Quantum Money based on Lattices

on YouTube ↗01h 13m

" summary

Proposal constructs money states as Gaussian superpositions of lattice points centered on dual-lattice serial numbers, created by Gaussian sampling then a lattice quantum Fourier transform and verified by interference between paired balls separated by a chosen vector l. Verification uses bounded-distance decoding and statistical repetition so tests approach probability 1. Broken simpler variants allow extracting lattice points and finding short vectors; security of the working scheme reduces to the shortest-vector hardness in lattices (polynomial factors), paper pending.

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" chapters (16)

1. 0:00Start
2. 0:33Outline
3. 3:19Proposals for Quantum Money
4. 4:37History
5. 6:00Cryptography Background and Motivation
6. 7:52Task: Quantum Money
7. 13:15How does our quantum money protocol work?
8. 15:15Bounded Distance Decoding
9. 15:48Gaussian Sampling
10. 16:25Gaussian superposition
11. 17:16Subclass of lattices
12. 18:13Dual of these lattices
13. 19:59Quantum Fourier transform on Z (Eldar and Shor)
14. 21:00Properties of Quantum Fourier transform on 2
15. 33:04Why shouldn't you be able to copy?
16. 34:32Why doesn't this protocol work?

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