Welcome to the resource topic for 2022/678
Title:
New Constructions of Collapsing Hashes
Authors: Mark Zhandry
Abstract:Collapsing is a post-quantum strengthening of collision resistance, needed to lift many classical results to the quantum setting. Unfortunately, the only existing standard-model proofs of collapsing hashes require LWE. We construct the first collapsing hashes from the quantum hardness of any one of the following problems: - LPN in a variety of low noise or high-hardness regimes, essentially matching what is known for collision resistance from LPN. - Finding cycles on exponentially-large expander graphs, such as those arising from isogenies on elliptic curves. - The “optimal” hardness of finding collisions in any hash function. - The polynomial hardness of finding collisions, assuming a certain plausible regularity condition on the hash. As an immediate corollary, we obtain the first statistically hiding post-quantum commitments and post-quantum succinct arguments (of knowledge) under the same assumptions. Our results are obtained by a general theorem which shows how to construct a collapsing hash H' from a post-quantum collision-resistant hash function H, regardless of whether or not H itself is collapsing, assuming H satisfies a certain regularity condition we call “semi-regularity.”
ePrint: https://eprint.iacr.org/2022/678
Talk: https://www.youtube.com/watch?v=rfpcHj599FA
Slides: https://iacr.org/submit/files/slides/2022/crypto/crypto2022/20/slides.pptx
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