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.
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Minimizing Trust in Hardware Wallets with Two Factor Signatures
We introduce the notion of two-factor signatures (2FS), a generalization of a two-out-of-two threshold signature scheme in which one of the parties is a hardware token which can store a high-entropy secret, and the other party is a human who knows a low-entropy password. The security (unforgeability) property of 2FS requires that an external adversary corrupting either party (the token or the computer the human is using) cannot forge a signature. This primitive is useful in contexts like hardware cryptocurrency wallets in which a signature conveys the authorization of a transaction. By the above security property, a hardware wallet implementing a two-factor signature scheme is secure against attacks mounted by a malicious hardware vendor; in contrast, all currently used wallet systems break under such an attack (and as such are not secure under our definition). We construct efficient provably-secure 2FS schemes which produce either Schnorr signature (assuming the DLOG assumption), or EC-DSA signatures (assuming security of EC-DSA and the CDH assumption) in the Random Oracle Model, and evaluate the performance of implementations of them. Our EC-DSA based 2FS scheme can directly replace currently used hardware wallets for Bitcoin and other major cryptocurrencies to enable security against malicious hardware vendors.
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- Award ID(s):
- 1704788
- NSF-PAR ID:
- 10094253
- Date Published:
- Journal Name:
- Financial Crypto
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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