Quantum Lightning Never Strikes the Same State Twice

TL;DR

This paper explores quantum lightning, a form of collision-free quantum money, demonstrating its applications, constructing it under certain assumptions, and linking it to other cryptographic primitives and schemes.

Contribution

It introduces quantum lightning, shows its potential applications, and constructs it based on multi-collision resistant polynomial systems and secure obfuscation.

Findings

Quantum lightning can generate entropy-proven random strings.

Either cryptographic primitives meet strong security notions or they imply quantum money.

Quantum lightning constructed from multi-collision resistant polynomial systems.

Abstract

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