The problem of resistance the popular cryptosystemsagainst quantum cryptanalysis is an urgent and importanttask, given the pace of development of quantum technologies.Resistance of all modern cryptosystems based on thecomplexity of solving certain mathematical problems. Suchmathematical problems tend to have exponential complexityor subexponential solutions, using quantum algorithmsthat have been proposed Shore and Grover the complexityof solving such problems is reduced to a polynomial. SoShor's algorithm reduces the complexity of cryptanalysistransformations in the ring, field and in the group of pointson elliptic curves. The article describes the using ofGrover's algorithm for cryptanalysis popular symmetricblock ciphers. The methods of quantum cryptosystemscryptanalysis NTRU, based on a combination of classicalattacks and meeting in the middle of Grover's quantumalgorithm. In this paper we proposed our estimates of resistanceof block popular ciphers and cryptosystemsNTRU with different sizes of the quantum system-wideparameters against cryptanalysis based on the use ofGrover's quantum algorithm. The article also shows thecharacteristics that must have a quantum computer forsuccessful cryptanalysis of certain cryptosystems.
The problem of resistance the popular cryptosystemsagainst quantum cryptanalysis is an urgent and importanttask, given the pace of development of quantum technologies.Resistance of all modern cryptosystems based on thecomplexity of solving certain mathematical problems. Suchmathematical problems tend to have exponential complexityor subexponential solutions, using quantum algorithmsthat have been proposed Shore and Grover the complexityof solving such problems is reduced to a polynomial. SoShor's algorithm reduces the complexity of cryptanalysistransformations in the ring, field and in the group of pointson elliptic curves. The article describes the using ofGrover's algorithm for cryptanalysis popular symmetricblock ciphers. The methods of quantum cryptosystemscryptanalysis NTRU, based on a combination of classicalattacks and meeting in the middle of Grover's quantumalgorithm. In this paper we proposed our estimates of resistanceof block popular ciphers and cryptosystemsNTRU with different sizes of the quantum system-wideparameters against cryptanalysis based on the use ofGrover's quantum algorithm. The article also shows thecharacteristics that must have a quantum computer forsuccessful cryptanalysis of certain cryptosystems.
The main trends of the science and technology development in the field of quantum physics and quantum calculations are considered in the paper. It has been shown that over the past few years plenty of new discoveries and achievements have been made in the field of quantum physics, all these events, anyway, had a great influence on the invention and production of quantum computers. Many communities around the world have been engaged in the development of quantum computers and some of them have achieved significant results in it by now.It is shown that using quantum algorithms of Shor and Grover, which can be fulfilled on a properly implemented quantum computer, can compromise some symmetric and asymmetric cryptosystems. The analysis results of endurance of the known block ciphers regarding the quantum cryptanalysis are given. It is also shown that some of them are not able to resist the quantum cryptanalysis method based on Grover's algorithm. The analysis of Shor's algorithm possibilities, which can significantly reduces computational costs for solving mathematical problems of endurance of modern asymmetric cryptoalgorithms, is given. Herewith, Shor's quantum algorithm diminishes the complexity of the cryptanalysis from exponential and subexponential to polynomial. In addition, the assessment of quantum computer resources is given in the paper, which are necessary for the quantum cryptanalysis concerning such cryptosystems as DSA, RSA, EC and NTRU.
The advent of quantum computing presents a paradigm shift in the field of cryptanalysis, challenging the security of classical encryption schemes that underpin modern digital communications. This study explores the capabilities of quantum algorithms, particularly Shor's algorithm and Grover's algorithm, in undermining widely used cryptographic systems. Shor's algorithm poses a direct threat to publickey cryptosystems such as RSA and ECC by enabling efficient integer factorization and discrete logarithm computation, which are computationally infeasible for classical computers. Meanwhile, Grover's algorithm provides a quadratic speedup for bruteforce attacks on symmetric-key cryptosystems like AES, significantly reducing their effective security. Through theoretical analysis and simulation-based evaluation, this paper highlights the vulnerabilities of classical encryption in the face of quantum advances and underscores the urgent need for post-quantum cryptographic solutions. The findings emphasize the critical importance of transitioning to quantum-resistant algorithms to ensure long-term data confidentiality in a future dominated by quantum technologies.
Modern public key cryptosystems rely on two assumptions regarding computational difficulty: the integer factorization problem (RSA) and the discrete logarithm problem (elliptic curve cryptography).These problems have stood the test of time for four decades of cryptanalysis.Yet, their algebraic and periodic nature makes them vulnerable to quantum algorithms, most notably Shor's algorithm (1994).This paper presents a detailed comparison between classical and quantum-resistant cryptographic systems with an emphasis on lattice-based systems.The Learning With Errors (LWE) problem and its variants (Ring-LWE, Module-LWE) do not have the same periodicity that makes problems like integer factorization and discrete logarithms susceptible to quantum algorithms.Furthermore, LWE problems have reductions from worst-case lattice problems and have mathematical proofs of quantum resistance.Due to the vulnerability of ECDSA algorithms for cryptocurrencies, it is estimated that current cryptocurrencies will no longer be secure once quantum computer technology matures within the next 10-30 years, potentially compromising holdings estimated at between $260 billion and $390 billion as of August 2026.The implications of cryptanalysis on public key cryptography systems motivate mathematical recommendations regarding the security of current cryptosystems and the need for a shift to post-quantum cryptographic standards.
Contemporary cryptographic algorithms are resistant to the strongest threats to cybersecurity and high-profile cyber-attacks. In recent times, information security scientists and researchers had developed various cryptographic schemes that defeated attacks using the most sophisticated (in terms of processor speed) classical computer. However, this resistance will soon erode with the arrival of quantum computers. In this paper, we profiled quantum computers and quantum algorithms based on their widely believed threat against currently secure cryptographic primitives. We found that Grover’s and Shor’s quantum-based algorithms actually pose a threat to the continued security of symmetric cryptosystems (e.g. 128-bit AES) and asymmetric (public key) cryptosystems (e.g. RSA, Elgamal, elliptic curve Diffie Hellman (ECDH), etc.) respectively.We discovered that the source of the algorithms’ cryptanalytic power against the current systems, stems from the fact that they (Grover and Shor) both equipped their respective algorithms with a quantum circuit component that can execute the oracle in parallel by applying a single circuit to all possible states of an n-qubit input. With this exponential level of processing characteristic of quantum computers and quantum-based algorithms, it is easy for the current cryptosystems to be broken since the algorithms can existentially solve the underlying mathematical problems such as integer factorization, discrete logarithm problem and elliptic curve problem, which formed the basis of the security of the affected cryptosystems. Based on this realization and as part of our readiness for a post quantum era, we explored other mathematical structures (lattices, hashes, codes, isogenies, high entropy-based symmetric key resistance, and multivariate quadratic problems) whose hardness could surpass the cryptanalytic nightmare posed by quantum computers and quantum-based algorithms. Our contribution is that, based on the findings of this research work, we can confidently assert that all hope is not lost for organizations heavily relying on protocols and applications like HTTPS, TLS, PGP, Bitcoin, etc., which derived their security from the endangered cryptosystems.
Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial encryption, these steps can be taken immediately to ensure that the impending development of large quantum computers does not compromise sensitive data.
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.