At present, quantum algorithm is a development direction of the early quantum algorithm in thinking. They are generally considered to be largely theoretical because the problems they solve are almost useless. In this paper, the applications of quantum algorithms in quantum key distribution, error correction, authentication and other fields are analyzed. Simon quantum algorithm benefits from the parallelism of quantum algorithms, and its fast finding function period property is used to construct a variety of attack forms, such as discrimination attack, key recovery attack, sliding attack, quantum forgery attack and so on. Simon algorithm uses register conversion to calculate the period in the process of key authentication, and applies this periodic feature to the interrogator in the process of key authentication, so as to achieve accurate key authentication.
At present, quantum algorithm is a development direction of the early quantum algorithm in thinking. They are generally considered to be largely theoretical because the problems they solve are almost useless. In this paper, the applications of quantum algorithms in quantum key distribution, error correction, authentication and other fields are analyzed. Simon quantum algorithm benefits from the parallelism of quantum algorithms, and its fast finding function period property is used to construct a variety of attack forms, such as discrimination attack, key recovery attack, sliding attack, quantum forgery attack and so on. Simon algorithm uses register conversion to calculate the period in the process of key authentication, and applies this periodic feature to the interrogator in the process of key authentication, so as to achieve accurate key authentication.
With the development of quantum technology, quantum computing has an increasingly significant impact on cryptanalysis. Several quantum algorithms, such as Simon’s algorithm, Grover’s algorithm, the Bernstein–Vazirani algorithm, Shor’s algorithm, and the Grover-meets-Simon algorithm, have been proposed successively. However, almost all cryptanalysis is based on the quantum chosen-plaintext attack (qCPA) model. This paper focuses on a powerful cryptanalytic model, quantum related-key attack (qRKA), and proposes a strategy of qRKAs against symmetric ciphers using Simon’s algorithm. We construct a periodic function to efficiently recover the secret key of symmetric ciphers if the attacked symmetric ciphers satisfy Simon’s promise, and present the complexity analysis on specific symmetric ciphers. Then, we apply qRKA to the Even–Mansour cipher and SoEM construction, recover their secret keys, and show their complexity comparison in the distinct attack models. This work is of great significance for the qRKA cryptanalysis of existing provably secure cryptographic schemes and the design of future quantum secure cryptographic schemes.
The work is devoted to the study of the problems of using the technology of quantum distribution of secret keys, namely the problems of using and forming new secret keys, based on the generation of quantum keys and the distribution of new keys in networks of complex topologies. In secure communication systems, information is transmitted over public networks, and thus is available to a potential attacker for carrying out various types of attacks. A potential attacker is able to store encrypted data transmitted over network channels, and attempt to decrypt it later, when technical means and attacks on information protection algorithms will allow, in an acceptable time, to carry out decryption. This is the basic principle of "Store now, decrypt later", which is one of the problems of information protection systems. For block ciphers, there is a parameter - the key load, which limits the amount of information that one key can process using the data protection algorithm. NIST recommends a time frame for using secret keys, calculated in years. In the field of information security, there are more significant restrictions on the key load, related to the number of blocks that can be processed by one key, caused by attacks on block ciphers. With these restrictions, there is a need to regularly change the secret key used, and search for options for generating and delivering keys between two network nodes that organize a secure information transmission channel. Changing the secret key to a new key, independent of the previous one, allows you to protect the transfer of confidential information when the key used is compromised. The technology of creating a quantum computer allows you to effectively attack known algorithms for generating secret keys based on the factorization of large numbers or the complexity of calculating a discrete logarithm. The quantum Shor algorithm [5, 6] allows you to solve these problems in polynomial time, so it is necessary to look for alternative solutions to the problem of regular changes in the network channel of the secret key in a pair of nodes. It is important to take into account the need to ensure the quality of Perfect forward secrecy, when the master key is compromised, all subsequent secret keys must not be compromised. To achieve this property of modern encryption algorithms, there is a periodic update of master keys. To prevent the accumulation of information, to successfully carry out attacks by the attacker and to comply with the load requirement on the secret key, it is necessary to solve the problem of regular changes of the secret, and regular generation/delivery of keys to network nodes. Given the urgent needs that are intensively developing today in the secure and high-speed transmission of information, and no less, the rapid growth of technical capabilities, there is a need to develop options in advance that will ensure the security of information during transmission. Regular change, in geographically dispersed data protection systems, of common secret keys, in the case of ensuring the independence of secret keys, allows successfully solving the task.
