of unpredictability. However, known systematic biases that can emerge from physical imperfections, environmental variations, and device aging in the processes exploited for random number generation must be carefully monitored. This article reports the implementation and characterization of an online procedure for the detection of anomalies in a true random bit stream. It is based on the NIST adaptive proportion and repetition count tests, complemented by statistical analysis relying on the Monobit and RUNS tests. The procedure is implemented in firmware through dedicated hardware accelerators processing configurable-length sequences, with automated anomaly detection triggering alerts after three consecutive threshold violations. The implementation is performed simultaneously with bit stream generation and also provides an estimate of the entropy of the source. A statistical analysis of the results from the NIST procedure to evaluate the symbols of the bit-stream as independently and identically distributed is also performed, leading to a computation of the minimum entropy of the source that cross-checks the previously mentioned estimate. The experimental validation of the approach is performed up the bit streams generated by a quantum, silicon-based entropy source.