Quantum Attacks on MIBS Block Cipher Based on Bernstein–Vazirani Algorithm

Huiqin Xie, Zhangmei Zhao, Ke Wang, Yanjun Li and Hongcai Xin ()
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Huiqin Xie: Department of Cryptography Science and Technology, Beijing Electronic Science and Technology Institute, Beijing 100070, China
Zhangmei Zhao: Department of Cryptography Science and Technology, Beijing Electronic Science and Technology Institute, Beijing 100070, China
Ke Wang: Department of Cryptography Science and Technology, Beijing Electronic Science and Technology Institute, Beijing 100070, China
Yanjun Li: Information Industry Information Security Evaluation Center, The 15th Research Institute of China Electronics Technology Group Corporation, Beijing 100083, China
Hongcai Xin: Department of Cryptography Science and Technology, Beijing Electronic Science and Technology Institute, Beijing 100070, China

Mathematics, 2024, vol. 12, issue 17, 1-20

Abstract: Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover’s algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover’s algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of 2 10.5 . An 8-round attack requires 179 qubits and has a time complexity of 2 22 . Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds.

Keywords: quantum cryptanalysis; MIBS; key-recovery attack; Bernstein–Vazirani algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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