135 research outputs found
Collapse-binding quantum commitments without random oracles
We construct collapse-binding commitments in the standard
model. Collapse-binding commitments were introduced by Unruh
(Eurocrypt 2016) to model the computational-binding property of commitments
against quantum adversaries, but only constructions in the random
oracle model were known.
Furthermore, we show that collapse-binding commitments imply
selected other security definitions for quantum commitments,
answering an open question by Unruh (Eurocrypt 2016)
Quantum Lightning Never Strikes the Same State Twice
Public key quantum money can be seen as a version of the quantum no-cloning
theorem that holds even when the quantum states can be verified by the
adversary. In this work, investigate quantum lightning, a formalization of
"collision-free quantum money" defined by Lutomirski et al. [ICS'10], where
no-cloning holds even when the adversary herself generates the quantum state to
be cloned. We then study quantum money and quantum lightning, showing the
following results:
- We demonstrate the usefulness of quantum lightning by showing several
potential applications, such as generating random strings with a proof of
entropy, to completely decentralized cryptocurrency without a block-chain,
where transactions is instant and local.
- We give win-win results for quantum money/lightning, showing that either
signatures/hash functions/commitment schemes meet very strong recently proposed
notions of security, or they yield quantum money or lightning.
- We construct quantum lightning under the assumed multi-collision resistance
of random degree-2 systems of polynomials.
- We show that instantiating the quantum money scheme of Aaronson and
Christiano [STOC'12] with indistinguishability obfuscation that is secure
against quantum computers yields a secure quantum money schem
Commitments to Quantum States
What does it mean to commit to a quantum state? In this work, we propose a
simple answer: a commitment to quantum messages is binding if, after the commit
phase, the committed state is hidden from the sender's view. We accompany this
new definition with several instantiations. We build the first non-interactive
succinct quantum state commitments, which can be seen as an analogue of
collision-resistant hashing for quantum messages. We also show that hiding
quantum state commitments (QSCs) are implied by any commitment scheme for
classical messages. All of our constructions can be based on
quantum-cryptographic assumptions that are implied by but are potentially
weaker than one-way functions.
Commitments to quantum states open the door to many new cryptographic
possibilities. Our flagship application of a succinct QSC is a
quantum-communication version of Kilian's succinct arguments for any language
that has quantum PCPs with constant error and polylogarithmic locality.
Plugging in the PCP theorem, this yields succinct arguments for NP under
significantly weaker assumptions than required classically; moreover, if the
quantum PCP conjecture holds, this extends to QMA. At the heart of our security
proof is a new rewinding technique for extracting quantum information
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