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Lecture notes in computer science

Quantum Circuit Implementations of AES with Fewer Qubits

Jian Xiao Zou, Zihao Wei, Siwei Sun, Ximeng Liu, Wenling Wu

Published Jan 1, 2020• 81 citations
Publisher
DOI
10.1007/978-3-030-64834-3_24

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Zhongguo kexue. Wulixue Lixue Tianwenxue•Dec 20, 2024•0 citations
Advanced Encryption Standard (AES) is one of the most widely used block ciphers nowadays, and has been established as an encryption standard in 2001. Here we design AES-128 and the sample-AES (S-AES) quantum circuits for deciphering. In the quantum circuit of AES-128, we perform an affine transformation for the SubBytes part to solve the problem that the initial state of the output qubits in SubBytes is not the ∣0⟩ ⊗8 state. After that, we are able to encode the new round sub-key on the qubits encoding the previous round sub-key, and this improvement reduces the number of qubits used by 224 compared with Langenberg et al. ’s implementation. For S-AES, a complete quantum circuit is presented with only 48 qubits, which is already within the reach of existing noisy intermediate-scale quantum computers.
Serpent, one of the AES candidate algorithms, is known for its high security and attack resistance. It is suitable for areas with high information security requirements. Serpent's distinctive nonlinear structure is the S-boxes. This paper studies how to build the quantum circuit for Serpent algorithm with lower costs. By combining with the quantum circuits of S-boxes with fewer qubits and quantum gates and the inverse quantum circuits of S-boxes, the key expansion quantum circuit can be constructed. Moreover, by decomposing the 3-controlledCNOT gates appearing in the quantum circuits of the S-boxes and optimizing the decomposed quantum circuits, the number of Toffoligates is further reduced. In conjunction with the proposed quantum circuits, two types of quantum circuits requiring 448 qubits and 92288 T gates and 384 qubits and 118944 T gates are given to realize the Serpent algorithm. In comparison with the previous study, which required 800 qubits and 132608 T gates, the quantum circuit in this paper requires fewer resources. Furthermore, the S-boxes and key expansion quantum circuits used in the study can reduce the quantum resources in implementing Serpent, reducing the quantum circuit scale required to attack Serpent by the Grover algorithm.