Scientific and methodological bases of analysis, evaluation and results of comparison of existing and promising (post-quantum) asymmetric cryptographic primitives of electronic signature, protocols of asymmetric encryption and key encapsulation protocols
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.
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.
At present and in the future, mathematical methods, mechanisms and algorithms of standardized asymmetric cryptotransformations such as electronic signature (ES) are and will be used for information cryptographic protection. Electronic signature is the main and essential component of cybersecurity, in terms of providing quality information security services such as integrity, irresistibility and authenticity of information and data processed. However, there are well-founded suspicions that in the post-quantum period the existing ES standards will be broken and compromised using classical and quantum cryptanalytic systems with appropriate mathematical, software and hardware-software. An analysis was performed, which confirms that quantum computers have already been developed, manufactured and used. It is believed that the actual state of development and use of powerful quantum computers and their mathematical and software is obviously strictly confidential and secure, and only publicly known data on quantum computers and their applications in cryptology are disclosed. A preliminary analysis has been carried out showing that in Ukraine there is an understanding of the existence of threats to cybersecurity and information security in the case of using available standardized ES in the transition and post-quantum periods. Currently, development and adoption of post-quantum ES standards is also one of the main issues in ensuring the necessary levels of security in the transition and post-quantum periods. The objective of this article is to substantiate, compare alternatives and develop proposals for the selection and standardization of post-quantum ES standards at the international and national levels, taking into account the results of the 2nd and 3rd rounds of the NIST US competition and national researches.
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.
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.
Information security is a fundamental and urgent issue in the digital transformation era. Cryptographic techniques and digital signatures have been applied to protect and authenticate relevant information. However, with the advent of quantum computers and quantum algorithms, classical cryptographic techniques have been in danger of collapsing because quantum computers can solve complex problems in polynomial time. Stemming from that risk, researchers worldwide have stepped up research on post-quantum algorithms to resist attack by quantum computers. In this review paper, we survey studies in recent years on post-quantum cryptography (PQC) and provide statistics on the number and content of publications, including a literature overview, detailed explanations of the most common methods so far, current implementation status, implementation comparisons, and discussion on future work. These studies focused on essential public cryptography techniques and digital signature schemes, and the US National Institute of Standards and Technology (NIST) launched a competition to select the best candidate for the expected standard. Recent studies have practically implemented the public key encryption/key encapsulation mechanism (PKE/KEM) and digital signature schemes on different hardware platforms and applied various optimization measures based on other criteria. Along with the increasing number of scientific publications, the recent trend of PQC research is increasingly evident and is the general trend in the cryptography industry. The movement opens up a promising avenue for researchers in public key cryptography and digital signatures, especially on algorithms selected by NIST.
Virtually all asymmetric cryptographic schemes currently in use are threatened by the potential development of powerful quantum computers. Although there is currently no definite answer and it is very unclear when or even if CRQC will ever be built and the gap between modern quantum computers and the envisioned CRQC is huge, the risk of creating CRQC means that currently deployed public key cryptography must be replaced by quantum-resistant ones alternatives. For example, information encrypted using modern public key cryptography can be recorded by cryptanalysts and then attacked if a QRQC can be created. The potential harm that CRQC could cause is the basis of the motivation to seek countermeasures, even though we have uncertainties about when and if these computers can be built. Deployed systems that use public key cryptography can also take years to update. Post-quantum cryptography is one way to combat quantum computer threats. Its security is based on the complexity of mathematical problems that are currently considered unsolvable efficiently – even with the help of quantum computers. Post-quantum cryptography deals with the development and research of asymmetric cryptosystems, which, according to current knowledge, cannot be broken even by powerful quantum computers. These methods are based on mathematical problems for the solution of which neither efficient classical algorithms nor efficient quantum algorithms are known today. Various approaches to the implementation of post-quantum cryptography are used in modern research, including: code-based cryptography, lattice-based cryptography, hashing-based cryptography, isogeny-based cryptography, and multidimensional cryptography. The purpose of this work is to review the computational model of quantum computers; quantum algorithms, which have the greatest impact on modern cryptography; the risk of creating cryptographically relevant quantum computers (CRQC); security of symmetric cryptography and public key cryptography in the presence of CRQC; NIST PQC standardization efforts; transition to quantum-resistant public-key cryptography; relevance, views and current state of development of quantum-resistant cryptography in the European Union. It also highlights the progress of the most important effort in the field: NIST's standardization of post-quantum cryptography.