# QUANTUM ROTATIONAL CRYPTANALYSIS FOR PREIMAGE RECOVER OF ROUND-REDUCED Keccak

QUANTUM INFORMATION & COMPUTATION（2023）

Abstract

This paper considers the preimage resistance of 4-round Keccak-224/256/384/512 in the quantum setting. In order to effectively find the corresponding rotational number for the rotational counterpart of preimage, we first establish a probabilistic algorithm based on the Grover search to guess a possible rotational number by using the fixed relations of bits pairs in some coordinates. This is committed to achieving that each iteration of searching the rotational counterparts contains only one run of 4-round Keccak variant applied for the verification, which can reduce the attack complexity in the quantum setting. Based on finding the rotational number under an acceptable randomness, we construct two attack models to focus on the recovery of preimage. In the first model, the Grover's algorithm serves as finding out a rotational counterpart of the preimage. Through 64 attempts, the desired preimage can be obtained. In the second model, we abstract the finding of rotational counterparts into searching vertexes on a hypercube, and then, the SKW quantum algorithm is used to deal with the finding of the vertexes acted as rotational counterparts. As a result of quantum preimage attacks on the round-reduced Keccak, the first attack model is superior to the generic quantum preimage attack for 4-round Keccak-224/256/384/512, and second model has slightly lower attack effect but more practicality on the 4-round Keccak-512/384, that is, the model is exponentially easier to implement in quantum circuit than both our first attack model and the generic quantum preimage attack.

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Key words

Keccak,Rotational Cryptanalysis,Preimage Attack,Grover' s Algorithm,SKW Algorithm

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