Grover on SM3

Abstract

Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To perform Grover’s search algorithm, the target algorithm should be implemented in a quantum circuit. For this reason, we propose an optimal SM3 hash function (Chinese standard) in a quantum circuit. We focused on minimizing the use of qubits and reducing the use of quantum gates. To do this, the on-the-fly approach is utilized for message expansion and compression functions. In particular, the previous value is restored and used without allocating new qubits in the permutation operation. Finally, we estimate the quantum resources required for the quantum pre-image attack based on the proposed SM3 hash function implementation in the quantum circuit.