Abstract Facing the threat of quantum computing to cryptography schemes, it is urgent to study the applications of quantum algorithms to cryptanalysis and evaluate the security of cryptographic schemes in a quantum computing environment. To do this, it is necessary to analyze the ability of cryptanalysis methods, such as integral and linear attacks, when combined with quantum algorithms. In this article, we investigate the properties of block ciphers with SPN structure and their security against a quantum adversary and apply the Bernstein-Vazirani algorithm to zero correlation linear attacks. Based on the relation between linear approximates of SPN ciphers and the dual cipher’s linear structures, we proposed a quantum algorithm that can find linear hulls with zero correlation of SPN ciphers. We show the validity of the proposed quantum algorithm and estimate the corresponding computational complexity. Implementing our quantum algorithm only costs polynomial qubits and quantum gates.
Abstract Facing the threat of quantum computing to cryptography schemes, it is urgent to study the applications of quantum algorithms to cryptanalysis and evaluate the security of cryptographic schemes in a quantum computing environment. To do this, it is necessary to analyze the ability of cryptanalysis methods, such as integral and linear attacks, when combined with quantum algorithms. In this article, we investigate the properties of block ciphers with SPN structure and their security against a quantum adversary and apply the Bernstein-Vazirani algorithm to zero correlation linear attacks. Based on the relation between linear approximates of SPN ciphers and the dual cipher’s linear structures, we proposed a quantum algorithm that can find linear hulls with zero correlation of SPN ciphers. We show the validity of the proposed quantum algorithm and estimate the corresponding computational complexity. Implementing our quantum algorithm only costs polynomial qubits and quantum gates.
Due to the powerful computing capability of quantum computers, cryptographic researchers have applied quantum algorithms to cryptanalysis and obtained many interesting results in recent years. In this paper, we study related-key attack in the quantum setting, and proposed a specific related-key attack which can recover the key of block ciphers efficiently, as long as the attacked block ciphers satisfy certain conditions. The attack algorithm employs Bernstein-Vazirani algorithm as a subroutine and requires the attacker to query the encryption oracle with quantum superpositions. Afterwards, we rigorously demonstrate the validity of the attack and analyze its complexity. Our work shows that related-key attack is quite powerful when combined with quantum algorithms, and provides some guidance for the design of block ciphers that are secure against quantum adversaries.
In this paper, we study applications of Bernstein–Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it, we propose new quantum distinguishers for the 3-round Feistel scheme and a new quantum algorithm to recover partial key of the Even–Mansour construction. Afterwards, by observing that the linear structures of a encryption function are actually high probability differentials of it, we apply our algorithm to differential analysis and impossible differential cryptanalysis respectively. We also propose a new kind of differential cryptanalysis, called quantum small probability differential cryptanalysis, based on the fact that the linear structures found by our algorithm are also the linear structure of each component function. To our knowledge, no similar method was proposed before. The efficiency and success probability of all attacks are analyzed rigorously. Since our algorithm treats the encryption function as a whole, it avoid the disadvantage of traditional differential cryptanalysis that it is difficult to extending the differential path.
Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover’s algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover’s algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of 210.5. An 8-round attack requires 179 qubits and has a time complexity of 222. Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds.
Abstract Recent research has demonstrated the potential of quantum algorithms to exploit vulnerabilities in various popular constructions, such as certain block ciphers like Feistel, Even-Mansour, and multiple MACs, within the superposition query model. In this study, we delve into the security of block ciphers against quantum threats, particularly investigating their susceptibility to cryptanalysis techniques, notably exploring quantum adaptations of differential cryptanalysis. Initially, we introduce a BV-based quantum algorithm for identifying linear structures with a complexity of O(n) O ( n ) , where n denotes the number of bits in the function. Subsequently, we illustrate the application of this algorithm in devising quantum differential cryptanalysis techniques, including quantum differential cryptanalysis, quantum small probability differential cryptanalysis, and quantum impossible differential cryptanalysis, demonstrating polynomial acceleration compared to prior approaches. By treating the encryption function as a unified entity, our algorithm circumvents the traditional challenge of extending differential paths in differential cryptanalysis.
Traditional cryptography is suffering a huge threat from the development of quantum computing. While many currently used public-key cryptosystems would be broken by Shor's algorithm, the effect of quantum computing on symmetric ones is still unclear. The security of symmetric ciphers relies heavily on the development of cryptanalytic tools. Thus, in order to accurately evaluate the security of symmetric primitives in the post-quantum world, it is significant to improve classical cryptanalytic methods using quantum algorithms. In this paper, we focus on two variants of differential cryptanalysis: truncated differential cryptanalysis and impossible differential cryptanalysis. Based on the fact that Bernstein-Vazirani algorithm can be used to find the linear structures of Boolean functions, we propose two quantum algorithms that can be used to find high-probability truncated differentials and impossible differentials of block ciphers, respectively. We rigorously prove the validity of the algorithms and analyze their complexity. Our algorithms treat all rounds of the reduced cipher as a whole and only concerns the input and output differences at its both ends, instead of specific differential characteristics. Therefore, to a certain extent, they alleviate the weakness of conventional differential cryptanalysis, namely the difficulties in finding differential characteristics as the number of rounds increases.
Block cryptanalysis has a major breakthrough in the model of superposition queries. For instance, Simon’s algorithm can efficiently break various constructions. In practice, Bernstein-Vaziran’s algorithm can also realize the periodic search of the vector function. Moreover, in some cases, it can have more advantages than the Simon’s algorithm.In the context of this study, we present an algorithm that combines Grover’s and Bernstein-Vazirani’s quantum algorithms. This algorithm empowers us to carry out key recovery attacks on Feistel structures. on Feistel structures, FX construction and Even Mansour construction. We exploit cryptosystems’ algebraic structure to launch successful key recovery attacks, considering that quantum attackers can only make classical queries. Through comparison, it can be concluded that this algorithm has stronger practicability in attacking block ciphers.