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SUMMARY:Proximity Gaps for Multilinear Interactive Oracle Proofs - Hadas Z
 eilberger (Yale)
DTSTART:20250925T090000Z
DTEND:20250925T100000Z
UID:TALK235534@talks.cam.ac.uk
CONTACT:Tom Gur
DESCRIPTION:A set displays a (delta\, gamma)-proximity gap to a linear cod
 e\, C\, if either all elements are delta-close in relative Hamming distanc
 e to a codeword in C or only gamma of them are. Proximity gaps of the set 
 A_{v\,u} := {v + r u : r in F }\, for fixed vectors v\,u\, are fundamental
  to the security and efficiency of an extremely efficient family of Intera
 ctive Oracle Proofs (IOPs) from FRI (ICALP 2018)\, where larger delta impl
 ies more efficient verifiers and smaller gamma implies more efficient prov
 ers. \n\nBuilding on FRI\, the authors of BaseFold (Crypto 2024) introduce
 d a new family of IOPs with concretely faster provers. However\, BaseFold 
 additionally requires that if all elements of A_{v\,u} are close to the co
 de\, then they all agree with their respective nearest codewords in a fixe
 d\, shared set of locations. \n\nWe prove this to be true for all linear c
 odes when delta < 1 -  (1 - Delta + epsilon)^{1/3} - eta and gamma < 1/(ep
 silon eta) (where Delta is the relative minimum distance of the code). Thi
 s improves the previous bound of delta < 1 - (1 - Delta/3) - eta from Base
 Fold\, and it recovers the original proximity gaps result for linear codes
 \, which is proven to be tight in DEEP-FRI (ITCS 2020).\n\nlink to paper: 
 https://eprint.iacr.org/2024/1843.pdf
LOCATION:Computer Laboratory\, William Gates Building\, Room SS03
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