Quantum Attacks on Hash Constructions with Low Quantum Random Access Memory

At ASIACRYPT 2022, Benedikt, Fischlin, and Huppert proposed the quantum herding attacks on iterative hash functions for the first time. Their attack needs exponential quantum random access memory (qRAM), more precisely 2(0.43n) quantum accessible classical memory (QRACM). As the existence of large qRAM is questionable, Benedikt et al. leave an open question on building low-qRAM quantum herding attacks. In this paper, we answer this open question by building a quantum herding attack, where the time complexity is slightly increased from Benedikt et al.'s 2(0.43n) to ours 2(0.46n), but it does not need qRAM anymore (abbreviated as no-qRAM). Besides, we also introduce various low-qRAM or no-qRAM quantum attacks on hash concatenation combiner, hash XOR combiner, Hash-Twice, and Zipper hash functions.