Abstract The quantum annealing algorithm leverages the global optimization capability of its unique quantum tunneling effect, making it well-suited for solving NP-hard combinatorial optimization problems. This research investigates its potential in symmetric cipher attacks, exemplified by the Mixed Integer Linear Programming (MILP) problems in symmetric ciphers. None of Google’s three generations of quantum chips can be used for cryptographic attacks. Due to the complexity of symmetric ciphers, attacks on real quantum computers have mostly focused on simplified versions, while key NP-hard problems in full-scale versions remain untouched. Amid slow progress in quantum computing for cryptographic attacks, this study proposes a novel Hybrid Quantum-Classical Attack (HyQCA) algorithm. In HyQCA, the propagation rules of integral properties in symmetric ciphers are encoded as MILP problems, leveraging the global optimization capability of quantum tunneling to escape local minima. Using the PUFFIN algorithm to validate HyQCA’s feasibility, we design the MILP model for PUFFIN and solve it on a real D-Wave quantum computer, successfully obtaining a 9-round integral distinguisher. It is surprising that, for the attack on the full-scale version of PUFFIN, the results achieved are comparable to traditional mathematical methods in terms of the same number rounds. This paper preliminarily validates the practical feasibility of quantum annealing in symmetric cipher attacks.
Abstract The quantum annealing algorithm leverages the global optimization capability of its unique quantum tunneling effect, making it well-suited for solving NP-hard combinatorial optimization problems. This research investigates its potential in symmetric cipher attacks, exemplified by the Mixed Integer Linear Programming (MILP) problems in symmetric ciphers. None of Google’s three generations of quantum chips can be used for cryptographic attacks. Due to the complexity of symmetric ciphers, attacks on real quantum computers have mostly focused on simplified versions, while key NP-hard problems in full-scale versions remain untouched. Amid slow progress in quantum computing for cryptographic attacks, this study proposes a novel Hybrid Quantum-Classical Attack (HyQCA) algorithm. In HyQCA, the propagation rules of integral properties in symmetric ciphers are encoded as MILP problems, leveraging the global optimization capability of quantum tunneling to escape local minima. Using the PUFFIN algorithm to validate HyQCA’s feasibility, we design the MILP model for PUFFIN and solve it on a real D-Wave quantum computer, successfully obtaining a 9-round integral distinguisher. It is surprising that, for the attack on the full-scale version of PUFFIN, the results achieved are comparable to traditional mathematical methods in terms of the same number rounds. This paper preliminarily validates the practical feasibility of quantum annealing in symmetric cipher attacks.
Quantum computing is generally considered non-threatening to symmetric ciphers. Quantum attacks on symmetric ciphers require a thorough analysis of their internal structures, posing considerable difficulties and challenges. As of 2023, Google's quantum supremacy chip, Sycamore, is still incapable of cryptanalysis. Leveraging D-Wave's quantum annealing exploits the unique quantum tunneling effect, providing an edge in solving combinatorial optimization problems. It can be regarded as a class of artificial intelligence algorithm that can achieve global optimization. We propose a quantum heuristic symmetric cipher attack algorithm for substitution-permutation network (SPN) symmetric ciphers, which transforms the plaintext-ciphertext propagation rules within SPN structure into the problem of solving a constrained quadratic model (CQM). A novel reduction algorithm is employed to eliminate redundant constraint conditions. The D-Wave Advantage quantum computer is used to recover the encryption sub-keys. Using the quantum approximate optimization algorithm, IBM Q Experience can only recover two rounds of the Heys Cipher sub-key, whereas D-Wave Advantage achieves complete key recovery, validating its potential in quantum symmetric cipher attacks.
This paper investigates the application of scalable quantum annealing to solve computationally challenging combinatorial optimization problems. The core idea is to map these problems into a quantum annealing framework, leveraging quantum tunneling to efficiently explore the solution space and ultimately converge to the global optimum. The research addresses the existing limitations in the scalability of quantum annealing, proposing a novel approach to tackle NP-hard problems effectively. We will demonstrate the potential of this methodology through a theoretical analysis and formulation of the quantum annealing algorithm, focusing on key parameters and their impact on solution quality and runtime. The ultimate goal is to provide a foundational understanding of applying quantum annealing to combinatorial optimization, paving the way for future developments and practical implementations. This work introduces a new framework for approaching complex optimization problems by harnessing the unique properties of quantum mechanics.
