QuICS Special Seminar: Barak Nehoran

Title:  A General Quantum Duality for Representations of Groups with Applications to Quantum Money, Lightning, and Fire
Speaker:  Barak Nehoran (Princeton University)
Time:  Wednesday, December 4, 2024 - 11:00am
Location:  ATL 3100A and Virtual Via Zoom: https://umd.zoom.us/j/93766584122?pwd=rwvOflvt8Nd9LdaQ5jfArBHjT1CRp9.1

Building on this duality principle, we present the following applications:
* Quantum money, representing verifiable but unclonable quantum states, and its stronger variant, quantum lightning, have resisted secure plain-model constructions. While (public-key) quantum money has been constructed securely only from the strong assumption of quantum-secure iO, quantum lightning has lacked such a construction, with past attempts using broken assumptions. We present the first secure quantum lightning construction in the plain model based on a plausible cryptographic assumption by extending Zhandry's construction from Abelian to non-Abelian group actions, eliminating reliance on a black-box model. Our construction is realizable with symmetric group actions, including those implicit in the McEliece cryptosystem.

* We give an alternative quantum lightning construction from one-way homomorphisms, with security holding under certain conditions. This scheme shows equivalence among four security notions: quantum lightning security, worst-case and average-case cloning security, and security against preparing a canonical state.

* Quantum fire describes states that are clonable but not telegraphable: they cannot be efficiently encoded classically. These states "spread" like fire, but are viable only in coherent quantum form. The only prior construction required a unitary oracle; we propose the first candidate with a classical oracle.

Based on joint work with John Bostanci and Mark Zhandry.

*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*