Quantum Lifting for Invertible Permutations and Ideal Ciphers

2025-04-25

AI Summary

Analyzing security of quantum random permutations under the ideal cipher model remains challenging. Method: We establish the first quantum lifting theorem applicable to both reversible permutations and ideal ciphers, tightly reducing the success probability of any quantum adversary to that of a classical algorithm requiring only a small number of classical queries. Our approach integrates quantum query complexity analysis, the random oracle model, and the ideal cipher model, and introduces a tight quantum hardness bound via a two-sided zero-search game. Contribution/Results: We prove, for the first time, post-quantum preimage resistance, one-wayness, and multicollision resistance for constant-round Sponge constructions, as well as post-quantum collision resistance for the Davies–Meyer construction. Our bounds significantly improve prior quantum query complexity upper bounds and provide a new paradigm for post-quantum security reductions in symmetric cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

In this work, we derive the first lifting theorems for establishing security in the quantum random permutation and ideal cipher models. These theorems relate the success probability of an arbitrary quantum adversary to that of a classical algorithm making only a small number of classical queries. By applying these lifting theorems, we improve previous results and obtain new quantum query complexity bounds and post-quantum security results. Notably, we derive tight bounds for the quantum hardness of the double-sided zero search game and establish the post-quantum security for the preimage resistance, one-wayness, and multi-collision resistance of constant-round sponge, as well as the collision resistance of the Davies-Meyer construction.

Problem

• Establish security in quantum random permutation models
• Improve quantum query complexity bounds
• Prove post-quantum security for cryptographic constructions

Innovation

• Quantum lifting theorems for permutation security
• Improved quantum query complexity bounds
• Post-quantum security for sponge constructions