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All-Russian Scientific and Practical Conference «Challenging Issues in Systems Modeling and Processes»

QUANTUM COMPUTING AS A THREAT TO MODERN CRYPTOGRAPHY. AN OVERVIEW OF SHOR'S ALOHORHYTHM AND POST-QUANTUM CRYPTOGRAPHY

A. Tyunina, A. Shpineva

Published Jan 15, 2026• 0 citations
Publisher

Abstract

The article is devoted to the study of the threat of the development of quantum computing for classical cryptographic systems vulnerable to the Shor algorithm. It is shown that the RSA and ECC protocols lose their stability with the advent of scalable quantum computers, while post-quantum lattice and code schemes demonstrate high stability. It is concluded that there is a need to move to post-quantum standards and develop hybrid cryptosystems.

DOI
10.58168/ppspm2025_217-232

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The article is devoted to the study of the threat of the development of quantum computing for classical cryptographic systems vulnerable to the Shor algorithm. It is shown that the RSA and ECC protocols lose their stability with the advent of scalable quantum computers, while post-quantum lattice and code schemes demonstrate high stability. It is concluded that there is a need to move to post-quantum standards and develop hybrid cryptosystems.
This article analyzes the threats to the security of modern cryptographic systems posed by the development of quantum computers, as well as the emergence of the concept of post-quantum cryptography as a solution to these problems. The study demonstrates that classical public-key cryptosystems, particularly RSA, DSA, and elliptic curve-based algorithms, can be broken using quantum algorithms. At the same time, new cryptographic systems based on hash functions, codes, lattices, and multivariate quadratic equations are considered a promising direction. The main challenges related to the efficiency, reliability, and applicability of post-quantum cryptography are also highlighted. As a result, the necessity of developing new cryptographic standards to ensure future information security is demonstrated.
Quantum computing has emerged as a disruptive technology with the potential to revolutionize various fields, including information security. Traditional cryptographic protocols, including RSA, ECC, and AES, rely on the difficulty of certain mathematical problems for their security. However, the advent of quantum computing poses a significant threat to these encryption methods, as quantum algorithms such as Shor's and Grover's algorithms can efficiently solve problems that are computationally hard for classical systems. This paper explores the implications of quantum computing on existing cryptographic systems and proposes strategies for future-proofing information security protocols. We examine the vulnerabilities introduced by quantum computing, highlight the role of post-quantum cryptography (PQC), and explore quantum key distribution (QKD) as potential solutions for ensuring the confidentiality, integrity, and authenticity of digital communications. The paper discusses various quantum-resistant algorithms and offers insights into the ongoing efforts by international standardization bodies to prepare for a post-quantum world.
As the development of quantum computing systems advances, the integrity of current public-key and symmetrickey cryptographic systems, such as RSA, ECC, and AES, faces unprecedented threats.These systems rely on mathematical problems like integer factorization and discrete logarithms, which quantum algorithms like Shor's can solve exponentially faster than classical ones.This review examines the vulnerability of widely used cryptographic systems and evaluates how close quantum hardware is to breaching real-world encryption.It also discusses the development of post-quantum cryptographic algorithms, specifically lattice-based, code-based, and multivariate polynomial systems designed to resist quantum attacks.This paper will also assess the strengths, limitations, and standardization progress of these post-quantum solutions to provide an understanding of the modern cryptographic landscape.
Quantum computing is a transformational technology once implemented, capable of addressing problems far beyond the capacity of classical computers. But this progress is also a real challenge to the core of today's modern security. Traditional cryptographic algorithms, such as those based on RSA, ECC, and Diffie-Hellman key exchange, are based on the computational hardness of problems such as prime factorization and discrete logarithms that quantum algorithms solve in polynomial time. As a particular research interesting example, with Shor's Algorithm one can factorize large numbers efficiently, rendering insecure the majority of public key cryptosystems used nowadays. This urgently demands a reevaluation of existing encryption schemes in the context of a post-quantum world. In this paper, we take a closer look at the threats that quantum computers pose