This paper explores the optimization of quantum circuits for Argon2, a memory-hard function used in password hashing applications. With the rise of quantum computers, the security of classical cryptographic systems is at risk. This paper emphasizes the need to accurately measure the quantum security strength of cryptographic schemes through highly optimized quantum circuits for the target cryptography algorithm. The proposed method focuses on two perspectives: qubit reduction (qubit-optimized quantum circuit) and depth reduction (depth-optimized quantum circuit). The qubit-optimized quantum circuit was designed to find a point where an appropriate inverse is possible and reuses the qubit through the inverse to minimize the number of qubits. The start and end points of the inverse are determined by identifying a point where qubits can be reused with minimal computation. The depth-optimized quantum circuit reduces the depth of the quantum circuit by using the minimum number of qubits necessary without performing an inverse operation. The trade-off between qubit and depth is confirmed by modifying the internal structure of the circuits and the quantum adders. The qubit optimization achieved up to a 12,229 qubit reduction, while the depth optimization resulted in an approximately 196,741 (approximately 69.02%) depth reduction. In conclusion, this research demonstrates the importance of implementing and analyzing quantum circuits from multiple optimization perspectives. The results contribute to the post-quantum strength analysis of Argon2 and provide valuable insights for future research on optimized quantum circuit design, considering the appropriate trade-offs of quantum resources in response to advancements in quantum computing technology.
This paper explores the optimization of quantum circuits for Argon2, a memory-hard function used in password hashing applications. With the rise of quantum computers, the security of classical cryptographic systems is at risk. This paper emphasizes the need to accurately measure the quantum security strength of cryptographic schemes through highly optimized quantum circuits for the target cryptography algorithm. The proposed method focuses on two perspectives: qubit reduction (qubit-optimized quantum circuit) and depth reduction (depth-optimized quantum circuit). The qubit-optimized quantum circuit was designed to find a point where an appropriate inverse is possible and reuses the qubit through the inverse to minimize the number of qubits. The start and end points of the inverse are determined by identifying a point where qubits can be reused with minimal computation. The depth-optimized quantum circuit reduces the depth of the quantum circuit by using the minimum number of qubits necessary without performing an inverse operation. The trade-off between qubit and depth is confirmed by modifying the internal structure of the circuits and the quantum adders. The qubit optimization achieved up to a 12,229 qubit reduction, while the depth optimization resulted in an approximately 196,741 (approximately 69.02%) depth reduction. In conclusion, this research demonstrates the importance of implementing and analyzing quantum circuits from multiple optimization perspectives. The results contribute to the post-quantum strength analysis of Argon2 and provide valuable insights for future research on optimized quantum circuit design, considering the appropriate trade-offs of quantum resources in response to advancements in quantum computing technology.
Quantum computing advancements pose security challenges for cryptography. Specifically, Grover’s search algorithm affects the reduction in the search complexity of symmetric-key encryption and hash functions. Recent efforts have been made to estimate the complexity of Grover’s search and evaluate post-quantum security. In this paper, we propose a depth-optimized quantum circuit implementation for ASCON, including both symmetric-key encryption and hashing algorithms, as a part of the lightweight cryptography standardization by NIST (National Institute of Standards and Technology). As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme, which is a symmetric-key algorithm. Also, our quantum circuit implementation of the ASCON-HASH achieves a reduction of more than 88.9% in the Toffoli depth and more than 80.5% in the full depth compared to the previous work. As per our understanding, the most effective strategy against Grover’s search involves minimizing the depth of the quantum circuit for the target cipher. We showcase the optimal Grover’s search cost for ASCON and introduce a proposed quantum circuit optimized for depth. Furthermore, we utilize the estimated cost to evaluate post-quantum security strength of ASCON, employing the relevant evaluation criteria and the latest advancements in research.
