Abstract
The Advanced Encryption Standard (AES) is widely used and well-studied for its efficiency and strong security. This paper presents quantum circuit designs for the AES S-box by introducing the composite field F((2⁴)²) to replace the traditional field F(2⁸) , enabling the inversion to be decomposed into operations over F(2⁴) . This work reduces the quantum resource overhead required for implementing the S-box by decreasing the number of CNOT gates in the matrix multiplication, lowering the depth of T gates in both the inversion circuit and the multiplication circuit. Besides, the widths for the S-box quantum circuits are also optimized during the inversion circuit and multiplication circuit. With a linear key schedule, the resulting AES-128 quantum circuit reduce the product of the circuit width and T depth to 102800, which is the lowest known to date.