to classical security infrastructure including encryption scheme and explore the impact that quantum computation can have on current cryptographic schemes. It calculates the cost in terms of symmetric and asymmetric security, accounting for effects of both Shor's and Grover's algorithms. Symmetric key systems such as AES are also harder hit—Grover's algorithm can give only a quadratic speedup here—but they do need to double key sizes for a sufficient level of post-quantum security. In reaction to those threats, the paper investigates nextgeneration post-quantum cryptographic (PQC) solutions resistant to quantum cryptanalysis. Lattice-based cryptosystems, hash-based signature schemes, multivariate polynomial systems, and code-based cryptosystems are some of the candidates that are being considered in international standardization work, including especially at NIST. In this paper, we compare those alternatives for security, performance, scalability, and feasibility of implementation in real system. An important aspect of this contribution is a comparative study of traditional and post-quantum cryptographic protocols in the context of a number of cybersecurity applications, including secure communications, blockchain networks and IoT contexts. It also covers the quantum readiness timeline and transitional issues, such as backward compatibility, standardization lag and the associated increased computational overhead. Through a mitigated risk evaluation and cryptanalytic attack simulation based on quantum-inspired algorithms, this analysis emphasizes the need to prepare ourselves against quantum-induced security issues. It provides strategic guidance to organizations as they plan for the post-quantum future, stressing cryptographic agility, hybrid encryption models and real-time threat monitoring. Ultimately, the results of this work add to the worldwide conversation on establishing secure systems within the digital age of quantum computing and recommend proactive migration plans for the integrity, confidentiality, and trust one should have in the future cyber world.
Quantum computing is one of the most significant technological revolutions in the 21st century. Its ability to compute complicated mathematical equations exponentially higher than classical computers poses a risk of becoming outdated to the present cryptographic systems. RSA and Elliptic Curve Cryptography (ECC)-based public key infrastructures are especially susceptible to the Shor algorithm that is capable of factoring large integers and calculating discrete logarithms on a sufficiently large quantum computer. The paper will discuss the principles of quantum computation and their applications in cryptography, as well as a new branch of cryptography, post-quantum cryptography (PQC). It discusses fabrics of key algorithmic contenders, the implementation issues, and the worldwide move to quantum resilient systems. The paper finds that hybrid encryption models, international standardization, and ethical governance are the key elements to achieving the digital future in the quantum era.
Quantum computing is the future of computing with promised radical increase in processing capability; however, it is a threat the existing cybersecurity paradigm. Classical encryption techniques especially the ones based on public-key cryptography are insecure against quantum algorithms such as Shor’s algorithm where typical cryptographic schemes the use of which was exemplified by the RSA and ECC will be threatened. While torrents of research have been accomplished in building and developing quantum computers, the importance of post-quantum cryptography (PQC) becomes more felt. This paper attempts to look at the threats that quantum technologies pose to current cryptographic methods and the countermeasures that are being worked on to counter them. We do so to evaluate the current status on quantum computing and its ramifications to data security, as well as the work that academic and government institutions and business enterprises have done on coming with Quantum-Resistant Cryptography. In addition, the paper gives an overview of the most promising post-quantum cryptographic techniques including lattice cryptography, hash-based signatures, and code-based cryptosystems and cryptographic protocols that are under consideration as the next generation cryptographic protocols. It also tackles the problems related to the migration to the post-quantum cryptographic systems the problem of standardisation the problem of compatibility, and the problem of growth of new algorithms. Moreover, prescriptive advice on the concept of quantum readiness and timely implementation of cyber defence plans to safeguard sensitive data and crucial infrastructure against quantum risks is provided. Finally, the paper offers suggestions for the organisations for starting to transition to the post-quantum landscape in terms of using hybrid cryptographic systems and promoting cooperation in the fight against the threats of quantum technology world-wide.