Welcome to the resource topic for 2023/1844
Title:
Unconditionally Secure Commitments with Quantum Auxiliary Inputs
Authors: Tomoyuki Morimae, Barak Nehoran, Takashi Yamakawa
Abstract:We show the following unconditional results on quantum commitments in two related yet different models:

We revisit the notion of quantum auxiliaryinput commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter,
as quantum auxiliary inputs. We show that computationallyhiding and statisticallybinding quantum auxiliaryinput commitments exist unconditionally, i.e., without relying on any unproven assumption, while Chailloux et al. assumed a complexitytheoretic assumption,
{\bf QIP}\not\subseteq{\bf QMA}. On the other hand, we observe that achieving both statistical hiding and statistical binding at the same time is impossible even in the quantum auxiliaryinput setting.
To the best of our knowledge, this is the first example of unconditionally proving computational security of any form of (classical or quantum) commitments for which statistical security is impossible. As intermediate steps toward our construction, we introduce and unconditionally construct postquantum sparse pseudorandom distributions and quantum auxiliaryinput EFI pairs which may be of independent interest. 
We introduce a new model which we call the common reference quantum state (CRQS) model where both the committer and receiver take the same quantum state that is randomly sampled by an efficient setup algorithm. We unconditionally prove that there exist statistically hiding and statistically binding commitments in the CRQS model, circumventing the impossibility in the plain model.
We also discuss their applications to zeroknowledge proofs, oblivious transfers, and multiparty computations.
ePrint: https://eprint.iacr.org/2023/1844
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