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Title:
Optimized Quantum Implementation of AES
Authors: Da Lin, Zejun Xiang, Runqing Xu, Shasha Zhang, Xiangyong Zeng
Abstract:In this paper, we research the implementation of the AES family with Pauli-X gates, CNOT gates and Toffoli gates as the underlying quantum logic gate set. First, we investigate the properties of quantum circuits and the influence of Pauli-X gates, CNOT gates and Toffoli gates on the performance of the circuits constructed with those gates. Based on the properties of quantum circuits as well as our observations on the classical ones built by Boyar \emph{et al.} and Zou \emph{et al.}, we research the construction of reversible 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, we propose a heuristic to search optimized reversible circuits for the first part and the third part. The application of our method reveals that the reversible circuits constructed for AES S-box and its inverse consume fewer qubits with optimized CNOT gate consumption and Toffoli depth. In addition, we study the construction of reversible circuits for the key schedule and the round function of AES by applying various number of S-boxes in parallel. As a result, we report quantum circuits of AES-128, AES-192 and AES-256 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.
ePrint: https://eprint.iacr.org/2023/146
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