Analysis of hardware implementations of electronic signature algorithms qTesla, Crystals-Dilitium and MQDSS at different levels of security

Abstract

It is known, that existing public-key cryptography algorithms based on RSA and elliptic curves provide security guarantees accompanied by complexity. Based on this one can talk about the impossibility to solve problems of integer factorization and discrete logarithm. However, experts predict that the creation of a quantum computer will be able to crack classical cryptographic algorithms. Due to this future problem, the National Institute of Standards and Technologies (NIST), together with leading scientists in the field of cryptography, began an open process of standardizing public-key algorithms for quantum attacks. An important feature of the post-quantum period in cryptography is the significant uncertainty regarding the source data for cryptanalysis and counteraction in terms of the capabilities of quantum computers, their mathematical and software, as well as the application of quantum cryptanalysis to existing cryptotransformations and cryptoprotocols. Mathematical methods of electronic signature (ES) have been chosen as the main methods of NIST USA, which have undergone significant analysis and substantiation in the process of extensive research by cryptographers and mathematicians at the highest level. These methods are described in detail and passed the research at the first stage of the international competition NIST USA PQC. Historically, in 1997, NIST sought public advice to determine the replacement of the data encryption standard (DES), Advanced Encryption Standard (AES). Since then, open cryptographic estimations have become a way of choosing cryptographic standards. For example, NESSIE (2000-2002), eSTREAM (2004-2008), CRYPTREC (2000-2002), SHA-3 (2007-2012) and CAESAR (2013-2019) have adopted this approach. Security was the main parameter in these estimations. Performance in software, performance in application-specific integrated circuits (ASICs), performance in FPGAs, and feasibility with limited resources (small microprocessors and low-power hardware) are secondary criteria. This paper presents the comparison of the hardware of three signature algorithms (qTesla, Crystals-Dilitium, MQDSS), which, in particular, are the candidates for the 2nd round of the NIST PQC competition, and the Crystals-Dilitium algorithm is the finalist of this competition. The objective of this work is to analyze and compare three hardware implementations of candidates for the second round of the NIST PQC contest for an electronic signature algorithm.