Quantum Lightning Never Strikes the Same State Twice
This work addresses foundational security challenges in quantum cryptography, with potential applications in decentralized systems, but it is incremental as it builds on existing formalizations and assumptions.
The paper tackles the problem of constructing secure quantum money and quantum lightning, formalizing collision-free quantum money where no-cloning holds even when adversaries generate states, and demonstrates applications like decentralized cryptocurrency. It constructs quantum lightning under multi-collision resistance assumptions and shows that instantiating a prior scheme with quantum-secure indistinguishability obfuscation yields secure quantum money.
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 scheme