Further insights on constructing quantum circuits for Camellia block cipher

The rapid development of quantum technology challenges the security of modern cryptography, which causes concern from the cryptographic community about the quantum implementation of cryptographic algorithms, as it is an important component of many quantum attacks. In this paper, the construction of quantum circuits for Camellia block cipher is investigated. Firstly, a 4-bit S-box is derived from the hardware circuit of the Camellia S-box, which divides the S-box circuit into three parts. Then, based on the rearranged circuit, as well as the implementation of the CCCNOT gate, the construction of the NCT-based circuit for the Camellia S-box is researched. Meanwhile, combined with the observations on the rearranged S-box circuit and the discussion on the in-place implementation of different matrices, a quantum circuit for the Camellia S-box with lower T-depth is presented. As an application, the various S-box circuits are used to construct quantum circuits for the Camellia family. The results reveal that the memory-efficient and depth-efficient quantum circuits of Camellia can be constructed with lower T-depth and T· M value. Besides, for each instance of Camellia, compared with existing state-of-the-art implementation with lowest T-depth and T· M value, the depth-efficient circuit designed in this work only costs about 35