In this paper, the essence is considered and security models of asymmetric post-quantum cryptographic primitives of different types are investigated. The basis taken security models that are recommended by NIST USA in the requirements of the PQC competition for candidates for post-quantum cryptographic primitives. Such algorithms include asymmetric cryptographic transformations such as asymmetric encryption, digital signature, and key encapsulation mechanism. The following security models are recommended, which are related to: the asymmetric encryption — IND-CCA2 (IND-CPA, IND-CCA); the digital signature — EUF-CMA (and its variations); the key encapsulation mechanisms — СK-model. In this paper, the basic essence of such security models is considered. The use of security models in research of cryptographic primitives is relatively new. A generalization of each of these models and a definition of the necessity and conditions, and the consequences of their application are required. Such models take into account the application environment in which an unauthenticated-links adversarial model and authenticated-links adversarial model can operate. The paper considers the concept of indistinguishability and security model of post-quantum asymmetric ciphers on its basis. The property of indistinguishability under chosen plaintext attack is determined. The concept of semantic security is considered. The types of most common attacks based on indistinguishability are given. Existing versions of the EUF-CMA security model — SUF-CMA, etc. are considered. Definitions of «forward security, forward secrecy» and «perfect forward secrecy (PFS)» are given. In addition, the paper considers the peculiarities of the application regarding to perspective asymmetric transformations of the «game theory». The definition of concept «game theory» is given
In this paper, the essence is considered and security models of asymmetric post-quantum cryptographic primitives of different types are investigated. The basis taken security models that are recommended by NIST USA in the requirements of the PQC competition for candidates for post-quantum cryptographic primitives. Such algorithms include asymmetric cryptographic transformations such as asymmetric encryption, digital signature, and key encapsulation mechanism. The following security models are recommended, which are related to: the asymmetric encryption — IND-CCA2 (IND-CPA, IND-CCA); the digital signature — EUF-CMA (and its variations); the key encapsulation mechanisms — СK-model. In this paper, the basic essence of such security models is considered. The use of security models in research of cryptographic primitives is relatively new. A generalization of each of these models and a definition of the necessity and conditions, and the consequences of their application are required. Such models take into account the application environment in which an unauthenticated-links adversarial model and authenticated-links adversarial model can operate. The paper considers the concept of indistinguishability and security model of post-quantum asymmetric ciphers on its basis. The property of indistinguishability under chosen plaintext attack is determined. The concept of semantic security is considered. The types of most common attacks based on indistinguishability are given. Existing versions of the EUF-CMA security model — SUF-CMA, etc. are considered. Definitions of «forward security, forward secrecy» and «perfect forward secrecy (PFS)» are given. In addition, the paper considers the peculiarities of the application regarding to perspective asymmetric transformations of the «game theory». The definition of concept «game theory» is given
The paper presents the results of substantiation and development of proposals for building a threat model for asymmetric cryptotransformations such as a promising electronic signature (ES), which can be used in the post-quantum period. The generalized models of threats concerning perspective ES are stated in detail and their estimation is given. Threat models for promising ES using classical and quantum cryptanalysis methods and tools, threat models for synthesis and application of ES in general, as well as threat models for synthesis and application of ES in the post-quantum period are proposed. Proposals are formulated for a list of threats for which protection should be provided. The list of possible security threats to existing and future ES is formed from the number of threats available in IT-Grundschutz Catalogs, taking into account hardware, software and hardware-software resources, data processing technologies and cryptographic protection mechanisms in the use of ES, including requirements and conditions of synthesis of promising ES and application of ES in the post-quantum period. The concepts of EUF-CMA and SUF-CMA security are considered. Algorithms of work of each of these schemes are given. The concept of a comprehensive security model is introduced and its components are presented. The model of the violator and its essence are considered. The main threats (attacks) are given using quantum mathematical methods that can be implemented on a quantum computer (of course, if it is built and available for use). Attacks (threats) against a promising ES are presented and considered. The analysis of signature schemes for compliance with the required security models is performed. The terms "forward secrecy" and "perfect forward secrecy" are introduced and used. An analysis of signature schemes that are EUF-CMA and SUF-CMA secure is performed. Signature schemes, that are key-dependent, with evolving keys, are considered in terms of compliance with the EUF-CMA or SUF-CMA security model. The stateless signature algorithm is also considered. Algorithms of operation of such signature schemes are given.
