Quantum Generic Attacks on Feistel Schemes

TL;DR

This paper presents quantum algorithms that significantly improve the ability to distinguish certain Feistel cipher structures from random permutations, highlighting potential quantum vulnerabilities in cryptographic schemes.

Contribution

It introduces efficient quantum algorithms for distinguishing classical Feistel schemes from random permutations, demonstrating exponential speed-up over classical methods.

Findings

Quantum algorithms outperform classical in distinguishing Feistel schemes

Exponential speed-up achieved over classical algorithms

Applicable to unbalanced Feistel schemes with expanding functions

Abstract

The Feistel scheme is an important structure in the block ciphers. The security of the Feistel scheme is related to distinguishability with a random permutation. In this paper, efficient quantum algorithms for distinguishing classical 3,4-round and unbalanced Feistel scheme with contracting functions from random permutation are proposed. Our algorithms realize an exponential speed-up over classical algorithms for these problems. Furthermore, the method presented in this paper can also be used to consider unbalanced Feistel schemes with expanding functions.