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We define the notion of one-shot signatures, which are signatures where any secret key can be used to sign only a single message, and then self-destructs. While such signatures are of course impossible classically, we construct one-shot signatures using quantum no-cloning. In particular, we show that such signatures exist relative to a classical oracle, which we can then heuristically obfuscate using known indistinguishability obfuscation schemes. We show that one-shot signatures have numerous applications for hybrid quantum/classical cryptographic tasks, where all communication is required to be classical, but local quantum operations are allowed. Applications include one-time signature tokens, quantum money with classical communication, decentralized blockchain-less cryptocurrency, signature schemes with unclonable secret keys, non-interactive certifiable min-entropy, and more. We thus position one-shot signatures as a powerful new building block for novel quantum cryptographic protocols. 

The quantum random oracle model (QROM) has become the standard model in which to prove the post-quantum security of random-oracle-based constructions. Unfortunately, none of the known proof techniques allow the reduction to record information about the adversary’s queries, a crucial feature of many classical ROM proofs, including all proofs of indifferentiability for hash function domain extension. In this work, we give a new QROM proof technique that overcomes this “recording barrier”. We do so by giving a new “compressed oracle” which allows for efficient on-the-fly simulation of random oracles, roughly analogous to the usual classical simulation. We then use this new technique to give the first proof of quantum indifferentiability for the Merkle-Damgård domain extender for hash functions. We also give a proof of security for the Fujisaki-Okamoto transformation; previous proofs required modifying the scheme to include an additional hash term. Given the threat posed by quantum computers and the push toward quantum-resistant cryptosystems, our work represents an important tool for efficient post-quantum cryptosystems. 

The Fiat-Shamir transformation is a useful approach to building non-interactive arguments (of knowledge) in the random oracle model. Unfortunately, existing proof techniques are incapable of proving the security of Fiat-Shamir in the quantum setting. The problem stems from (1) the difficulty of quantum rewinding, and (2) the inability of current techniques to adaptively program random oracles in the quantum setting. In this work, we show how to overcome the limitations above in many settings. In particular, we give mild conditions under which Fiat-Shamir is secure in the quantum setting. As an application, we show that existing lattice signatures based on Fiat-Shamir are secure without any modifications. 

A k-collision for a compressing hash function H is a set of k distinct inputs that all map to the same output. In this work, we show that for any constant k, \Theta(N^(1/2(1-1/(2^k-1)))) quantum queries are both necessary and sufficient to achieve a k-collision with constant probability. This improves on both the best prior upper bound (Hosoyamada et al., ASIACRYPT 2017) and provides the first non-trivial lower bound, completely resolving the problem. 

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, we investigate quantum lightning where no-cloning holds even when the adversary herself gener- ates 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 beyond quan- tum money by showing several potential applications, such as gen- erating random strings with a proof of entropy, to completely decen- tralized cryptocurrency without a block-chain, where transactions is instant and local. – We give Either/Or results for quantum money/lightning, showing that either signatures/hash functions/commitment schemes meet very strong recently proposed notions of security, or they yield quan- tum money or lightning. Given the difficulty in constructing public key quantum money, this suggests that natural schemes do attain strong security guarantees. – We show that instantiating the quantum money scheme of Aaron- son and Christiano [STOC’12] with indistinguishability obfuscation that is secure against quantum computers yields a secure quantum money scheme. This construction can be seen as an instance of our Either/Or result for signatures, giving the first separation between two security notions for signatures from the literature. – Finally, we give a plausible construction for quantum lightning, which we prove secure under an assumption related to the multi- collision resistance of degree-2 hash functions. Our construction is inspired by our Either/Or result for hash functions, and yields the first plausible standard model instantiation of a non-collapsing col- lision resistant hash function. This improves on a result of Unruh [Eurocrypt’16] which is relative to a quantum oracle.