The mathematical model of a binary discrete source is proposed, which is close to the practical conditions for the operation of cryptographic key generation devices. The model takes into account the non-stationarity of such devices, as well as the presence of statistical dependencies between their output bits. Within the framework of the model, an achievable and easily computable lower estimate of the practical secrecy of the key is obtained. It is shown that with certain parameters of the model, the assessment allows us to draw meaningful conclusions about the cryptographic quality of keys, while other well-known estimates do not cope with this.
The mathematical model of a binary discrete source is proposed, which is close to the practical conditions for the operation of cryptographic key generation devices. The model takes into account the non-stationarity of such devices, as well as the presence of statistical dependencies between their output bits. Within the framework of the model, an achievable and easily computable lower estimate of the practical secrecy of the key is obtained. It is shown that with certain parameters of the model, the assessment allows us to draw meaningful conclusions about the cryptographic quality of keys, while other well-known estimates do not cope with this.
Randomness plays a central role in computer science, in particular cryptography. Almost all cryptographic primitives depend crucially on randomness because randomness and unpredictability in secret keys provides the means for security. Usually one assumes that perfect randomness, a sequence of independently and uniformly distributed bits, are accessible to algorithms. This is a strong assumption. Physical sources of randomness are neither uniformly random, nor produce necessarily independent bits. Therefore, the aim of this thesis is to start from a realistic model of randomness, investigate notions of secrecy and their randomness requirements and finally find practical methods for generation of randomness that matches the requirements of cryptographic primitives. We consider a model of random source where the source output follows one distribution from a set of possible distributions, each with the property that the maximum probability of symbols is bounded and can not be arbitrarily close to 1. This model does not assume independence or uniformity of the output symbols, and is considered to be a realistic model of randomness. From this point, the thesis can be divided into two main parts: In the first part, considering various notions of information theoretic secrecy, a fundamental problem is to find the properties of randomness needed to achieve security in these notions. Traditional cryptographic protocols simply assume perfect randomness and build on this assumption. We explore the results that show secrecy can not be based on imperfect randomness that is not uniform or independent. Thus a line of work attempts to relax notions of secrecy in such a way that they can be constructed with non-perfect sources, and possibly require smaller key sizes. Yet they should match real life applications. An important work in this context is entropic security where the key size could be smaller than the message depending on message distribution. Inspired by this, we propose two relaxed notions of secrecy that are motivated by practical applications. In the first notion, motivated by an application in biometrics authentication, we propose guessing secrecy where the probability of guessing the message for a computational unbounded adversary with the best strategy remains the same when a ciphertext is given or when it is not. We compare the randomness requirements of guessing secrecy with stronger notions and show that in some cases such as key length, the requirements are the same. For key distribution however, we found a family of distributions that provide guessing secrecy but not perfect secrecy. In the second notion, we investigate randomness requirements of multiple message encryption. Considering a natural extension of secrecy definition to multiple messages, we show that independent keys are needed to encrypt each message. We then propose a relaxed notion in which the security of last message is more important than past messages, although the leakage of past messages is bounded using entropic security. By this assumption, we achieve smaller key length compared to indistinguishability, and comparable to key length for entropic security. This notion has applications such as location privacy. In the second part of the thesis, since secrecy crucially depends on perfect randomness, we investigate how perfect randomness can be practically generated, specifically from human game-play. Unlike many random number generators that assume independent or uniform random bits in the random source, we base our work on the realistic model of randomness. Our main observation is that human game-play has an element of randomness coming from the errors in their game-play which is the main entertaining factor of the game. We also observed that this game-play can distinguish among a group of people if the right features are collected from the game-play. We incrementally changed our game design until the distinguishability among a small population is maximized, and then run the experiments required to show the viability of this approach over a larger population. This approach can also provide a hard to delegate authentication property where a human could not emulate the behavior of another human even given statistical information about their game-play.
Often the key bits generated by physical random number generators are not realizations of jointly independent uniformly distributed random variables, which gives rise to the concept of “practical key secrecy”. For some physical random number generators this deviation is caused by the discreteness of time measured by electronic components. In this paper, for a physical random number generator model based on the interval scheme, we obtain bounds on the practical secrecy of keys taking into account the impact of measurement time discretization.
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.
Introduction/purpose: The problem of efficient distribution of cryptographic keys in communication systems has existed since its first days and is especially emphasized by the emergence of mass communication systems. Defining and implementing efficient protocols for symmetric cryptographic keys establishment in such circumstances is of great importance in raising information security in cyberspace. Methods: Using the methods of Information Theory and Secure Multiparty Computation, protocols for direct establishment of cryptographic keys between communication parties have been defined. Results: The paper defines two new approaches to the problem of establishing cryptographic keys. The novelty in the protocol defined in the security model based on information theory is based on the source of common randomness, which in this case is the EEG signal of each subject participating in the communication system. Experimental results show that the amount of information leaking to the attacker is close to zero. A novelty in the second case, which provides security with keys at the level of computer security by applying Secure Multiparty Computation, is in the new application field, namely generation and distribution of symmetric cryptographic keys. It is characteristic of both approaches that within the framework of formal theories, it is possible to draw conclusions about their security characteristics in a formal way. Conclusions: The paper describes two new approaches for establishing cryptographic keys in symmetric cryptographic systems with experimental results. The significance of the proposed solutions lies in the fact that they enable the establishment of secure communication between communication parties from end to end, avoiding the influence of a trusted third party. In that way, the achieved communication level security significantly increases in relation to classical cryptographic systems.
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.