Delegation with Updatable Unambiguous Proofs and PPAD-Hardness
Name
Yang-lisayang-SM-EECS-2021-thesis.pdf
Description
Thesis PDF
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2.33 MB
Format
Adobe PDF
Checksum (MD5)
04b8e58c151f601f97d5f0bf718324ce
Author(s)
Yang, Lisa L.
Advisor(s)
Vaikuntanathan, Vinod
Kalai, Yael
Date Issued
September 2021
Publisher
Massachusetts Institute of Technology
Abstract
In this work, we construct an updatable and unambiguous delegation scheme based on the decisional assumption on bilinear groups introduced by Kalai, Paneth and Yang [STOC 2019]. Using this delegation scheme, we show PPAD-hardness (and hence the hardness of computing Nash equilibria) based on the quasi-polynomial hardness of this bilinear group assumption and any hard language that is decidable in quasi-polynomial time and polynomial space.
The delegation scheme is for super-polynomial time deterministic computations and is publicly verifiable and non-interactive in the common reference string (CRS) model. It is updatable meaning that given a proof for the statement that a Turing machine reaches some configuration C in T steps, it is efficient to update it into a proof for the statement that the machine reaches the next configuration C' in T+1 steps. It is unambiguous meaning that it is hard to produce two different proofs for the same statement.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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