Processes and methods for selecting system-wide parameters and analysis of resistance against third-party channel attacks for the key encapsulation mechanism DSTU 8961:2019
In recent years, there has been significant progress in the creation of quantum computers. If scalable quantum computers are implemented in the near future, this will jeopardize the security of the most widely used public key cryptosystems. The most vulnerable are public-key schemes based on factorization, discrete logarithms and elliptic curve cryptography. Currently, the main task is to develop, evaluate, study and standardize asymmetric crypto transformations at the international level, including mechanisms of key encapsulation and directional encryption, resistant to attacks by violators of the post-quantum period. An important feature of the transition and post-quantum period is the usage of new mathematical methods to opposite quantum crypto analysis. The paper considers the main attacks on the mechanisms of key encapsulation and directional encryption, as well as system-wide parameters of the DSTU 8961: 2019 standard, which affect the resistance to attacks and the complexity of transformations. Methods for generating system-wide parameters of 5 and 7 levels of stability – 512 bits of classical and 256 bits of quantum security, as well as the protection of the algorithm from attacks by third-party channels are considered. The dependence of encryption and decryption time on the level of stability is analyzed. The results of calculations of system-wide parameters for stability levels 256/128, 384/192 and 512/256 are presented, as well as recommendations for the selection of system-wide parameters depending on the environment and computing capabilities. Sets of parameters selected and recommended for use in the DSTU 8961: 2019 standard are given. Conclusions are drawn about the possibility of applying the DSTU 8961 standard in the post-quantum period.
In recent years, there has been significant progress in the creation of quantum computers. If scalable quantum computers are implemented in the near future, this will jeopardize the security of the most widely used public key cryptosystems. The most vulnerable are public-key schemes based on factorization, discrete logarithms and elliptic curve cryptography. Currently, the main task is to develop, evaluate, study and standardize asymmetric crypto transformations at the international level, including mechanisms of key encapsulation and directional encryption, resistant to attacks by violators of the post-quantum period. An important feature of the transition and post-quantum period is the usage of new mathematical methods to opposite quantum crypto analysis. The paper considers the main attacks on the mechanisms of key encapsulation and directional encryption, as well as system-wide parameters of the DSTU 8961: 2019 standard, which affect the resistance to attacks and the complexity of transformations. Methods for generating system-wide parameters of 5 and 7 levels of stability – 512 bits of classical and 256 bits of quantum security, as well as the protection of the algorithm from attacks by third-party channels are considered. The dependence of encryption and decryption time on the level of stability is analyzed. The results of calculations of system-wide parameters for stability levels 256/128, 384/192 and 512/256 are presented, as well as recommendations for the selection of system-wide parameters depending on the environment and computing capabilities. Sets of parameters selected and recommended for use in the DSTU 8961: 2019 standard are given. Conclusions are drawn about the possibility of applying the DSTU 8961 standard in the post-quantum period.
Modern cryptographic transformations require provable security against a relatively wide class of threats. Typically, such evidentiary security is achieved through formal analysis within the chosen security model. The development of quantum computers led to the emergence of new attack vectors to which classical cryptography was vulnerable. However, there are cryptographic systems that are considered resistant to quantum attacks and some of them are even standardized. The formal analysis of such systems has faced difficulties for a long time, which were associated with the impossibility of applying classical methods of proof to formal models that take into account quantum effects. However, in recent years, many new results have appeared that allow obtaining formal security proofs for quite complex cryptographic transformations, and most of the existing post-quantum asymmetric encryption and key encapsulation schemes currently have corresponding formal proofs within the quantum random oracle model, the most widespread security model for of post-quantum cryptography. DSTU 8961:2019 is the Ukrainian post-quantum standard for asymmetric encryption and key encapsulation. However, security proofs in the quantum random oracle model have not yet been published for it. As part of this work, security evidence was obtained for the design of the key encapsulation mechanism described in DSTU 8961:209. The obtained result is generalized for an arbitrary asymmetric encryption scheme, which may contain decryption errors and can be used to assess the security of not only DSTU 8961:2019, but also other similar asymmetric transformations.
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.
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.
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.
In recent years, there has been a significant amount of research related to the development of quantum computers. If such a computer were to be built, it would be able to break existing public-key cryptosystems that are currently used for many purposes. This will seriously affect the privacy and integrity of digital communications, etc. That is why special attention is currently being paid to post-quantum cryptography, the main goal of which is the development of cryptographic systems that are protected from both quantum and classical attacks, and will also be able to interact with existing communication protocols and networks. In view of the significant importance of the practical application of directional encryption algorithms, at the international and state level, special attention was paid to the implementation of the proposed requirements for key encapsulation protocols. Key-establishment algorithms (KEA) form a common secret – the key for a symmetric encryption algorithm. The paper considers two KEA algorithms that use algebraic lattices: one of the finalists of the 3rd round Crystals-Kyber and the Skelya algorithm (DSTU 8961-2019). The Kyber algorithm first performs asymmetric encryption of a 32-byte message, and then generates a shared secret. The Skelya algorithm performs the same actions, but for asymmetric encryption, it uses messages of any length that do not exceed the maximum possible. That is why the last algorithm can be used not only as a KEA algorithm, but also as an asymmetric encryption algorithm. According to the NIST Security level, the Kyber algorithm provides cryptographic 1, 3, and 5 security levels, and the Rock algorithm provides cryptographic 3, 5, and 7 security levels. The cryptographic stability that is ensured for both algorithms is determined by a set of parameters. Thus, the purpose of this work is to review the details of the implementation of each of the mentioned algorithms, to compare the speed of the key generation, encapsulation and decapsulation algorithms for the Kyber and Skelya algorithms in terms of key data lengths, and the encapsulation result and computational complexity of both algorithms.
An important feature of the transition and post-quantum period is the application of new mathematical methods to counteract quantum cryptanalysis. The world cryptographic community pays special attention to the open competition for the post-quantum standard of electronic signature. The problem is to prove the stability of new mathematical methods for the synthesis of transformations such as electronic signature, in particular with the use of algebraic lattices. The existing algorithms of electronic signature of the 2nd stage of the NIST competition are analyzed. Among the selected candidates for the EP 2 standard, 3 of the 3 algorithms are based on algebraic lattices, CRYSTALS-DILITHIUM and FALCON. The NIST has issued a statement saying that it is most likely that one of the algorithms will be chosen due to the same mathematical basis used in both algorithms. The main attacks on electronic signature algorithms based on the problem of learning with errors, as well as the parameters of the EP Dilithium algorithm, which affect the stability and complexity of transformations, are considered. Methods for generating system-wide parameters of stability levels of 512 bits of classical and 256 bits of quantum security, as well as the protection of the algorithm againstfrom attacks by third-party channels are considered. The dependence of the time of electronic signature production on the keys is analyzed. The results of calculations for the level of stability 512/256 are given, and also recommendations on the choice of system-wide parameters are given. The results of the 2nd stage of the NIST competition of post quantum cryptographic algorithms, as well as the prospects of standardization of transformations such as electronic signature at the 3rd stage are considered. Conclusions are made about the need for a more detailed study of attacks on algorithms based on the problem of learning with errors, as well as the importance of generating system-wide parameters of higher levels.