Quantum Circuits for Quantum Algorithms Shor's factoring algorithm and solving discrete log problem. Cryptanalysis which makes encryption and digital signature schemes such as RSA and Elliptic Curve Cryptography (ECC) vulnerable to quantum attacks. Quantum algorithms such as class number and triangle finding algorithms, and scientific algorithms in quantum chemistry.
Quantum Circuits for Quantum Algorithms Shor's factoring algorithm and solving discrete log problem. Cryptanalysis which makes encryption and digital signature schemes such as RSA and Elliptic Curve Cryptography (ECC) vulnerable to quantum attacks. Quantum algorithms such as class number and triangle finding algorithms, and scientific algorithms in quantum chemistry.
In quantum cryptanalysis, Shor's algorithm provides exponential acceleration of solving factorization problems, discrete logarithm problem, and elliptic curve discrete logarithm problems, widely used in cryptographic applications in cyberspace. Shor's quantum algorithm can potentially crack most protocols and schemes of asymmetric encryption (public key cryptography). In general, all known quantum algorithms can be divided into two groups: providing exponential gain (for example, Shor's algorithm) and providing quadratic gain (for example, Grover's algorithm). Particular attention is paid to the Shor quantum algorithm and other polynomial algorithms capable of solving cryptanalysis problems with the required reliability and complexity in polynomial time. For quantum computing, all cryptographies are divided into quantum-secure and quantum-insecure. Algorithms and cryptosystems of symmetric encryption are attributed to quantum-secure but with at least twice the key length increased. This chapter presents an overview of the concepts discussed in the subsequent chapters of this book.
Today we witness an explosive growth in attention to Q-computing. Q-computing technologies, along with artificial intelligence (AI) and machine learning (ML) technologies, cloud and foggy computing, as well as technologies for collecting and streaming processing of Big Data and ETL, are constantly leading the lists of ""end-to-end"" information technologies for the digital economy of technologically developed countries of the world. One of the main reasons for this is the potential ability of quantum computers to solve some computational problems more efficiently than any of the most modern classical computers of the von Neumann architecture (supercomputers). The most expressive and interesting, from an applied point of view, examples of such problems are integer factorization, effectively performed by Shor's quantum algorithm, as well as record search in an unordered database, effectively solved by Grover's algorithm. This monograph contains the best practice for solving problems of quantum cryptanalysis to improve cyber security and resilience of the digital economy. The book discusses well-known and author's software implementations of promising quantum Shor algorithms, Grover, Simon et al. Shor's algorithm provides exponential acceleration of solving factorization problems, discrete logarithm problems (DLPs) and elliptic curve discrete logarithm problems (ECDLPs). The mentioned tasks are widely used in TLS, SSH or IPsec cryptographic applications of Internet/Intranet and IIoT/IoT networks, communication protocols based on Diffie–Hellman key agreements (dependent on the strength of the DLP or ECDLP), digital signature algorithms (DSA, ECDSA, RSA-PSS), public key encryption algorithms (El Gamal, RSA-OAEP), etc. In other words, Shor's quantum algorithm is potentially capable of violating these algorithms, and with them all the mechanisms of public-key cryptography deployed in cyberspace.
Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum computers it is important to have an estimate of the resources needed to implement these quantum attacks. For attacking symmetric cryptography and hash functions, generic quantum attacks are substantially less powerful than they are for today's public-key cryptography. So security will degrade gradually as quantum computing resources increase. At present, there is a substantial resource overhead due to the cost of fault-tolerant quantum error correction. We provide estimates of this overhead using state-of-the-art methods in quantum fault-tolerance. We use state-of-the-art optimized circuits, though further improvements in their implementation would also reduce the resources needed to implement these attacks. To bound the potential impact of further circuit optimizations we provide cost estimates assuming trivial-cost implementations of these functions. These figures indicate the effective bit-strength of the various symmetric schemes and hash functions based on what we know today (and with various assumptions on the quantum hardware), and frame the various potential improvements that should continue to be tracked. As an example, we also look at the implications for Bitcoin's proof-of-work system. For many of the currently used asymmetric (public-key) cryptographic schemes based on RSA and elliptic curve discrete logarithms, we again provide cost estimates based on the latest advances in cryptanalysis, circuit compilation and quantum fault-tolerance theory. These allow, for example, a direct comparison of the quantum vulnerability of RSA and elliptic curve cryptography for a fixed classical bit strength.
Quantum-resistant cryptography develops cryptographic protocols and algorithms that can withstand attacks from quantum computers. Quantum computers can solve certain mathematical problems much faster than classical computers, making current encryption techniques like RSA and ECC vulnerable to quantum algorithms such as Shor's algorithm. To address this, quantum-resistant cryptography focuses on creating new algorithms based on mathematical problems that are difficult for quantum computers to solve efficiently. Examples include lattice-based, code-based, hash-based, and multivariate polynomial cryptography. The National Institute of Standards and Technology (NIST) is leading efforts to standardize these algorithms to ensure they are compatible with various systems and applications. While these quantum-resistant algorithms offer protection, they may involve higher computational complexity and larger key sizes compared to traditional methods, posing implementation challenges that ongoing research aims to address.
Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum computers it is important to have an estimate of the resources needed to implement these quantum attacks. For attacking symmetric cryptography and hash functions, generic quantum attacks are substantially less powerful than they are for today's public-key cryptography. So security will degrade gradually as quantum computing resources increase. At present, there is a substantial resource overhead due to the cost of fault-tolerant quantum error correction. We provide estimates of this overhead using state-of-the-art methods in quantum fault-tolerance. We use state-of-the-art optimized circuits, though further improvements in their implementation would also reduce the resources needed to implement these attacks. To bound the potential impact of further circuit optimizations we provide cost estimates assuming trivial-cost implementations of these functions. These figures indicate the effective bit-strength of the various symmetric schemes and hash functions based on what we know today (and with various assumptions on the quantum hardware), and frame the various potential improvements that should continue to be tracked. As an example, we also look at the implications for Bitcoin's proof-of-work system. For many of the currently used asymmetric (public-key) cryptographic schemes based on RSA and elliptic curve discrete logarithms, we again provide cost estimates based on the latest advances in cryptanalysis, circuit compilation and quantum fault-tolerance theory. These allow, for example, a direct comparison of the quantum vulnerability of RSA and elliptic curve cryptography for a fixed classical bit strength.
The advent of quantum computing poses an existential threat to classical cryptographic systems. Shor’s algorithm (1994) can factor large integers and compute discrete logarithms in polynomial time, breaking widely used schemes like RSA, ECC, and Diffie-Hellman. This paper surveys the state-of-the-art in quantum cryptanalysis, examining its impact on symmetric and asymmetric cryptography, recent progress in quantum attacks, and defenses via post-quantum cryptography (PQC). We analyze key quantum algorithms (Shor’s, Grover’s), their real-world feasibility given current hardware (NISQ-era limitations), and emerging PQC standards (NIST’s CRYSTALS-Kyber, Dilithium). We also discuss novel attack vectors (e.g., hybrid quantum-classical cryptanalysis) and future research directions.