Quantum Miss-in-the-Middle Attack

TL;DR

This paper introduces a quantum algorithm that efficiently finds impossible differentials in block ciphers, enhancing cryptanalysis capabilities against symmetric encryption using quantum computing.

Contribution

It presents a novel quantum algorithm for identifying impossible differentials in block ciphers, requiring no queries and effective for ciphers with many rounds.

Findings

Quantum algorithm has polynomial complexity.

It does not require oracle queries.

More effective for ciphers with many rounds.

Abstract

Traditional cryptography is facing great challenges with the development of quantum computing. Not only public-key cryptography, the applications of quantum algorithms to symmetric cryptanalysis has also drawn more and more attention. In this paper, we apply quantum algorithms to the miss-in-the-middle technique and propose a quantum algorithm for finding impossible differentials of general block ciphers. We prove that, as long as the attacked block cipher satisfies certain algebraic conditions, the outputs of the quantum algorithm will be impossible differentials of it except for a negligible probability. The proposed quantum algorithm has polynomial quantum complexity and does not require any quantum or classical query to the encryption oracle of the block cipher. Compared with traditional miss-in-the-middle technique, which is difficult to find impossible differentials as the number of rounds increases, the quantum version of miss-in-the-middle technique proposed in this paper is more conducive to find impossible differentials when the block cipher has a large number of rounds.