Paper 2026/017

Grover-Based Quantum Attack on Atom

Abstract

In this paper, we present some research on quantum complexity measurements for applying Grover's search algorithm to recover the key of a stream cipher, Atom. As a foundational step, we propose a novel and complete quantum gate-level design of Atom. We incorporate a quantum lookup table to implement the key filtering with a specific decimal counter value during the keystream generation phase, which is absent in the only known previous work on the quantum attack against Atom. Based on the proposed design, we present an algorithm based on Grover's search to recover the key of Atom. Considering the limited qubit capacity of the IBM Qiskit simulator, the proposed search algorithm, with a round-reduced initialization phase, is simulated for 3-qubit key recovery with a probability greater than 0.9. We provide resource estimations for the proposed quantum algorithms. We also perform optimizations on the resources required by the proposed Grover oracle and present a benchmark for Grover's search algorithm on Atom. The research findings in this paper claim that Atom satisfies NIST Level 1 security.