Quantum key recovery attack on SIMON32/64

The development of quantum computation is a threat to classical cryptosystems. Shor's algorithm can break the security of some public-key cryptosystems and Grover's algorithm can help gain quadratic speed-up in the cryptanalysis of block ciphers. There are two security models in quantum cryptanalysis against block ciphers, Q1 model and Q2 model. The lightweight block ciphers receive much attention in recent years. It's vital to study the quantum security of lightweight block ciphers in quantum setting to prepare for the future with large-scale quantum computers. There are some results focusing on the quantum circuit design of exhaustive search on some lightweight block ciphers. However, the quantum attacks combined with classical cryptanalysis methods on lightweight block ciphers haven't been studied further. In this paper, we focus on the quantum key recovery attack of SIMON 32/64. At first, we reestimate the quantum resources of quantum exhaustive search on SIMON 32/64. We find that the cost of multi controlled-NOT cannot be ignored. Then, using the differential trial given by Birykov in FSE 2014 as a distinguisher, we give our quantum key recovery attack of SIMON 32/64. We treat the two phrases of key recovery attack as two QAA instances separately. Then, we give quantum circuit design of these two instances and their corresponding quantum resources estimate. We conclude that our quantum key recovery attack is better than quantum exhaustive search in terms of quantum gate resources and qubit resources. Our result studies the quantum dedicated attack from the perspective of quantum resource, which gives a more fine-grained analysis.

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