Tweakable block ciphers are more flexible than traditional block ciphers and widely used in modes of operation such as MAC and authenticated encryption. With the development of quantum computing, the threat of quantum algorithms to the security of cryptosystems is increasing. Research shows that some classical secure symmetric cryptographic constructions or schemes become vulnerable to the quantum attacks based on Simon's algorithm. This paper studies the security of tweakable block cipher constructions under quantum attacks based on Simon's algorithm, summarizes the quantum attack methods of Simon's algorithm and quantum-resistant constructions, and provides methods to enhance the quantum security of tweakable block ciphers.
Abstract Due to its innovative and performance advantages, Prøst‐COPA and Prøst‐OTR have attracted widespread attention. For the Prøst‐COPA without associated data and with associated data, the corresponding quantum key recovery attacks are proposed using Simon's algorithm, respectively. In the first scenario, the messages are used to calculate the Message Authentication Code (MAC) and construct a period function to recover the secret parameter . Then, utilizing ciphertext, a periodic function is constructed with a periodic value equal to the key value. MAC is calculated from messages and the associated data in the second scenario. Considering the impact of the associated data on the periodicity of the function, the messages are treated as a constant and further construct two periodic functions to recover the secret parameter and the key. For Prøst‐OTR, by constructing two periodic functions using two tags with different numbers of message blocks, the secret parameter can be recovered, and then the key can be recovered using Simon's algorithm. Compared to the classical attacks, the quantum‐based methods only require quantum queries (where is the message block size), resulting in an exponential speed acceleration and the success probability of the method is close to 1. These methods also show a lower query complexity than the state‐of‐the‐art quantum methods.
Cryptography has long been an essential tool in safeguarding digital communication and securing sensitive information. As technology has progressed, so has the complexity of the methods used to protect our data. In the wake of quantum computing's rise, traditional cryptographic systems face serious challenges, demanding a new understanding of how quantum algorithms could both undermine and enhance security. Chapter 1 deals with the Basics of Cryptography lays the groundwork by introducing classical cryptography, tracing its evolution from ancient ciphers to modern cryptosystems. In Chapter 2, readers are introduced to Quantum Algorithms, the principles of quantum mechanics relevant to computing, including qubits, superposition, and entanglement. The Chapter 3 focuses on Shor’s algorithm, a landmark quantum algorithm that threatens the security of widely used public-key cryptosystems like RSA and ECC. In Chapter 4 Grover’s Algorithm is examined in the context of brute-force attacks on symmetric key cryptography. Chapter 5 focusing on Simon’s Algorithm and its role in breaking cryptographic primitives through structure exploitation. In Chapter 6 a broader discussion about Cryptographic Implications of Quantum Computing is given on how quantum computing affects modern cryptographic systems. Finally, in Chapter 7, the future of cryptography in the quantum era is discussed.
Present cryptography algorithms are based on mathematical problem such as factoring two large prime numbers and N vs NP problem. But computing power and evolution in mathematics increases day by day so it’s easy to reverse one way function to quickly such as that of factoring large integers. So the solution is to build a cryptosystem which secure our communication even the computing power is to high so we introduce quantum physics in cryptography which lead to evaluation of quantum cryptography. Quantum cryptography one of the emerging topics in field of computer industry. This paper is an attempt to review fundamentals of quantum cryptography and also analyses few application areas of quantum cryptography and it’s limitation.