Today, the question of the stability of modern existing cryptographic mechanisms to quantum algorithms of cryptanalysis in particular and quantum computers in general is quite acute. This issue is actively discussed at the international level. Therefore, to solve it, NIST USA has decided to organize and is currently holding a competition for candidates for post-quantum cryptographic algorithms NIST PQC. The result of the competition should be the adoption of various types of cryptographic algorithms for standardization, namely, asymmetric encryption, key encapsulation and electronic signature (at least one algorithm of each type). 82 algorithms were submitted by the start of the competition for the standardization process. Based on the minimum eligibility criteria defined by NIST, 69 algorithms were considered for the 1st round. Given several parameters, namely, security, cost, performance, implementation characteristics, etc., 43 and 11 algorithms were excluded at the end of the 1st and 2nd rounds, respectively, and the other 15 algorithms were left for participation in the 3rd round. The algorithms left in the 2nd round can be divided into 5 different categories depending on their mathematical basis: those based on the isogeny of elliptic curves, those based on algebraic lattices, those based on mathematical code, those based on multivariate transformations and those based on hash functions. Security is the main evaluation criterion that determines competition in the NIST competition, and it is clear that candidates' software implementations are focused mainly on it. However, it is extremely important that the algorithm has an effective hardware implementation. Timely identification of hardware inefficiencies will help focus the cryptographic community efforts on more promising candidates, potentially saving a large amount of time that can be spent on cryptanalysis. This paper discusses and compares the FPGAs of Xilinx family. Data on the implementation of the candidates of the 2nd round in the process of standardization of post-quantum cryptography NIST, which are focused on the FPGA of the Xilinx family, are presented and compared.

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 digital signature (DS) 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. They are described in detail and studied at the first stage of the US NIST International Competition. In the second round, a number of decisions were made to merge some candidates for the post-quantum DS standard. 9 candidates were left for further research at the 2nd round: Crystals-Dilithium, Falcon, GeMSS, LUOV, MQDSS, Picnic, qTESLA, Rainbow and SPHINCS+. Three of them (Dilithium, Falcon, qTeSLA) are based on the stability of algebraic lattices (Lattice-based), four (GeMSS, LUOV, MQDSS, Rainbow) are based on multivariate transformations (MQ-transformations), one (SPHINCS+) is based on the stability of hash-function, one (Picnic) is based on the stability of the hash-function and block stream ciphers. During the 2nd round of the US NIST Competition the following finalist algorithms and alternative algorithms were selected as digital signatures according to the results of research on promising post-quantum cryptographic algorithms. As finalists algorithms such DS algorithms as Crystals-Dilithium, Falcon and Rainbow. Alternative algorithms are GeMSS, Picnic and SPHINCS+ were selected. This paper studies the peculiarities of construction of the digital signature algorithm considered as a candidate for the promising post-quantum standard of the NIST PQC competition – Picnic, also it analyzes the protection of the algorithm from known attacks. Data from the comparison of post-quantum algorithms such as digital signature are given. The description of the Picnic algorithm and its parameters are given.

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.