Quantum Circuits of SM4 and Camellia with Lower T$T$‐depth
Da Lin, Zhenqiang Li, Bing Sun, Bo Yu · Advanced Quantum Technologies · 2025
Abstract With the rapid development of quantum technology, modern cryptography is facing an increasing number of security threats. Given that the quantum circuit of symmetric‐key ciphers frequently serves as the core element of quantum attacks, it has attracted extensive attention. In this work, it is investigated that how the quantum circuit of SM4 and Camellia can be implemented with lower ‐depth. First, a general framework is proposed for designing Substitution‐box (S‐box) circuits with optimized ‐depth. Based on the framework, quantum circuits are respectively designed for SM4 S‐box and Camellia S‐box with ‐depth 4. Compared with existing quantum circuits requiring a ‐depth of 4, our circuits consume fewer qubits and quantum gates, as well as lower full depth. Besides, S‐box quantum circuits are introduced with ‐depth 3 for SM4 and Camellia for the first time. As an application, the designed S‐box circuits can reduce the ‐depth requiring for the subroutine and stand‐alone circuits of SM4 from 132 and 260 in the previous work to 99 and 195. Additionally, the ‐depth requiring for the subroutine and stand‐alone circuits of Camellia‐128/‐192/‐256 can be reduced from 92/126/126 and 108/150/150 in the previous work to 70/96/96 and 82/114/114, respectively.