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.
Tunneling as a quantum mechanical effect takes place in a classically forbidden region between two regions of classically allowed motion. While the term “dynamical tunneling” typically refers to tunneling of quantum states across dynamical barriers in classical phase space [1], the original problem simply intended tunneling across a potential barrier. Both types of tunneling are addressed in this chapter, with major focus on situations in which external forces make the studied systems intrinsically time-dependent and allow for a dynamical control of tunneling through potential barriers or across band gaps which are dynamically explored by the system.
Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.