Quantum Free-Start Collision Attacks on Double Block Length Hashing with Round-Reduced AES-256

Abstract

Recently, Hosoyamada and Sasaki (EUROCRYPT 2020), and Xiaoyang Dong et al. (ASIACRYPT 2020) proposed quantum collision attacks against AES-like hashing modes AES-MMO and AES-MP. Their collision attacks are based on the quantum version of the rebound attack technique exploiting the differential trails whose probabilities are too low to be useful in the classical setting but large enough in the quantum setting. In this work, we present dedicated quantum free-start collision attacks on Hirose’s double block length compression function instantiated with AES-256, namely HCF-AES-256. The best publicly known classical attack against HCF-AES-256 covers up to 9 out of 14 rounds. We present a new 10-round differential trail for HCF-AES-256 with probability 2⁻¹⁶⁰, and use it to find collisions with a quantum version of the rebound attack. Our attack succeeds with a time complexity of 2^85.11 and requires 2¹⁶ qRAM in the quantum-attack setting, where an attacker can make only classical queries to the oracle and perform offline computations. We also present a quantum free-start collision attack on HCF-AES-256 with a time complexity of 2^86.07 which outperforms Chailloux, Naya-Plasencia, and Schrottenloher’s generic quantum collision attack (ASIACRYPT 2017) in a model when large qRAM is not available.