Resource-Efficient Reversible Quantum Circuit for Theta Function in SHA-3

With the advancement of quantum computing, traditional hash based security structures are increasingly exposed to threats posed by quantum algorithms. In particular, Grover's algorithm enables significantly faster pre-image attacks on hash functions than classical approaches, highlighting the need for circuit-level quantum countermeasures. To break with quantum computer, implementation of quantum circuit for the hash function is essential. However, the existing approaches require too many gates or discard ancilla qubits. In this paper, we propose a reversible quantum circuit for the $\theta$ operation in the Keccak algorithm a core component of SHA-3, by explicitly implementing the inverse function $\theta^{-1}$. The proposed circuit allows for ancilla qubit reuse and achieves a substantial reduction in number of CNOT gates and qubits compare to previous researches. While the depth of our circuit slightly exceeds that of some existing approaches, the compact and modular design of the $\theta$ operation provides a solid foundation for further enhancement.