Paper 2023/146

Optimized Quantum Implementation of AES

Da Lin, Hubei University
Zejun Xiang, Hubei University
Runqing Xu, Hubei University
Shasha Zhang, Hubei University
Xiangyong Zeng, Hubei University

This work researches the implementation of the AES family with Pauli-X gates, CNOT gates and Toffoli gates as the underlying quantum logic gate set. First, the properties of quantum circuits are investigated, as well as the influence of Pauli-X gates, CNOT gates and Toffoli gates on the performance of the circuits constructed with those gates. Based on these properties and the observations on the hardware circuits built by Boyar \emph{et al.} and Zou \emph{et al.}, it is possible to construct quantum circuits for AES's Substitution-box (S-box) and its inverse (S-box$^{-1}$) by rearranging the classical implementation to three parts. Since the second part is treated as a 4-bit S-box in this paper and can be dealt with by existing tools, a heuristic is proposed to search optimized quantum circuits for the first and the third parts. In addition, considering the number of parallelly executed S-boxes, the trade-offs between the qubit consumption and $T\cdot M$ values for the round function and key schedule of AES are studied. As a result, quantum circuits of AES-128, AES-192 and AES-256 can be constructed with 269, 333 and 397 qubits, respectively. If more qubits are allowed, quantum circuits that outperform state-of-the-art schemes in the metric of $T\cdot M$ value for the AES family can be reported, and it needs only 474, 538 and 602 qubits for AES-128, AES-192 and AES-256, respectively.

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Publication info
Published elsewhere. Minor revision. Quantum Information Processing
AESreversible circuitquantum gateToffoli depth
Contact author(s)
linda @ stu hubu edu cn
xiangzejun @ hubu edu cn
xurq5953 @ stu hubu edu cn
amushasha @ 163 com
xzeng @ hubu edu cn
2023-09-22: revised
2023-02-08: received
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      author = {Da Lin and Zejun Xiang and Runqing Xu and Shasha Zhang and Xiangyong Zeng},
      title = {Optimized Quantum Implementation of {AES}},
      howpublished = {Cryptology ePrint Archive, Paper 2023/146},
      year = {2023},
      note = {\url{}},
      url = {}
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