Knowledge-preserving interactive coding

Kai Min Chung, Rafael Pass, Sidharth Telang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

How can we encode a communication protocol between two parties to become resilient to adversarial errors on the communication channel? If we encode each message in the communication protocol with a "good" error-correcting code (ECC), the error rate of the encoded protocol becomes poor (namely O(1/M) where M is the number of communication rounds). Towards addressing this issue, Schulman (FOCS'92, STOC'93) introduced the notion of interactive coding. We argue that whereas the method of separately encoding each message with an ECC ensures that the encoded protocol carries the same amount of information as the original protocol, this may no longer be the case if using interactive coding. In particular, the encoded protocol may completely leak a player's private input, even if it would remain secret in the original protocol. Towards addressing this problem, we introduce the notion of knowledgepreserving interactive coding, where the interactive coding protocol is required to preserve the "knowledge" transmitted in the original protocol. Our main results are as follows.The method of separately applying ECCs to each message has essentially optimal error rate: No knowledge-preserving interactive coding scheme can have an error rate of 1/M, where M is the number of rounds in the original protocol.If restricting to computationally-bounded (polynomial-time) adversaries, then assuming the existence of one-way functions (resp. subexponentially-hard one-way functions), for every ε > 0, there exists a knowledge-preserving interactive coding schemes with constant error rate and information rate n (resp. 1/polylog(n)) where n is the security parameter; additionally to achieve an error of even 1/m requires the existence of one-way functions.Finally, even if we restrict to computationallybounded adversaries, knowledge-preserving interactive coding schemes with constant error rate can have an information rate of at most o(1/ log n). This results applies even to non-constructive interactive coding schemes.

Original languageEnglish
Title of host publicationProceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Pages449-458
Number of pages10
DOIs
StatePublished - 2013
Externally publishedYes
Event2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 - Berkeley, CA, United States
Duration: 27 Oct 201329 Oct 2013

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Country/TerritoryUnited States
CityBerkeley, CA
Period27/10/1329/10/13

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