The computational hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP) directly determines Elliptic-Curve Cryptography (ECC) security. Quantum Annealing (QA) leverages its unique tunneling effects to effectively escape local optima. This paper proposes a quantum-annealing-based computational framework for attacking ECDLP by integrating QA with the index calculus method, achieving a quantum-solving attack on ECDLP. First, a relation-generation method based on Semaev summation polynomials is used to map the complex elliptic-curve point-addition constraints onto an Ising Hamiltonian. Next, by restructuring the penalty-term formulation and applying dynamic coefficient optimization, the parameter scale of the Ising Hamiltonian is compressed by 80%, thereby improving the QA success probability. Finally, the ECDLP is successfully modeled and solved on the D-Wave Advantage2 quantum computer. Experimental results demonstrate that the proposed quantum computing framework solves a 16-bit prime-field elliptic curve ECDLP on real quantum hardware, representing the highest experimental record publicly reported to date internationally, and further validating the practical attack potential and scalability of QA in cryptanalytic scenarios.
A primary challenge of computational science is solving NP-hard optimization problems since they are too complicated and cannot be effectively solved deterministically in large instances. Even though quantum computing can solve these problems with the help of its key properties quantum parallelism and tunneling, the modern hardware is yet not sufficiently developed. In this case, QICAs are considered as a new method in which the key aspects of quantum mechanics, such as superposition, entanglement, interference and tunneling are replicated in classical, non-quantum computers. It aims to attain rapid optimization of NP-hard problems through a hybrid approach that combines cartography-based exploration, variable state reduction with tensor networks as well as an inclusion of a variant-based approach inspired by QAOA. A number of standard problems are used to test the model, e.g., the Traveling Salesman Problem (TSP), the 0/1 Knapsack Problem and Max-Cut Problem. Genetic Algorithms, Simulated Annealing and Ant Colony Optimization trials all concur that QICA converges to superior solutions much faster and it can nonetheless handle bigger-sized problems. More precisely, the algorithm provides better approximation results as well as lesser computing power requirements, thus demonstrating the effectiveness of quantum-inspired methods in the case of classical systems. They establish the fact that QICAs have the potential to solve challenging optimization problems, particularly in the cases where quantum machines are absent or inaccessible. The way of solving the problem represented in the study is quite innovative and serves as a bridge between the theory of quantum and practical implementation in the optimization field.
The security level of a cipher is a key parameter. While general-purpose quantum computers significantly threaten modern symmetric ciphers, other quantum approaches like quantum annealing have been less concerning. However, this paper argues that a quantum annealer specifically designed to attack Grain 128 and Grain 128a ciphers could soon be technologically feasible. Such an annealer would require 5,751 (6,761) qubits and 77,496 (94,865) couplers, with a qubit connectivity of 225 (245). This work also shows that modern stream ciphers like Grain 128 and Grain 128a may be vulnerable to quantum annealing attacks. Although the exact complexity of quantum annealing is unknown, heuristic estimates suggest that for many problems withNvariables, aNexponential advantage over simulated annealing may hold. We detail how to transform algebraic attacks on Grain ciphers into the QUBO problem, making our attack potentially more efficient than classical brute-force methods. We demonstrate that applying our attack to rescaled Grain cipher versions, Grainland Grainla, overtakes brute-force and Grover’s attacks for sufficiently largel, assuming quantum annealing’s exponential benefit over simulated annealing.
While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical relevance, and classical counterparts outperform them. To practically benefit from quantum architecture, one has to identify problems and algorithms with favorable scaling and improve on corresponding limitations depending on available hardware. For this reason, we developed an algorithm that solves integer linear programming problems, a classically NP-hard problem, on a quantum annealer, and investigated problem and hardware-specific limitations. This work presents the formalism of how to map ILP problems to the annealing architectures, how to systematically improve computations utilizing optimized anneal schedules, and models the anneal process through a simulation. It illustrates the effects of decoherence and many body localization for the minimum dominating set problem, and compares annealing results against numerical simulations of the quantum architecture. We find that the algorithm outperforms random guessing but is limited to small problems and that annealing schedules can be adjusted to reduce the effects of decoherence. Simulations qualitatively reproduce algorithmic improvements of the modified annealing schedule, suggesting the improvements have origins from quantum effects.