Substantiation and proposals for the selection, improvement and standardization of the post-quantum electronic signature mechanism at the national and international levels
І.Д. Горбенко, О.Г. Качко, Олександр Володимирович Потій, Yu.I. Gorbenko, Volodymyr Ponomar, Maryna V. Yesina, І.В. Стельник, Serhii Kandii, K.O. Kuznetsova
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.
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.
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.
An important feature of the post-quantum period in cryptography is the significant uncertainty about the input data for cryptanalysis and counteracting the capabilities of quantum computers, their mathematical and software, and the application of quantum cryptanalysis to existing cryptoprotocols and cryptotransformations. Mathematical electronic signature (ES) methods have been selected as the main methods in the work, which have undergone significant analysis and substantiation in the process of extensive research by cryptologists and mathematicians at the highest level. The article analyzes the existing electronic signature algorithms based on the lattices of stage 2 of the NIST competition. The possibility of using the post-quantum electronic signature mechanism based on algebraic lattices as the post-quantum national electronic signature standard is considered. It is proposed to use the post-quantum Сrystals-Dilithium algorithm as such electronic signature algorithm. The article considers this algorithm and substantiates the possibility of its application. The algorithm parameters and rules for their construction are considered. The differences and features of safe implementation of the algorithm in comparison with stage 1 are analyzed. The analysis is conducted and it is concluded that the Crystals-Dilithium algorithm can be taken as one of the candidates for the development of a national electronic signature standard using cryptographic algorithms, standardized in Ukraine, such as the hashing function described in DSTU 7564:2014. According to the authors of the article, the post-quantum period national standard of Ukraine should include at least 3 algorithms based on different types of mathematical transformations, which are recognized by the world cryptographic community as those that can provide the necessary level of stability in the conditions of quantum cryptanalysis.
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.
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.
The paper considers post-quantum projects of the Falcon and Dilithium electronic signature standards (ES), which are finalists of the NIST USA competition. The mathematical apparatus of algebraic lattices and appropriate methods are used in their construction. In further study and comparison of these post-quantum ES draft standards, both from a theoretical and practical standpoint, it is fundamental to substantiate the requirements for parameters and keys and in general to calculate the main indicators according to the accepted conditional and unconditional criteria. In such studies, it is important to determine the sufficiency of ensuring the guarantee of their security against classical, quantum, special and error-based attacks. This can be ensured, inter alia, through a reasonable choice of the sizes of common parameters and keys, and their practical construction in accordance with the adopted security model. However, when choosing the sizes of common parameters and keys, a significant contradiction arises between the properties of the draft of the Falcon and Dilithium ES standards, So increasing the size of the general parameters and keys leads to an increase in the complexity of transformations, and vice versa. The purpose of this article consists in analysis of problematic issues of choosing the size of parameter and keys for post-quantum ES projects based on mathematical methods of Falcon and Dilithium, and features of their implementation, including implementation according to the adopted security model. Comparative analysis of the stability and complexity of the Falcon and Dilithium ES draft standards depending on the size of the parameters and keys, including for 6 and 7 security levels. Development of proposals for decisions on the adoption of national post-quantum ES standards based on the mathematical methods Falcon and Dilithium. Determining the influence of unconditional, conditional and pragmatic criteria on the advantages when deciding on the ES standardization based on Falcon and Dilithium mathematical methods, including taking into account the availability of patents and the need to obtain licenses, etc.