Quantum circuit for implementing Serpent algorithm with low costs

Serpent, one of the AES candidate algorithms, is known for its high security and attack resistance. It is suitable for areas with high information security requirements. Serpent's distinctive nonlinear structure is the S-boxes. This paper studies how to build the quantum circuit for Serpent algorithm with lower costs. By combining with the quantum circuits of S-boxes with fewer qubits and quantum gates and the inverse quantum circuits of S-boxes, the key expansion quantum circuit can be constructed. Moreover, by decomposing the <italic>3-controlled</italic>CNOT gates appearing in the quantum circuits of the S-boxes and optimizing the decomposed quantum circuits, the number of <italic>Toffoli</italic>gates is further reduced. In conjunction with the proposed quantum circuits, two types of quantum circuits requiring 448 qubits and 92288 T gates and 384 qubits and 118944 T gates are given to realize the Serpent algorithm. In comparison with the previous study, which required 800 qubits and 132608 T gates, the quantum circuit in this paper requires fewer resources. Furthermore, the S-boxes and key expansion quantum circuits used in the study can reduce the quantum resources in implementing Serpent, reducing the quantum circuit scale required to attack Serpent by the Grover algorithm.