There have been a lot of researches about algebric analysis of AES. In this paper, we turned to quantum algorithm to analyze security of AES-128 against the modified HHL algorithm, which is a quantum algorithm used to get classical solutions of multivariate equation system. We constructed two types of equation systems of AES, and solved them with several variants of HHL algorithms respectively. The resulting complexities involved the condition number are given. We analyzed the reasons for the different complexity of the two equation systems and their solution methods, and pointed out that the combination of the boolean equation system and (the improved) BoolSol is more threatening to AES. With a lower bound on the condition number presented by Ding et al., we show that, for AES-128, HHL algorithm is difficult to achieve better attack effect than Grover algorithm. Our results have some enlightening significance for analyzing the post-quantum security of AES-like block ciphers.
There have been a lot of researches about algebric analysis of AES. In this paper, we turned to quantum algorithm to analyze security of AES-128 against the modified HHL algorithm, which is a quantum algorithm used to get classical solutions of multivariate equation system. We constructed two types of equation systems of AES, and solved them with several variants of HHL algorithms respectively. The resulting complexities involved the condition number are given. We analyzed the reasons for the different complexity of the two equation systems and their solution methods, and pointed out that the combination of the boolean equation system and (the improved) BoolSol is more threatening to AES. With a lower bound on the condition number presented by Ding et al., we show that, for AES-128, HHL algorithm is difficult to achieve better attack effect than Grover algorithm. Our results have some enlightening significance for analyzing the post-quantum security of AES-like block ciphers.
Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if FS does have solutions with any given success probability. The runtime complexity of the algorithm is polynomial in the size of FS and the condition number of FS. As a consequence, we give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are small, say polynomial in the size of FS. We apply our quantum algorithm for solving Boolean equations to the cryptanalysis of several important cryptosystems: the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large. This leads to a new criterion for designing cryptosystems that can against the attack of quantum computers: their corresponding equation systems must have large condition numbers.
In this paper we analyze for the first time the post-quantum security of AES. AES is the most popular and widely used block cipher, established as the encryption standard by the NIST in 2001. We consider the secret key setting and, in particular, AES-256, the recommended primitive and one of the few existing ones that aims at providing a post-quantum security of 128 bits. In order to determine the new security margin, i.e., the lowest number of non-attacked rounds in time less than 2128 encryptions, we first provide generalized and quantized versions of the best known cryptanalysis on reduced-round AES, as well as a discussion on attacks that don’t seem to benefit from a significant quantum speed-up. We propose a new framework for structured search that encompasses both the classical and quantum attacks we present, and allows to efficiently compute their complexity. We believe this framework will be useful for future analysis.Our best attack is a quantum Demirci-Selçuk meet-in-the-middle attack. Unexpectedly, using the ideas underlying its design principle also enables us to obtain new, counter-intuitive classical TMD trade-offs. In particular, we can reduce the memory in some attacks against AES-256 and AES-128.One of the building blocks of our attacks is solving efficiently the AES S-Box differential equation, with respect to the quantum cost of a reversible S-Box. We believe that this generic quantum tool will be useful for future quantum differential attacks. Judging by the results obtained so far, AES seems a resistant primitive in the post-quantum world as well as in the classical one, with a bigger security margin with respect to quantum generic attacks.
The advancement in the field of technology and science has rendered the classical algorithms used for securing data vulnerable to attacks by quantum computers. Post quantum cryptography aims at establishing quantum safe algorithms so that data can be secured. Advanced Encryption Standard (AES) is a symmetric key block cipher which provides security against known quantum attacks. The Shor’s and Grover’s algorithms are the quantum algorithms which have proved to break encryption provided by security mechanisms like RSA and even have the potential to break AES-128 in future. However, if key size of symmetric key security mechanisms is increased then security provided by them cannot be broken by both classical and quantum computers in near future. Quantum computers are becoming more and more prevalent, but there is still some concern about their security. In this paper, we will show that the current quantum computers in use cannot break AES-256 encryption with Grover’s algorithm. We have implemented AES-256 for encryption of files in our system and proposed a proof that the qubits used by quantum computers are not enough to break AES-256 with Grover’s algorithm. We believe that this provides strong evidence that current quantum computers are not a threat to encrypted data using AES-256. We hope this will ease concerns about using quantum computing for secure applications and encourage further development of these powerful machines.
Abstract In this paper, we analyse the impact of the HHL quantum algorithm on stream ciphers in a black-box setting. We assume a black-box access to an oracle MS M S defining the output of the stream cipher. For a state k encapsulating the key material, the value MS⋅k M S · k is the keystream (k1′,k2′,...,kN′) ( k 1 ′ , k 2 ′ , . . . , k N ′ ) generated by some stream cipher S. We translate this scenario into the quantum setting and describe how the HHL algorithm could be used to attack this construction. Further, we give simple and verifiable criteria under which a black-box attack on stream ciphers with the HHL algorithm is not efficiently feasible. Usually, these criteria follow from already known design principles for symmetric ciphers and should apply to the ciphers used today. We complement the criteria with a simple test, which confirms the resistance of said cipher. Moreover, we use our technique to test the currently used stream ciphers: Trivium, HC-128, and Salsa20.
Quantum computing poses a significant threat to classical cryptographic algorithms, particularly the Advanced Encryption Standard (AES). This study investigates the impact of Grover's algorithm on the AES S-box, a fundamental component of the AES encryption process. By leveraging quantum mechanics, Grover's algorithm can potentially reduce the time required to break AES encryption from 2128operations to 264operations, thus presenting a substantial security risk. This research aims to evaluate the feasibility of such quantum attacks on AES S-box by conducting experiments using virtual quantum simulators. The study examines the resource requirements, including the number of gates and qubits, and assesses the scalability of Grover's algorithm across different data sizes and types. The findings indicate that, while theoretically effective, the practical implementation of Grover's algorithm is currently hindered by significant resource constraints on existing quantum hardware. These results underscore the need for continued advancements in quantum technology and the development of quantum-resistant cryptographic methods to ensure data security in the quantum era. This research contributes to the understanding of quantum vulnerabilities in classical cryptography and supports the development of robust encryption strategies that can withstand future quantum attacks.
The progression of quantum computing is considered a potential threat to traditional cryptography system, highlighting the significance of post-quantum security in cryptographic systems. Regarding symmetric key encryption, the Grover algorithm can approximately halve the search complexity. Despite the absence of fully operational quantum computers at present, the necessity of assessing the security of symmetric key encryption against quantum computing continues to grow.In this paper, we implement the ARIA block cipher in a quantum circuit and compare it with previous research. Our implementation of the ARIA quantum circuit achieves over 92.5% improvement in full depth and over 98.7% improvement in Toffoli depth compared to the implementation proposed in Chauhan et al. Compared to Yang et al.’s implementation, our implementation is improved the full depth by 36.7% and the number of qubits by 8%. Additionally, we analyze the complexity of Grover’s search attack and compare it with NIST criteria. We confirm that ARIA achieves quantum security level 1, 3, and 5 (ARIA-128, 192, and 256, respectively).