An efficient quantum circuit implementation of ZUC-128 cipher with low T-depth
Abstract
The Zu Chongzhi cryptographic algorithm (ZUC) is a stream cipher algorithm published in China. This paper focuses on the realization of the complete quantum circuit for the ZUC-128 algorithm with low T-depth. The S-box is a crucial component of the nonlinear aspect of the ZUC-128 algorithm. Initially, we derive the classical circuit implementations of S_0 and S_1 using an exhaustive pruning strategy and tower domain decomposition technology. Subsequently, we develop quantum circuits for S_0 and S_1 in two steps: first by reducing the AND-depth of the classical circuit, and then by ensuring that the T-depth of the quantum circuit equals the AND-depth of the classical circuit. Our new S_0 and S_1 quantum circuits both have a T-depth of 7. We are currently researching the quantum circuit implementation of the adder and L function in order to minimize the T-depth of the entire circuit. Finally, we propose the construction of quantum circuit to realize the whole process of ZUC-128 algorithm with low T-depth. When the number of rounds L=32 in the working step, this quantum circuit requires 46008 qubits, 682340 T gates, 2008535 CNOT gates and 42680 NOT gates, with the T-depth of 11341, and the number of qubits multiplied by T-depth is 5.22 × 10^8
