The asymmetric encryption and keys encapsulation in polynomial rings (algebraic lattices) built algorithms are presented and considered, the essence of used asymmetric encryption transformations and key encapsulation protocols are analyzed. Encryption and encapsulation mechanisms with different sets of parameters that determine stability are considered.
The asymmetric encryption and keys encapsulation in polynomial rings (algebraic lattices) built algorithms are presented and considered, the essence of used asymmetric encryption transformations and key encapsulation protocols are analyzed. Encryption and encapsulation mechanisms with different sets of parameters that determine stability are considered.
Key encapsulation mechanisms play a main role in post-quantum cryptography, particularly in constructing encryption schemes. Understanding the design principles behind them is crucial not only for ensuring the efficient operation of the cryptographic protocols that employ them, but also for evaluating the security guarantees that these key encapsulation mechanisms provide. In this work, three lattice-based key encapsulation mechanism design paradigms are compared, and it is proved that asymmetric key consensus-based and encryption-based key encapsulation mechanisms are equivalent and that it is possible to construct a transformation from one approach to another.
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
Recent developments in quantum computing have shed light on the shortcomings of the conventional public cryptosystem. Even while Shor's algorithm cannot yet be implemented on quantum computers, it indicates that asymmetric key encryption will not be practicable or secure in the near future. The National Institute of Standards and Technology (NIST) has started looking for a post-quantum encryption algorithm that is resistant to the development of future quantum computers as a response to this security concern. The current focus is on standardizing asymmetric cryptography that should be impenetrable by a quantum computer. This has become increasingly important in recent years. Currently, the process of standardizing asymmetric cryptography is coming very close to being finished. This study evaluated the performance of two post-quantum cryptography (PQC) algorithms, both of which were selected as NIST fourth-round finalists. The research assessed the key generation, encapsulation, and decapsulation operations, providing insights into their efficiency and suitability for real-world applications. Further research and standardization efforts are required to enable secure and efficient post-quantum encryption. When selecting appropriate post-quantum encryption algorithms for specific applications, factors such as security levels, performance requirements, key sizes, and platform compatibility should be taken into account. This paper provides helpful insight for post-quantum cryptography researchers and practitioners, assisting in the decision-making process for selecting appropriate algorithms to protect confidential data in the age of quantum computing.
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 analyzes the current state and prospects of the standardization of post-quantum algorithms for asymmetric cryptographic transformations at the national and international levels. The main reasons for the transition to post-quantum cryptography are discussed, particularly the potential threats posed by quantum computers to existing cryptographic algorithms (RSA, ECC, etc.). An overview of the NIST competition for selecting standards for post-quantum key encapsulation mechanisms (KEM) and electronic signatures is provided, with detailed descriptions of the algorithms chosen for standardization (CRYSTALS-Kyber, CRYSTALS-Dilithium, FALCON, SPHINCS+, and HQC). Additionally, the article examines the role of ISO/IEC, ETSI, and IETF in developing international standards and recommendations. Special attention is given to Ukrainian national standards and initiatives, particularly the algorithms “Skelya” and “Vershyna,” their features, and their prospects for integration into international standards. The article emphasizes the importance and complexity of transitioning to quantum-resistant algorithms and outlines further steps for the successful implementation of post-quantum cryptography. Keywords: post-quantum cryptography, key encapsulation mechanisms, electronic signatures, standardization.