With the constantly advancing capabilities of quantum computers, conventional cryptographic systems relying on complex math problems may encounter unforeseen vulnerabilities. Unlike regular computers, which are often deemed cost-ineffective in cryptographic attacks, quantum computers have a significant advantage in calculation speed. This distinction potentially makes currently used algorithms less secure or even completely vulnerable, compelling the exploration of post-quantum cryptography (PQC) as the most reasonable solution to quantum threats. This review aims to provide current information on applications, benefits, and challenges associated with the PQC. The review employs a systematic scoping review with the scope restricted to the years 2022 and 2023; only articles that were published in scientific journals were used in this paper. The review examined the articles on the applications of quantum computing in various spheres. However, the scope of this paper was restricted to the domain of the PQC because most of the analyzed articles featured this field. Subsequently, the paper is analyzing various PQC algorithms, including lattice-based, hash-based, code-based, multivariate polynomial, and isogeny-based cryptography. Each algorithm is being judged based on its potential applications, robustness, and challenges. All the analyzed algorithms are promising for the post-quantum era in such applications as digital signatures, communication channels, and IoT. Moreover, some of the algorithms are already implemented in the spheres of banking transactions, communication, and intellectual property. Meanwhile, despite their potential, these algorithms face serious challenges since they lack standardization, require vast amounts of storage and computation power, and might have unknown vulnerabilities that can be discovered only with years of cryptanalysis.

翻译：随着量子计算机能力的不断提升，依赖复杂数学问题的传统密码系统可能面临不可预见的脆弱性。与在密码攻击中通常被认为成本效益低的常规计算机不同，量子计算机在计算速度上具有显著优势。这一区别可能使当前使用的算法安全性降低甚至完全脆弱，从而促使探索后量子密码学作为应对量子威胁的最合理解决方案。本综述旨在提供关于后量子密码学应用、优势及挑战的最新信息。综述采用系统性范围综述方法，时间范围限定在2022年和2023年；仅使用科学期刊上发表的文献。综述考察了量子计算在各领域应用的相关文献，但本文范围限定在后量子密码学领域，因为大多数分析文献聚焦于此。随后，本文分析了各种后量子密码算法，包括基于格的密码学、基于哈希的密码学、基于编码的密码学、多元多项式密码学以及基于同源性的密码学。每种算法均根据其潜在应用、鲁棒性和挑战进行评估。所有被分析的算法在数字签名、通信信道和物联网等应用中，对于后量子时代都展现出前景。此外，部分算法已在银行交易、通信和知识产权领域得到实际应用。然而，尽管潜力巨大，这些算法仍面临严峻挑战，包括缺乏标准化、需要大量存储和计算资源，以及可能存在仅能通过多年密码分析才能发现的未知漏洞。