The results of the analysis of electronic signatures with one-time keys for the post-quantum period are given. The requirements are justified and an improved mechanism of electronic signature is presented for the criteria of spatial complexity of keys and signatures. A model of the violator and threats is proposed. The main types of attacks on the electronic signature with one-time keys are substantiated. The main relations of the post-quantum cryptanalysis complexity estimation are presented. The main recommendations and the main spheres of using the electronic signature in the post-quantum period are given.
The results of the analysis of electronic signatures with one-time keys for the post-quantum period are given. The requirements are justified and an improved mechanism of electronic signature is presented for the criteria of spatial complexity of keys and signatures. A model of the violator and threats is proposed. The main types of attacks on the electronic signature with one-time keys are substantiated. The main relations of the post-quantum cryptanalysis complexity estimation are presented. The main recommendations and the main spheres of using the electronic signature in the post-quantum period are given.
The results of the analysis of electronic signatures with one-time keys for the post-quantum period are given. The requirements are justified and an improved mechanism of electronic signature is presented for the criteria of spatial complexity of keys and signatures. A model of the violator and threats is proposed. The main types of attacks on the electronic signature with one-time keys are substantiated. The main relations of the post-quantum cryptanalysis complexity estimation are presented. The main recommendations and the main spheres of using the electronic signature in the post-quantum period are given.
The necessity of developing new electronic signature mechanisms, which will be relevant and can be applied in the post-quantum period, is grounded. The main properties of existing mechanisms, their advantages and disadvantages are given. An improved POTS mechanism is proposed. The essence is described, research of properties by criteria of complexity - cryptographic stability is presented, advantages and disadvantages and conditions and possibilities of its use in various applications of the post-quantum period are determined.
Necessity of developing the new electronic signature mechanisms, which will be relevant and can be applied in the post-quantum period, is grounded. The main properties of existing mechanisms, their advantages and disadvantages are given. An improved POTS mechanism is proposed. The essence is described, research of properties by criteria of complexity - cryptographic stability is presented, advantages and disadvantages, and conditions and possibilities of its use in various applications of the post-quantum period are determined.
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.
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.
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.