Cryptanalysis of the «Vershyna» digital signature algorithm

Abstract

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.