A Novel Framework to Construct S-Box Quantum Circuits Using System Modeling: Application to 4-Bit S-Boxes.

Quantum computers accelerate many algorithms based on the superposition principle of quantum mechanics. The Grover algorithm provides significant performance to malicious users attacking symmetric key systems. Since the performance of attacks using quantum computers depends on the efficiency of the quantum circuit of the encryption algorithms, research research on the implementation of quantum circuits is essential. This paper presents a new framework to construct quantum circuits of substitution boxes (S-boxes) using system modeling. We model the quantum circuits of S-boxes using two layers: Toffoli and linear layers. We generate vector spaces based on the values of qubits used in the linear layers and apply them to find quantum circuits. The framework finds the circuit by matching elements of vector spaces generated from the input and output of a given S-box, using the forward search or the meet-in-the-middle strategy. We developed a tool to apply this framework to 4-bit S-boxes. While the 4-bit S-box quantum circuit construction tool LIGHTER-R only finds circuits that can be implemented with four qubits, the proposed tool achieves the circuits with five qubits. The proposed tool can find quantum circuits of 4-bit odd permutations based on the controlled NOT, NOT, and Toffoli gates, whereas LIGHTER-R is unable to perform this task in the same environment. We expect this technique to become a critical step toward optimizing S-box quantum circuits. [ABSTRACT FROM AUTHOR]