【摘要】 祖冲之密码算法（ZUC-128）是我国发布的商用密码算法中的序列密码算法,在4G移动通信领域发挥重要作用,本文主要研究如何以较少的量子比特实现ZUC-128算法的完整量子电路.S盒是ZUC-128算法非线性组件的重要组成部分,因此本文详细研究S盒量子电路的优化实现.32比特S盒是由4个8×8 S盒组成,即S=（S₀,S₁,S₂,S₃）,其中S₀=S₂,S₁=S₃.首先通过穷搜剪枝的策略非就地实现了S₀;其次重点研究通过同构映射将S₁的主要部分F₂₈乘法求逆转换为F₂₄上的乘法求逆运算,完成了只需要8个辅助量子位的S₁就地实现量子电路.S₁电路总共需要16个量子比特、96个Toffoli门、224个CNOT门、4个NOT门,Toffoli深度为78.最后探索出以较少的量子比特实现ZUC-128算法整个流程的量子电路构造,当工作步骤中轮数L=32时,该量子电路需要6244个量子比特、85 843个Toffoli门、245 304个CNOT门和66 512个NOT门,Toffoli深度为52 074.更多还原

【Abstract】 The ZUC-128 cipher algorithm is one of the commercial stream cipher algorithms published in China,which plays an important role in the field of 4G mobile communication.This work mainly studies how to realize the complete quantum circuit of ZUC-128 algorithm with less qubits.The S-box is an important part of the nonlinear component of the ZUC-128 algorithm,therefore,the optimized implementation of the S-box quantum circuit is studied in detail.The 32 bit S-box is composed of four 8×8 S-boxes,denoted as S=（S₀,S₁,S₂,S₃）,with the property that S₀=S₂,S₁=S₃.Firstly,we achieve S₀through a strategy of exhaustive search and pruning,using an out-place implementation.Secondly,we focus on the transformation of the main part of S₁,F₂₈multiplication inversion,into F₂₄multiplication inversion through isomorphic mapping.We successfully complete the S₁in-place implementation quantum circuit with only 8 auxiliary qubits.The S₁circuit requires 16 qubits,96Toffoli gates,224 CNOT gates,4 NOT gates,with the Toffoli-depth of 78.Finally,we propose the construction of quantum circuit to realize the whole process of ZUC-128 algorithm with less quantum bits.When the number of rounds L=32 in the working step,this quantum circuit requires 6244qubits,85 843 Toffoli gates,245 304 CNOT gates,and 66 512 NOT gates,with the Toffoli-depth of52 074.更多还原