Currently, world civilization is taking significant steps in science and practice related to quantum calculations. Significant steps are being taken to achieve the competitive advantage of countries in the field of quantum information science and the practice of introducing quantum technologies. Scientific and practical research is first aimed at reducing the risks related to quantum computers on cybersecurity, economic and national security. Although the full range of quantum computers is still unknown, it is obvious that further technological and scientific leadership of states will at least partially depend on the country's ability to maintain a competitive advantage in quantum computing and quantum information science. However, along with the potential advantages, quantum calculations are likely to cause significant risks about economic and national security. Specific actions are determined that technologically developed states that begin a long-term process of transferring vulnerable computer systems to quantum-resistant cryptography. An important problem in cryptology is to analyze ways of reducing risks for vulnerable cryptographic systems and the state of their development, adoption and implementation at the international and national levels of post-quantum standards of asymmetric cryptotransformations of electronic signatures (ES), asymmetric ciphers (AC) and key encapsulation protocols (KEP). Therefore, the processes of reducing risks for vulnerable existing standardized cryptographic systems and determining the directions of development of mathematical methods and the study of the prospects for their application in the creation of standardized AC, KEP and ES are significantly significant. They are reduced to justification and definition of mathematical methods and mechanisms that will create promising (post-quantum) standardized AC, KEP and ES. The course of analysis, evaluation and results of comparison of existing and post-quantum asymmetric cryptotransformations of AC, KEP and ES, and standardization at the international and national levels, including for transitional and post-quantum periods, are the main objective of this article.
The article takes a verifier of equivalence of the quality of indistinguishability (uncertainty) of the semantic security for the cryptosystems defense against of attacker's cryptanalyses based on matched (selected) open text. The issues of analysis and research of security models of post-quantum cryptoalgorithms in relation to cryptoprimitives of all types, the definition of criteria for assessing their compliance with different security models (according to different types of crypto-transformations) are relevant and of practical importance. The indistinguishability (uncertainty) of encrypted text is an important property of the security of many encryption schemes. The indistinguishability (uncertainty) property when attacking on the basis of matched (selected) plain text is considered a basic requirement for the majority of reliably protected public-key cryptosystems. Some schemes also provide an indistinguishability for attack based on selected (selected) encrypted text and attack based on adaptively picked (selected) encrypted text. The indistinguishability (uncertainty) of an attack on the basis of a selected (selected) open text is equivalent to the properties of semantic security. If the cryptosystem has the property of indistinguishability, the attacker will not be able to distinguish between pairs of encrypted texts based on the message that they encrypt. In the case of non-differentiation (uncertainty) of ciphertext protects all known cryptosystems from the intruder which: is a probabilistic Turing machine of polynomial time; has all algorithms; has full access to communications. Using the property of the indeterminacy (uncertainty) of the encrypted text at the present time, it is guaranteed to protect all known symmetric and asymmetric cryptosystems from the classical or quantum cryptanalysis of the intruder. Here are a review of mostly attacks on the encryption security namely an attack based on adaptively matched (selected) ciphertexts, an attack based on adaptively matched (selected) open texts, an attack based on both of this types of texts, an attack based on matched (selected) ciphertexts, an attack based on matched (selected) open texts and a recognition attacks (recognizability).
