Tutte Colloquium | Jake Doliskani, Quantum Money: From Wiesner to Standard Assumptions

Abstract: Quantum money is one of the earliest ideas in quantum cryptography: a banknote is represented by a quantum state that cannot simply be copied. Wiesner’s original proposal required the bank to verify every transaction, motivating the notion of public-key quantum money, where anyone can verify a banknote while only the bank can create new ones.

In this talk, I will trace the story of quantum money from Wiesner’s scheme, through the hidden-subspace construction of Aaronson and Christiano, to Zhandry’s recent construction from abelian group actions. I will discuss why previous proposals were either broken or relied on non-standard assumptions, and then present recent work showing that Zhandry’s construction can be based, in the generic group-action model, on the standard group-action discrete logarithm assumption. I will conclude with the main idea behind the security proof.