Globally, the efforts of a significant number of crypto-theorists, mathematicians and cryptologists-practitioners are focused on the NIST PQC open competition. One of the main tasks of the competition is the development and adoption of post-quantum ES standard or standards. The finalists of the second stage of the NIST competition were three ES mechanisms – CRYSTALS-DILITHIUM, Falcon and Rainbow. In addition, three alternative candidates have been identified who need more detailed research. In general, a comprehensive analysis of the finalists is an important task for cryptologists in the global cryptocommunity. Moreover, security, i.e. proving the cryptographic stability of two finalist candidates, to the ES standard – CRYSTALS-DILITHIUM and Falcon, is based on problems in the theory and practice of algebraic lattices. Studies show that among the ES schemes on lattices it differs slightly from other candidates and has prospects for the adoption as a standard the Falcon algorithm. The main and dominant approach to the design of the Falcon ES mechanism is the use of the Fiat-Shamir transformation with interruptions. For the safe use of the Falcon ES, the sets of system-wide parameters that ensure resistance to all known and potential attacks must be found. In the process of forming the requirements for ES NIST within the competition was interested only in sets of system-wide parameters up to 256 bits of classical security inclusive. However, according to the authors of this work, in the future it is advisable to provide at least 384 and 512 bits of security for classical cryptanalysis and at least 192 and 256 bits of security for quantum cryptanalysis. The article brie
Globally, the efforts of a significant number of crypto-theorists, mathematicians and cryptologists-practitioners are focused on the NIST PQC open competition. One of the main tasks of the competition is the development and adoption of post-quantum ES standard or standards. The finalists of the second stage of the NIST competition were three ES mechanisms – CRYSTALS-DILITHIUM, Falcon and Rainbow. In addition, three alternative candidates have been identified who need more detailed research. In general, a comprehensive analysis of the finalists is an important task for cryptologists in the global cryptocommunity. Moreover, security, i.e. proving the cryptographic stability of two finalist candidates, to the ES standard – CRYSTALS-DILITHIUM and Falcon, is based on problems in the theory and practice of algebraic lattices. Studies show that among the ES schemes on lattices it differs slightly from other candidates and has prospects for the adoption as a standard the Falcon algorithm. The main and dominant approach to the design of the Falcon ES mechanism is the use of the Fiat-Shamir transformation with interruptions. For the safe use of the Falcon ES, the sets of system-wide parameters that ensure resistance to all known and potential attacks must be found. In the process of forming the requirements for ES NIST within the competition was interested only in sets of system-wide parameters up to 256 bits of classical security inclusive. However, according to the authors of this work, in the future it is advisable to provide at least 384 and 512 bits of security for classical cryptanalysis and at least 192 and 256 bits of security for quantum cryptanalysis. The article brie
Globally, the efforts of a significant number of crypto-theorists, mathematicians and cryptologists-practitioners are focused on the NIST PQC open competition. One of the main tasks of the competition consists in development and adoption of a post-quantum ES standard or standards. The finalists of the second stage of the NIST competition were three ES mechanisms – CRYSTALS-DILITHIUM, Falcon and Rainbow. In addition, three alternative candidates were identified that require more detailed research. In general, a comprehensive analysis of the finalists is an important task for cryptologists in the global cryptocommunity. Moreover, security, i.e. brining the cryptographic stability of two finalist candidates, to the ES standard – CRYSTALS-DILITHIUM and Falcon, is based on problems in the theory and practice of algebraic lattices. Studies show that among the ES schemes on lattices it differs slightly from other candidates and has prospects for the adoption as the Falcon algorithm standard. The main and dominant approach to the design of the Falcon ES mechanism is the use of the Fiat-Shamir transformation with interruptions. The sets of system-wide parameters that ensure resistance to all known and potential attacks should be found for the safe use of the Falcon ES. In the process of forming the requirements for ES within the competition, the NIST was interested only in sets of system-wide parameters up to 256 bits of classical security inclusive. However, according to the authors of this work, in the future it is advisable to provide at least 384 and 512 bits of security for classical cryptanalysis and at least 192 and 256 bits of security for quantum cryptanalysis. The article briefly considers the essence of the Falcon electronic signature (ES) algorithm. An analysis of possible attacks on the algorithm and the mechanisms of their implementation is also performed. The process of generating system-wide parameters for 256, 384, 512 stability bits is considered. Conclusions and recommendations are given. The objective of the work is the classification and initial analysis of known attacks on the ES Falcon cryptosystem, setting limits and developing practical algorithms for calculating (generating) system-wide parameters to provide not less than 256, 384 and 512 security bits for classical and not less than 128, 192 and 256 security bits for quantum cryptanalysis.
