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.
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.
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.
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.
A quantum computer can destroy most, if not all, of the traditional cryptosystems used in practice, namely, all the systems on the basis of the integer factorization problem (e. g. RSA) or the discrete logarithm problem (both traditional and elliptic curve Diffie-Hellman and DSA, and the whole cryptography based on the pairing). Some classic cryptosystems based on computationally difficult problems are very different from the above and more difficult to solve, they are independent of the quantum computation. In this paper, a review of methods of information security based on quantum and post-quantum technologies was carried out. For each of the methods of information security based on quantum technologies are the advantages and disadvantages. Describes the system of post-quantum cryptography based on lattice theory. The results of the survey allow to formalize the direction of future research of post-quantum methods and development of new effective information security systems using quantum technologies.
As quantum computing technology evolves, it poses greater risks to current cryptography schemes such as RSA and Elliptic Curve Cryptography (ECC), widely used to secure digital communications These classical algorithms are based on mathematical problems that quantum algorithms such as Shore-Grover deal with. Both, can resolve much faster, making them vulnerable to quantum attack This has given rise to post-quantum cryptography (PQC), which focuses on developing quantum-resistant algorithms to protect data in the future of quantum computers classical cryptography Can Break This paper aims to provide a comprehensive insight into quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariable polynomial methods. It examines the efficiency, benefits, and challenges associated with implementing these algorithms in real-world applications. By comparing key parameters such as key size, encryption/decryption speed, and signature size, this study examines the relative strengths and limitations of post-quantum algorithms to their classical counterparts The results show that lattice-based algorithms , such as NTRU and Kyber, offer promising solutions with relative efficiency and manageable key sizes, making them potential candidates for quantum-resistant cryptography but other approaches , such as SPHINCS+ (hash-based) and McEliece (code-based), large -Face challenges of key size and slow encryption speed, which may limit their usefulness in some applications Despite these challenges, quantum post-cryptography is necessary to secure the future of digital communications.
The rapid growth of quantum computing poses a critical threat to classical cryptographic systems. That is due in large part to the fact that they represent efficient solutions for some of the most challenging mathematical problems such as integer factoring or finding discrete logarithms. Schemes currently in wide use including RSA, Diffie–Hellman, and elliptic curve cryptography are particularly susceptible to being attacked by quantum computers, using algorithms like Shor's Algorithm and Grover's Algorithm. The advent of post-quantum cryptography (PQC) provides a promising potential answer to providing longterm security from adversaries using quantum computing capabilities. This paper presents a comprehensive state-of-the-art review of various PQC techniques currently being researched, including lattice-based methods, code-based methods, multivariate methods, hash-based methods, and isogeny-based methods. key challenges that will need to be addressed include computational overhead, large key sizes and implementation complexity. Furthermore the study reviews the current standardization efforts by the National Institute of Standards and Technology related to PQC and discusses some of the very specific practical considerations that need to be considered before widely deploying these techniques. The paper concludes by a complete list of existing research challenges and proposed future work that will assist in the development of efficient and scalable systems that will resist attacks from quantum computers.