Rational sumchecks

Siyao Guo*, Pavel Hubáček, Alon Rosen, Margarita Vald

*Corresponding author for this work

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


Rational proofs, introduced by Azar and Micali (STOC 2012) are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. In recent work, Guo et al. (ITCS 2014) demonstrated their relevance to delegation of computation by showing that, if the rational prover is additionally restricted to being computationally bounded, then every language in NC1 admits a singleround delegation scheme that can be verified in sublinear time. We extend the Guo et al. result by constructing a single-round delegation scheme with sublinear verification for all languages in P. Our main contribution is the introduction of rational sumcheck protocols, which are a relaxation of classical sumchecks, a crucial building block for interactive proofs. Unlike their classical counterparts, rational sumchecks retain their (rational) soundness properties, even if the polynomial being verified is of high degree (in particular, they do not rely on the Schwartz-Zippel lemma). This enables us to bypass the main efficiency bottleneck in classical delegation schemes, which is a result of sumcheck protocols being inapplicable to the verification of the computation’s input level.

Original languageEnglish
Title of host publicationTheory of Cryptography - 3th International Conference, TCC 2016-A, Proceedings
EditorsEyal Kushilevitz, Tal Malkin
PublisherSpringer Verlag
Number of pages33
ISBN (Print)9783662490983
StatePublished - 2016
Event13th International Conference on Theory of Cryptography, TCC 2016 - Tel Aviv, Israel
Duration: 10 Jan 201613 Jan 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Conference on Theory of Cryptography, TCC 2016
CityTel Aviv


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