Globally, the efforts of a significant number of crypto-theorists, mathematicians and cryptologists-practitioners are focused on the NIST PQC open competition. One of the main tasks of the competition consists in development and adoption of a post-quantum ES standard or standards. The finalists of the second stage of the NIST competition were three ES mechanisms – CRYSTALS-DILITHIUM, Falcon and Rainbow. In addition, three alternative candidates were identified that require more detailed research. In general, a comprehensive analysis of the finalists is an important task for cryptologists in the global cryptocommunity. Moreover, security, i.e. bringing the cryptographic stability of two finalist candidates, to the ES standard – CRYSTALS-DILITHIUM and Falcon, is based on problems in the theory and practice of algebraic lattices. The EP Dilithium method (scheme) is based on the approach called "Fiat-Shamir Interruptions". The essence of the CRYSTALS-DILITHIUM ES algorithm is considered in the article. A detailed analysis of possible attacks on the algorithm and the mechanisms of their implementation is also carried out. Models of violator, threats and security are considered and analyzed. The main definitions of ES security models are provided. The main design elements of the mechanism of perspective post-quantum ES Dilithium are described in the generalized form. General estimations of the ES Dilithium security level are given. The substantiation and essence of models of threats, violator and security are given. The stability of the ES Dilithium algorithm is investigated. The purpose of the article is to substantiate a security model, classification, primary analysis and assessment of known attacks on the CRYSTALS-DILITHIUM EP cryptosystem, to establish restrictions and develop practical algorithms for calculating (generating) system-wide parameters to ensure 128, 256, 384 and 512 bits of security relative to classical and 64, 128, 192 and 256 bits relative to quantum cryptanalysis.
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.
The National Institute of Standards and Technology (NIST) has recently concluded the third round of its Post Quantum Cryptography Standardization Process, selecting four finalist algorithms for standardization: CRYSTALS Kyber, CRYSTALS-Dilithium, FALCON, and SPHINCS+. These algorithms are designed to withstand attacks from both classical and quantum computers, ensuring the long-term security of digital communications. This paper presents a comprehensive comparative analysis of the security margins and practical deployment readiness of these finalist algorithms. CRYSTALS-Kyber, a key encapsulation mechanism based on the hardness of the Module Learning With Errors problem, offers strong security and efficient performance. CRYSTALS-Dilithium, a digital signature algorithm based on module lattices, provides robust security guarantees and relatively straightforward implementation. FALCON, a lattice-based digital signature algorithm utilizing the Fast Fourier Transform, offers compact signatures and fast verification but faces implementation challenges due to its reliance on floating-point arithmetic. SPHINCS+, a hash-based signature scheme, stands out as a conservative choice with security based solely on the well-established security of hash functions. The analysis reveals that while each algorithm has its strengths, they also face unique challenges in terms of side-channel vulnerabilities, formal security proofs, and performance trade-offs. The practical deployment of these algorithms requires careful consideration of specific security requirements, performance needs, and resource constraints. Ongoing research efforts aim to enhance the algorithms' resistance against advanced attacks, optimize their performance across diverse platforms, and develop standardized and secure hybrid cryptographic systems. The transition to post-quantum cryptography will involve challenges such as interoperability with legacy systems, the need for clear standards and regulatory guidance, and the costs associated with software and hardware updates. Continued engagement with the cryptographic community and monitoring of the evolving security landscape will be crucial for ensuring a secure and effective migration to post-quantum cryptography.
The advent of quantum computing will pose a substantial threat to the security of classical cryptographic methods, which could become vulnerable to quantum-based attacks. In response to this impending challenge, the field of post-quantum cryptography has emerged, aiming to develop algorithms that can withstand the computational power of quantum computers. This study addressed the pressing concern of classical cryptographic methods becoming vulnerable to quantum-based attacks due to the rise of quantum computing. The emergence of post-quantum cryptography has led to the development of new resistant algorithms. Our research focused on four quantum-resistant algorithms endorsed by America’s National Institute of Standards and Technology (NIST) in 2022: CRYSTALS-Kyber, CRYSTALS-Dilithium, FALCON, and SPHINCS+. This study evaluated the security, performance, and comparative attributes of the four algorithms, considering factors such as key size, encryption/decryption speed, and complexity. Comparative analyses against each other and existing quantum-resistant algorithms provided insights into the strengths and weaknesses of each program. This research explored potential applications and future directions in the realm of quantum-resistant cryptography. Our findings concluded that the NIST algorithms were substantially more effective and efficient compared to classical cryptographic algorithms. Ultimately, this work underscored the need to adapt cryptographic techniques in the face of advancing quantum computing capabilities, offering valuable insights for researchers and practitioners in the field. Implementing NIST-endorsed quantum-resistant algorithms substantially reduced the vulnerability of cryptographic systems to quantum-based attacks compared to classical cryptographic methods.
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.