## Cryptology ePrint Archive: Report 2020/315

plookup: A simplified polynomial protocol for lookup tables

Ariel Gabizon and Zachary J. Williamson

Abstract: We present a protocol for checking the values of a committed polynomial $f\in \mathbb{F}_{<n}[X]$ over a multiplicative subgroup $H\subset \mathbb{F}$ of size $n$, are contained in the values of a table $t\in \mathbb{F}^d$. Our protocol can be viewed as a simplification of one from Bootle et. al [BCGJM, ASIACRYPT 2018] for a similar problem, with potential efficiency improvements when $d\leq n$. In particular, [BCGJM]'s protocol requires comitting to several auxiliary polynomials of degree $d\cdot \log n$, whereas ours requires three commitments to auxiliary polynomials of degree $n$, which can be much smaller in the case $d\sim n$. One common use case of this primitive in the zk-SNARK setting is a batched range proof'', where one wishes to check all of $f$'s values on $H$ are in a range $[0,\ldots,M]$. We present a slightly optimized protocol for this special case, and pose improving it as an open problem.

Category / Keywords: zk-SNARKs, Polynomial Commitment Schemes

Date: received 13 Mar 2020, last revised 21 Mar 2020

Contact author: ariel at aztecprotocol com

Available format(s): PDF | BibTeX Citation

Note: small corrections

Short URL: ia.cr/2020/315

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