Methods for calculating system parameters for electronic signature "Crystals-Dilithium" 128, 256, 384 and 512 bits of security levels - Горбенко, І.Д.; Олексійчук, А.М.; Качко, О.Г.; Горбенко, Ю.І.; Єсіна, М.В.; Кандій, С.О. (Radiotekhnika, 2020)
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.