# Challenging $O(2^{n/2})$ for hash collisions using quantum computers

In "Finding Hash Collisions with Quantum Computers by Using Differential Trails with Smaller Probability than Birthday Bound" the authors Akinori Hosoyamada and Yu Sasaki state that it may be possible to perform collision attacks with of a lower order than $$O(2^{n/3})$$ using BHT [1]. Bernstein remarked for BHT that it would have the same space-time complexity or worse than classical attacks [2].

However, the attack seems specific to increasing the number of rounds that can be attacked, without a direct result on the full hash algorithm (in this case AES and Whirlpool).

Does this result have any direct or indirect impact on SHA-256? In other words could these findings have a significant impact on the space-time complexity of finding collisions for SHA-256?

If so, can a space-time complexity be given? Or are the results too experimental for that to be calculated?

1. Brassard, G., Høyer, P., Tapp, A.: Quantum cryptanalysis of hash and claw-free functions. In: LATIN 1998. LNCS, vol. 1380, pp. 163{169. Springer (1998)
2. Bernstein, D.J.: Cost analysis of hash collisions: Will quantum computers make SHARCS obsolete? In: SHARCS (2009)