# Performance Analysis of Post-Quantum Cryptography Algorithms for Digital Signature
## 6 Conclusions  
This paper emphasizes the fundamental role of post-quantum cryptography in enhancing digital signatures against the emerging threats associated with the potential of quantum computers. Through the implementation and testing of selected algorithms, the ability of post-quantum algorithms in application to digital signatures has been demonstrated. They are undoubtedly an alternative to the cryptographic solutions currently in use and a promising candidate for their replacement.  
To conclude on the practical applications of post-quantum algorithms for digital signatures, it is necessary to state that the implementations have been positively verified in several usage scenarios. The results are consistent with the benchmarking of the liboqs library [19]. In the analysis of time performance, the Dilithium algorithm (especially Dilithium5) proved to be the best candidate for digital signatures. Although it performed slightly behind some competitors during signature verification, it clearly dominated during key pair generation and signing processes. An additional fact in its favour is the size of the generated signatures. All three available variants of the Dilithium algorithm generate a signature several times smaller than the SPHINCS+ group algorithms. But if the size of the generated signature is the primary criterion, the Falcon algorithm appears to be the favourite, achieving the smallest signatures. Representing a hash function approach, the algorithms in the SPHINCS+ group show great diversity due to their ability to cooperate with different hash functions. When deciding between implementations from this particular group, algorithms optimized for signature size would be a better choice. This is because, as the file size increases, the disparity between the two variants of the SPHINCS+ algorithm decreases. In the final analysis, it can be concluded that there are algorithms that can replace RSA with marginal overhead in time, while diametrically increasing security, whereas the choice of a particular algorithm may be determined by the needs of a particular case.  
Research on the evaluation and standardization of post-quantum algorithms is constantly in progress, with NIST leading the way. Therefore, the optimization of post-quantum solutions can be expected, as well as the emergence of new solutions. On 17 July 2023, NIST announced additional candidates for digital signatures in the PQC standardization process. The list can be found on the institution's website, and more information can be expected in 2024, when the fifth PQC standardization conference will be held [23]. As NIST is continually engaged in standardization projects, future work may involve testing new algorithms suggested by the institution.  
Conceptualization, F.O. and M.N.; methodology, F.O. and M.N.; software, F.O.; validation, F.O.; formal analysis, F.O. and M.N.; investigation, F.O., M.N. and M.A.K.; writing--original draft preparation, F.O. and M.N.; writing--review and editing, F.O., M.N., M.G. and M.A.K.; visualization, F.O.; supervision, M.N., M.G. and M.A.K.; project administration, M.N.; funding acquisition, M.N. All authors have read and agreed to the published version of the manuscript.  
This research project was partly supported by the program \"Excellence initiative--research university\" for the AGH University of Krakow. This work was also supported by the EU Horizon Europe Framework Program under Grant Agreement no. 101119547 (PQ-REACT).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.