The CRYSTALS-Dilithium digital signature algorithm, which was selected as the prototype of the new «Vershyna» digital signature algorithm, is analyzed in this paper. The characteristics of the National Digital Signature Standard Project and the construction of the «Vershyna» algorithm are also presented. During the analysis of the project, the predicted number of iterations that the algorithm must perform to create the correct signature was calculated. In addition, basic theoretical information about the structure of Fiat-Shamir with aborts and its security in quantum and classical models oracle models is also provided. We obtain our own results on the resistance of the «Vershyna» algorithm to the attack without the use of a message in classical and quantum oracle models. The resistance of the «Vershyna» algorithm to a key recovery attack is based on the assumption of the hardness of the MLWE~problem, and the resistance to existential signature forgery is based on the assumption of the hardness of the MSIS~problem. In this work, the expected level of hardness of SIS~and LWE~problems is calculated, to which there are reductions from MSIS~and MLWE~problems.
The CRYSTALS-Dilithium digital signature algorithm, which was selected as the prototype of the new «Vershyna» digital signature algorithm, is analyzed in this paper. The characteristics of the National Digital Signature Standard Project and the construction of the «Vershyna» algorithm are also presented. During the analysis of the project, the predicted number of iterations that the algorithm must perform to create the correct signature was calculated. In addition, basic theoretical information about the structure of Fiat-Shamir with aborts and its security in quantum and classical models oracle models is also provided. We obtain our own results on the resistance of the «Vershyna» algorithm to the attack without the use of a message in classical and quantum oracle models. The resistance of the «Vershyna» algorithm to a key recovery attack is based on the assumption of the hardness of the MLWEproblem, and the resistance to existential signature forgery is based on the assumption of the hardness of the MSISproblem. In this work, the expected level of hardness of SISand LWEproblems is calculated, to which there are reductions from MSISand MLWEproblems.
The development of quantum computers is a threat to current cryptographic algorithms, such as the RSA algorithm. Due to this, the development of post quantum cryptography is a topic of research. One digital signature algorithm that is proposed as a quantum proof solution is the Dilithium digital signature system. Dilithium is based on a learning with errors problem (LWE) in which the value of generated signatures includes an error term. The security of Dilithium is based on previous re- search on topics such as the Module LWE problem, the Fiat Shamir transformation with aborts and the Module Short integer solution problem (MSIS ). The reference implementation includes optimization in the signature generation process. By using the number theoretic transform the multiplication of the ring elements is point-wise or in other words in linear time. This thesis presents the mathematical foundations on which the systems security is based on. In addition, the security of digital signatures, identification schemes and the LWE problem are discussed. In the final chapter these topics are brought together to present the Dilithium scheme.
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 long-term security of public blockchains strictly depends on the hardness assumptions of the underlying digital signature schemes. In the current scenario, most deployed cryptocurrencies and blockchain platforms rely on elliptic-curve cryptography, which is vulnerable to quantum attacks due to Shor's algorithm. Therefore, it is important to understand how post-quantum (PQ) digital signatures behave when integrated into real blockchain systems. This report presents a blockchain prototype that supports multiple quantum-secure signature algorithms, focusing on CRYSTALS-Dilithium, Falcon and Hawk as lattice-based schemes. This report also describes the design of the prototype and discusses the performance metrics, which include key generation, signing, verification times, key sizes and signature sizes. This report covers the problem, background, and experimental methodology, also providing a detailed comparison of quantum-secure signatures in a blockchain context and extending the analysis to schemes such as HAETAE.
Due to the development of quantum computers and quantum methods and algorithms, in order to ensure the security of information after the development of cryptographically relevant quantum computers, NIST conducted the NIST PQC competition. As a result of conducting three rounds of NIST PQC, NIST selected 4 candidates for standardization and four candidates for the fourth round (key encapsulation mechanisms BIKE, Classic McEliece, HQC, and SIKE (which the developers considered unreliable)). Due to the fact that selected algorithms are based on the use of lattices and to add diversity to this list through the use of general-purpose signatures, the process of standardizing additional digital signatures for quantum-resistant cryptography has been initiated. The following types of signatures are considered for the first round of this standardization process: code-based signatures, isogeny signatures, multivariate signatures, symmetric signatures, MPC-in-the-head, and NIST-defined "other" signatures. These "other" digital signatures are mostly based on new and promising post-quantum (quantum-resistant) problems. The purpose of the work is to analyze and compare candidates for quantum-resistant digital signatures, based on new and promising quantum-resistant problems, resistant to classical and quantum attacks and side-channel attacks. The paper provides comparison of four digital signatures classified by NIST as "other", namely: ALTEQ, eMLE-Sig 2.0, KAZ-SIGN, Xifrat1-Sign.I. For this purpose, the paper presents the basic principles of each of these digital signatures, their main parameters and available at the time of consideration attack vectors. The paper also provides unconditional criteria necessary for comparison. Digital signatures were compared according to such unconditional criteria as: possible lengths of the public key, possible lengths of the personal (secret) key, length of the result of cryptographic algorithm; and conclusions are made regarding the completeness of given comparison and the possibility of further research is highlighted.
To overcome the issue of traditional blind signature schemes being vulnerable to quantum computing attacks during interactions over the consumer electronic Internet of Things (CIoT), a new blind signature scheme called CDBS has been developed. The post quantum digital signature technique CRYSTALS-Dilithium, which was standardized by NIST, serves as the foundation for the quantum-resistant blind signature scheme, CDBS, presented in this study. This system is appropriate for a variety of internet application scenarios, including e-ticketing, anonymous payments, and privacy protection, because it integrates the idea of blind signatures, which is not included in typical digital signature schemes. This scheme is designed to resist quantum computing attacks and is based on the post-quantum digital signature algorithm CRYSTALS-Dilithium, which NIST has selected. The whole technique utilizes the Fiat-Shamir signature structure, which consists of five stages: key creation, blinding, signing, unblinding, and verification. The security of the proposed scheme is dependent on the resolution of the Module Learning with Errors (MLWE) problem and the Short Integer Solution (SIS) problem. Additionally, the scheme must satisfy the criteria of correctness, blindness, and unforgeability. According to the test results, the CRYSTALS-Dilithium scheme requires an average of 401.89 μ s for a single round of verification and signing. The CDBS technique takes an average of 657.65 ls for one round of signing and verification since the blinding and unblinding modules are added on top of the original algorithm, increasing the algorithm’s complexity. The software testing results indicate that the average time required to complete a single full blind signature and verification operation is 657.65 microseconds. The suggested system offers a framework for expanding the CRYSTALS-Dilithium digital signature algorithm.
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.