Analysis and comparison of the security of electronic signatures based on new quantum-resistant problems

Abstract

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.