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Article Dans Une Revue Journal of computational science Année : 2023

First Attempts at Cryptanalyzing a (Toy) Block Cipher by Means of Quantum Optimization Approaches

Résumé

The discovery of quantum algorithms that may impact cryptography is one of the main reasons for the rise of quantum computing. Currently, all quantum cryptanalysis techniques are purely theoretical and none of them can be executed on quantum devices already existing or available in the near term. So, this paper investigates the capability of presently existing quantum computers to attack a toy block cipher (namely the Heys cipher) using the Quantum Approximate Optimization Algorithm (QAOA) on gate-based quantum computers and a variant of the Quantum Annealing (QA) algorithm on analog quantum computers. Starting from a known-plaintext key recovery problem, we transform it into an instance of the MAX-SAT problem. For the QAOA approach, we propose two ways to implement it in a quantum circuit and try to solve it using publicly available IBM Q Experience quantum computers. For the QA approach, we compare two reductions into a Quadratic Unconstrained Binary Optimization (QUBO) instance by solving their output on D-Wave quantum annealers. The results suggest that the limited number of qubits (especially for gate-based quantum computers) requires the use of exponential algorithms to achieve the transformation of our problem into a MAX-SAT instance. Furthermore, despite encouraging simulation results on QAOA, the quantum circuits are too deep to work on nowadays (too-)noisy gate-based quantum computers. Finally, even if the QA algorithm seems better than QAOA on quantum hardware, it needs more complex instance transformations that reduce its scaling abilities. Our results show that the attack is not feasible on real hardware even in very simplified settings, at least as long as there is no significant improvement of quantum processors.
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Dates et versions

hal-04495468 , version 1 (08-03-2024)

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Luca Phab, Stéphane Louise, Renaud Sirdey. First Attempts at Cryptanalyzing a (Toy) Block Cipher by Means of Quantum Optimization Approaches. Journal of computational science, 2023, 69, pp.102004. ⟨10.1016/j.jocs.2023.102004⟩. ⟨hal-04495468⟩
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