This paper presents an optimized quantum circuit for the scrypt cryptographic algorithm. We applied various optimization techniques to reduce the DW cost, which is the product of the time and space complexity of quantum circuits. In our proposed method, the number of ancilla qubits was significantly reduced through the use of optimized inverse operations, while the depth was minimized by implementing parallel structures. For the SHA-256, we devised a structure that achieves a substantial reduction in the number of ancilla qubits with only a slight increase in quantum circuit depth. By cleaning the dirty ancilla qubits used in the previous round through inverse operations, we enabled their reuse in each subsequent round. Specifically, we reduced the number of 8128 ancilla qubits, achieving this with an increase of only 6 in the full depth of the quantum circuit. Additionally, within Salsa20/8 in SMix, we reused qubits through inverse operations and performed some operations in parallel to reduce both the number of qubits and the overall quantum circuit depth. Finally, our quantum circuit for scrypt demonstrates a significant reduction in the width (the number of qubits) with only a minimal increase in the full quantum circuit depth.
To build a secure cryptography system in the post-quantum era, one must find the minimum security parameters against quantum attacks by estimating the quantum resources of a fault-tolerant quantum computer. In a fault-tolerant quantum computer, errors must reach an acceptable level for practical uses according to error detection and error correction processes. However, these processes utilize additional quantum resources. As the depth of the quantum circuit increases, the computation time per qubit increases together with the processing errors. Therefore, in terms of errors in quantum circuits, it is a fundamental requirement to reduce the depth by trading off the number of qubits. This paper proposes novel low-depth SHA3 quantum circuit implementations for fault-tolerant quantum computers to reduce errors. The proposed SHA3 quantum circuit was implemented with the aim of optimizing the quantum circuit depth through a trade-off between the number of qubits, the quantum gate, and the quantum depth in each function. Compared to other state-of-art techniques, the proposed method achieved T-depth and full-depth reductions of 30.3% and 80.05%, respectively. We believe that this work will contribute to the establishment of minimum security parameters for SHA3 in the quantum era.
Quantum computers have the potential to solve a number of hard problems that are believed to be almost impossible to solve by classical computers. This observation has sparked a surge of research to apply quantum algorithms against the cryptographic systems to evaluate its quantum resistance. In assessing the security strength of the cryptographic algorithms against the upcoming quantum threats, it is crucial to precisely estimate the quantum resource requirement (generally in terms of circuit depth and quantum bit count). The National Institute of Standards and Technology by the US government specified five quantum security levels so that the relative quantum strength of a given cipher can be compared to the standard ones. There have been some progress in the NIST-specified quantum security levels for the odd levels (i.e., 1, 3 and 5), following the work of Jaques et al. (Eurocrypt’20). However, levels 2 and 4, which correspond to the quantum collision finding attacks for the SHA-2 and SHA-3 hash functions, quantum attack complexities are arguably not well-studied. This is where our article fits in. In this article, we present novel techniques for optimizing the quantum circuit implementations for SHA-2 and SHA-3 algorithms in all the categories specified by NIST. After that, we evaluate the quantum circuits of target cryptographic hash functions for quantum collision search. Finally, we define the quantum attack complexity for levels 2 and 4, and comment on the security strength of the extended level. We present new concepts to optimize the quantum circuits at the component level and the architecture level.
This paper presents quantum cryptanalysis for binary elliptic curves from a time-efficient implementation perspective (i.e., reducing the circuit depth), complementing the previous research that focuses on the space-efficiency perspective (i.e., reducing the circuit width). To achieve depth optimization, we propose an improvement to the existing circuit implementation of the Karatsuba multiplier and FLT-based inversion, then construct and analyze the resource in the Qiskit quantum computer simulator. The proposed multiplier architecture, which improves the quantum Karatsuba multiplier from the previous study, reduces the depth and yields a lower number of CNOT gates that bound toO(nlog2(3))while maintaining a similar number of Toffoli gates and qubits. Furthermore, our improved FLT-based inversion reduces CNOT count and overall depth, with a tradeoff of higher qubit size. Finally, we employ the proposed multiplier and FLT-based inversion for performing quantum cryptanalysis of binary point addition as well as the complete Shor’s algorithm for the elliptic curve discrete logarithm problem (ECDLP). As a result, apart from depth reduction, we are also able to reduce up to 90% of the Toffoli gates required in a single-step point addition compared to prior work, leading to significant improvements and giving new insights on quantum cryptanalysis for a depth-optimized implementation.
Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover’s algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover’s search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works.