Quantum Truncated Differential and Boomerang Attack

TL;DR

This paper develops quantum algorithms for cryptanalysis techniques like truncated differential and boomerang attacks, demonstrating their efficiency and effectiveness in analyzing symmetric ciphers in the quantum era.

Contribution

It introduces novel quantum algorithms for truncated differential and boomerang cryptanalysis, capable of handling complex cipher features with polynomial complexity.

Findings

Quantum algorithms find high-probability truncated differentials for most keys.

Quantum boomerang distinguisher algorithms are efficient with polynomial quantum gates.

The methods leverage quantum computing strengths, improving cryptanalysis capabilities.

Abstract

Facing the worldwide steady progress in building quantum computers, it is crucial for cryptographic community to design quantum-safe cryptographic primitives. To achieve this, we need to investigate the capability of cryptographic analysis tools when used by the adversaries with quantum computers. In this article, we concentrate on truncated differential and boomerang cryptanalysis. We first present a quantum algorithm which is designed for finding truncated differentials of symmetric ciphers. We prove that, with a overwhelming probability, the truncated differentials output by our algorithm must have high differential probability for the vast majority of keys in key space. Afterwards, based on this algorithm, we design a quantum algorithm which can be used to find boomerang distinguishers. The quantum circuits of both quantum algorithms contain only polynomial quantum gates. Compared to classical tools for searching truncated differentials or boomerang distinguishers, our algorithms fully utilize the strengths of quantum computing, and can maintain the polynomial complexity while fully considering the impact of S-boxes and key scheduling.