Random number generators are essential components of many cryptographic systems. Inappropriate random number generators may weaken the security properties of the system considerably. This paper considers evaluation criteria for true (physical) random number generators. General objectives are formulated and possible criteria and measures are discussed which shall ensure these goals. Central parts of the mathematical-technical reference of the German evaluation guidance document AIS 31 ([],[]) are cited and rationale is given.
Random number generators are essential components of many cryptographic systems. Inappropriate random number generators may weaken the security properties of the system considerably. This paper considers evaluation criteria for true (physical) random number generators. General objectives are formulated and possible criteria and measures are discussed which shall ensure these goals. Central parts of the mathematical-technical reference of the German evaluation guidance document AIS 31 ([],[]) are cited and rationale is given.
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.
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 chapter provides a concise yet thorough examination of Quantum True Random Number Generators (QTRNGs), focusing on their critical role in generating truly unpredictable and irretrievable random numbers, essential for various security algorithms. The study delves into the foundational principles of QTRNGs, highlighting the physical processes that enable genuine randomness. It also evaluates the security attributes of QTRNGs, discussing potential vulnerabilities and defenses against manipulation and attacks. The chapter concludes by assessing the practical applications and limitations of QTRNGs, offering insights into their current and future relevance in enhancing security in computational systems.
Cryptography is the study and practice of secure communication with digital data and focuses on confidentiality, integrity, and authentication. Random number generators (RNGs) generate random numbers to enhance security. Even though the cryptographic algorithms are public and their strength depends on the keys, cryptoanalysis of encrypted ciphers can significantly contribute to the unveiling of the cipher’s key. Therefore, to ensure high data security over a network, researchers need to improve the randomness of keys as they develop cryptosystems. Quantum particles have a leading edge in advancing RNG technology as they can provide true randomness, unlike pseudo-random numbers generators (PRNGs). In order to increase the level of the security of cryptographic systems based on random numbers, this survey focuses on three objectives: Cryptosystems with related cryptographic attacks, RNG-based cryptosystems, and the design of quantum random number generators (QRNGs). This survey aims to provide researchers with information about the importance of RNG-based ciphers and various research techniques for QRNGs that can incorporate quantum-based true randomness in cryptosystems.
Random number generators are indispensable for a multi- tude of tasks; from electronic games to secure communications. Most gen- erators have been made either in software or determinist hardwired de- vices such as the Linear-Feedback-Shift-Registers; while gaining in costs or speed, the “random” sequences generated are actually deterministic, obeying clear generating algorithms, despite all randomness appearance of their outputs. From the other side, Nature presents a multitude of sources of true randomness that can be explored. Commercial random generators exist based on physical processes as the source of randomness. Difficulties are always present to extract Nature’s randomness. This paper presents guidelines for construction of a fast (telecommunication speed) Physical Random Number Generator. It discusses the fundamental physical ele- ments involved, technicalities of signal recording and its limitations, and the final bit extraction. The need for randomness tests is emphasized and the impossibility of guaranteeing true randomness of a finite sequence is discussed.
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.