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.

One of the key research focuses in quantum annealing is the design and optimization of annealing schedules to enhance computational efficiency, enabling large-scale applications. QuantumZero (QZero) pioneered the integration of Monte Carlo Tree Search (MCTS) with neural networks to autonomously design annealing schedules within a hybrid quantum-classical framework. This approach is distinguished by its ability to enhance the performance of Monte Carlo Tree Search through the integration of neural networks, enabling the efficient design of annealing paths even with limited annealing time. The paper presents an optimized QZero method based on intuitive reasoning theory and MindSpore, which further enhances QZero’s ability to conserve computational resources and resist noise. In terms of learning efficiency, the optimized QZero algorithm improves the convergence speed of the neural network by 93% compared to the original algorithm. Notably, the average number of quantum annealing queries required to achieve 99% fidelity is reduced by 45.09%. Regarding noise resistance, the optimized QZero algorithm requires 34.27% fewer quantum annealing queries to reach 99% fidelity compared to the original algorithm. The optimized QZero algorithm demonstrates strong competitiveness in optimizing quantum annealing schedules.

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.

Integer factorization, the core of the Rivest−Shamir−Adleman (RSA) attack, is an exciting but formidable challenge. As of this year, a group of researchers’ latest quantum supremacy chip remains unavailable for cryptanalysis. Quantum annealing (QA) has a unique quantum tunneling advantage, which can escape local extremum in the exponential solution space, finding the global optimal solution with a higher probability. Consequently, we consider it an effective method for attacking cryptography. According to Origin Quantum Computing, QA computers are able to factor numbers several orders of magnitude larger than universal quantum computers. We try to transform the integer factorization problem in RSA attacks into a combinatorial optimization problem by using the QA algorithm of D-Wave quantum computer, and attack RSA-2048 which is composed of a class of special integers. The experiment factored this class of integers of size 2²⁰⁴⁸, N=p×q. As an example, the article gives the results of 10 RSA-2048 attacks in the appendix. This marks the first successful factorization of RSA-2048 by D-Wave quantum computer, regardless of employing mathematical or quantum techniques, despite dealing with special integers, exceeding 2¹⁰⁶¹−1 of California State University. This experiment verifies that the QA algorithm based on D-Wave is an effective method to attack RSA.