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CRYPTOGRAPHIC SECURITY IN THE ERA OF QUANTUM COMPUTERS: THE CONCEPT AND DEVELOPMENT PROSPECTS OF POST-QUANTUM CRYPTOGRAPHY

Dilnoz Muhamediyeva, Farhad Tagaev

Published May 3, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.19995716

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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.
This article analyzes the threats to the security of modern cryptographic systems as a result of the development of quantum computers, as well as the formation of the concept of post-quantum cryptography as a solution to these problems. The study justifies the fact that algorithms based on classical public-key cryptosystems, notably RSA, DSA, and elliptic curves, can be corrupted using quantum algorithms. At the same time, new cryptographic systems based on hash-based, code-based, Lattice-based and multivariate quadratic equations are considered as promising directions. The main problems of Post-quantum cryptography with efficiency, reliability and applicability capabilities are also highlighted. As a result, it is indicated that it is necessary to develop new cryptographic standards to ensure future information security.
Quantum computing holds an enormous power to transform cryptography because it protects secured communication. RSA together with elliptic curve cryptography functions based on mathematical challenges like integer factorization and discrete logarithms until quantum computers present security risks to these traditional systems. Such problems become solvable with efficiency through Shor's algorithm running on quantum computers which threatens the security of multiple widely used cryptographic protocols. The document examines quantum computing effects on cryptography to explain why quantum algorithms break classic cryptographic system security. Post-quantum cryptography (PQC) acts as a protective solution against quantum-based attacks through its mission to create cryptographic techniques which demonstrate quantum attack resilience. This paper examines quantum-age security design protocols for cryptographic keys using both quantum key distribution and lattice-based cryptography and hash-based cryptography and multivariate polynomial cryptography. The research analyzes the effectiveness and protective capability of new PQC solutions by connecting theoretical concepts with practical applications. The study points out advancements in quantum cryptography as well as the quantum hardware obstacles and the global initiative to establish post-quantum algorithms standards. The authors stress the urgent need for up-to-date quantum-resistant measures because of swift quantum technology progress. The protection of sensitive materials and communications networks from destructive quantum computing threats requires immediate focus because this need drives the necessity of properly preparing for post-quantum cryptography.
With the rapid advancement of information technologies, cybersecurity threats are increasing at an alarming rate. In particular, the emergence of quantum computers poses a serious risk to traditional cryptographic algorithms such as RSA, ECC, and DSA, which rely on mathematical problems that are difficult to solve using classical computing. However, these same problems can be efficiently solved on a quantum computer using Shor’s algorithm, thus endangering the security of nearly all current public-key cryptosystems. In response, the concept of Post-Quantum Cryptography (PQC) is gaining global attention as a future-proof solution.
The rapid development of quantum computing technologies poses a serious threat to modern public-key cryptographic systems. Classical cryptographic algorithms such as RSA and elliptic-curve cryptography rely on mathematical problems that can be efficiently solved using quantum algorithms. Post-quantum cryptography (PQC) aims to develop cryptographic schemes that remain secure even in the presence of quantum adversaries. This paper investigates the mathematical foundations of PQC, focusing on lattice-based, code-based, and hash-based cryptographic constructions. Security models based on computational complexity theory are analyzed, and illustrative examples using Learning With Errors (LWE) and decoding problems are presented. Experimental analysis demonstrates that PQC schemes provide strong resistance against both classical and quantum attacks when appropriate parameters are selected. The results highlight the importance of adopting new cryptographic standards to ensure long-term data security in quantum computing environments.
The emergence of quantum computing poses a serious threat to traditional communication systems, endangering the security of digital communications and critical infrastructure. Although existing cryptographic algorithms (such as RSA and ECC) rely on the inefficiency of computing large numbers or solving logarithm inequality problems, quantum algorithms (especially Shor's algorithm) can solve these problems efficiently. To mitigate this threat, the field of post-quantum cryptography (PQC) has emerged and focuses on developing cryptographic systems that are resilient to quantum attacks. The main techniques in PQC include lattice-based, hash-based, code-based, and multivariate polynomial cryptography. Lattice-based cryptography is the leading contender, providing high security and supporting good properties such as fully homomorphic encryption, but facing issues related to size and computational efficiency. Hash-based encryption enables strong digital signatures but has limitations. Code-based encryption based on error-correcting codes provides proof of security but requires small size. Multivariate polynomial cryptography has good performance but has drawbacks in some applications. While standardization efforts led by organizations such as NIST continue, PQC is at the forefront of protecting the digital future from the impact of quantum computing, ensuring the integrity and confidentiality of information in the post-quantum era.
The ongoing development of powerful quantum computers poses a significant threat to the security of conventional encryption methods such as Rivest Shamir Adleman (RSA) and Elliptic Curve Cryptography (ECC). With algorithms such as Shor's Algorithm, quantum computers can solve the mathematical problems on which these methods are based and thus break them within a few hours. This work highlights this development's challenges and examines post-quantum cryptography (PQC) as a solution. PQC offers quantum-safe encryption based on mathematical problems that are difficult to solve, even for quantum computers. The text analyzes lattice, hash, and isogeny-based approaches and introduces the new NIST standards, including Kyber, Dilithium, and Sphinx+. It also discusses practical challenges in implementing quantum-safe systems, including performance degradation and cryptographic agility. It concludes with recommendations for migrating to PQC to ensure long-term security in an era increasingly characterized by quantum computing.