Quantum Resource Analysis of Low-Round Keccak/SHA-3 Preimage Attack: From Classical 2^57.8 to Quantum 2^28.9 using Qiskit Modeling

Abstract

This paper presents a hardware-conscious analysis of the quantum acceleration of the classical 3-round Keccak-256 preimage attack using Grover's Algorithm. While the theoretical quantum speed-up from T_cl=2^{57.8} (classical) to T_qu = 2^{28.9} (quantum) is mathematically sound, the practical implementation overhead is so extreme that attacks remain wholly infeasible in both resource and runtime dimensions. Using Qiskit-based circuit synthesis, we derive that a 3-round Keccak quantum oracle requires: 9,600 Toffoli gates (with uncomputation for reversibility); 3,200 logical qubits (1,600 state + 1,600 auxiliary); 7.47 * 10^{13} total 2-qubit gates (full Grover search); 3.2 million physical qubits (with quantum error correction)PROHIBITIVE; 0.12 years (43 days) to 2,365+ years execution time, depending on machine assumptions. These barriers -- particularly the physical qubit requirements, circuit depth, and error accumulation -- render the quantum attack infeasible for any foreseeable quantum computer. Consequently, SHA-3 security is not threatened by quantum computers for preimage attacks. We emphasize the critical importance of hardware-aware complexity analysis in quantum cryptanalysis: the elegant asymptotic theory of Grover's Algorithm hides an engineering overhead so prohibitive that the quantum approach becomes infeasible from both resource and implementation perspectives.