Due to the development of technologies for quantum computing and the introduction of quantum computer, there is a threat to the current state of protection of cryptographic systems with a public key. With an advent of quantum computer that would have the volume of register required for the methods of quantum cryptanalysis, the stability of existing crypto algorithms will significantly degrade. This necessitates the creation of algorithms resistant to the methods of quantum cryptanalysis. The European project «New European Schemes for Signatures, Integrity, and Encryptions» (NESSIE) and the National Institute of Standards and Technologies (NIST) of the USA announced a start of recruiting the applicants for the contest of post-quantum algorithms whose standards are planned to be adopted over 2020–2022. In order to compare, a procedure for evaluation was selected based on integral assessments of unconditional and conditional criteria. An analysis was conducted among the algorithms that fulfilled general unconditional criteria. As conditional criteria, we chose numerical characteristics of algorithms. In addition, additional unconditional criteria were put forward.A relevant task is the comparative analysis and evaluation of a possibility to use the post-quantum mechanisms, which are represented by the algorithms that already exist, depending on the conditions of applying them. At present, only the possibility of using the appropriate crypto transformations over a post-quantum period is being examined, but the analysis of advantages of one over another has not been run yet. In addition, it is necessary to evaluate the very possibility to use such algorithms taking into account those constraints that are imposed by the existing information systems.Results of present research allow us to understand current state in the development of post-quantum crypto algorithms and to predict their possible further development.This forecast is important in that the post-quantum cryptographic mechanisms represent a new stage in the development and use of cryptography. In addition, the practical value of the research consists in obtaining the evaluation for post-quantum algorithms.
Recent advances in quantum technology and the potential that practical quantum computers may become a reality in the future have led to renewed interest in developing cryptographic technologies that are secure against conventional and quantum attacks. Currently, virtually all asymmetric cryptographic schemes in use are threatened by the potential development of powerful quantum computers. Post-quantum cryptography is one of main the ways to combat this threat. Its security is based on the complexity of mathematical problems that are currently considered unsolvable efficiently, even with the help of quantum computers. The security of information systems is ensured through protection against various threats that use system vulnerabilities. Security protocols are the building blocks of secure communication. They implement security mechanisms to provide security services. Security protocols are considered abstract when analyzed, but may have additional vulnerabilities in implementation. This work contains a holistic study of security protocols. Basics of security protocols, taxonomy of attacks on security protocols and their implementation are considered, as well as various methods and models of protocol security analysis. In particular, the differences between information-theoretic and computational security, computational and symbolic models are specified. In addition, an overview of the computational security models for Authenticated Key Exchange (AKE) and Password Authentication Key Exchange (PAKE) protocols is provided. The most important security models for the AKE and PAKE protocols were also described. With the emergence of new technologies that may have different security requirements, as well as with increased opportunities for competition, there is always a need to develop new protocols. Thus, the purpose of this article is to review, classify, analyze, and research the vulnerabilities of information systems from classical, quantum, and special attacks, performed taking into account the forecast regarding the possibilities of attacks on post-quantum cryptographic transformations; studying security assessment models for existing cryptographic protocols, as well as reviewing and benchmarking security models and providing suggestions for protection against existing potential attacks.
Cryptography has evolved from ancient substitution ciphers to modern mathematical algorithms including Rivest–Shamir–Adleman (RSA), elliptic curve cryptography (ECC), and advanced encryption standard (AES) that form the core of security systems, along with the major information security objectives: confidentiality, integrity, authenticity, availability, accountability, nonrepudiation, and privacy and their practical applications in protocols such as transport layer security (TLS), Internet Protocol Security (IPsec), and Secure/Multipurpose Internet Mail Extensions (S/MIME). The security of RSA, ECC, and symmetric-key ciphers has been threatened by quantum computers that exploit Shor’s and Grover’s algorithms. In response to this quantum threat, NIST has standardized post-quantum cryptographic PQC) algorithms: ML-KEM, a lattice-based key encapsulation mechanism and ML-DSA, a lattice-based digital signature scheme. This chapter surveys the development of cryptographic systems from transposition ciphers to post-quantum cryptography, examining their mathematical foundations, operational mechanisms, and respective security properties. In addition to these, the PQC algorithms have been implemented in TLS 1.3, and a comparative analysis has been performed. The study traces the history of cryptography while understanding post-quantum standards as the necessary foundation for long-term information security in the quantum era.