Quantum Implementation of S-Boxes Based on Polynomial Evaluation

Quantum computing environments make block ciphers susceptible to exhaustive key search attacks utilizing Grover's algorithm. However, such quantum-based attacks remain impractical unless the targeted cipher is directly implemented on a quantum platform. Moreover, their efficiency significantly depends on the quantum circuit design and optimization of the block cipher in question. The cost of a quantum circuit implementation is typically measured by two main metrics: the number of qubits and the circuit depth (T-depth). For most block ciphers, the S-box is the principal factor contributing to increased T-depth and additional qubit requirements. This paper presents a method for generating quantum circuits directly from lookup tables of S-boxes applicable to arbitrary block ciphers. We illustrate our approach using quantum circuit implementations of the PRESENT and DES ciphers as practical examples. Our proposed method is expected to efficiently implement arbitrary S-boxes by employing polynomial evaluation, thus balancing time–space complexity.