{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/140059"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/140059","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Delegation with Updatable Unambiguous Proofs and PPAD-Hardness","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Yang, Lisa L."],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Delegation with Updatable Unambiguous Proofs and PPAD-Hardness"]}]}],"canonical_facts":{"dc:contributor.advisor":["Vaikuntanathan, Vinod","Kalai, Yael"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Yang, Lisa L."],"dc:date.accessioned":["2022-02-07T15:21:45Z"],"dc:date.available":["2022-02-07T15:21:45Z"],"dc:date.issued":["2021-09"],"dc:description.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. 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