### Arithmetization of Σ¹₁ relations with polynomial bounds in Halo 2

##### Abstract

Previously [4], Orbis Labs presented a method for compiling (“arithmetizing”) relations, expressed as Σ¹₁ formulas in the language of rings, into Halo 2 [1, 2, 3] arithmetic circuits. In this research, we extend this method to support polynomial quantifier bounds, in addition to constant quantifier bounds. This allows for more efficient usage of rows in the resulting circuit.

Available format(s)
Category
Applications
Publication info
Preprint.
Keywords
PLONK Halo 2 arithmetization logic second order arithmetic
Contact author(s)
team @ orbislabs com
team @ orbislabs com
History
2022-08-29: approved
See all versions
Short URL
https://ia.cr/2022/1105

CC BY

BibTeX

@misc{cryptoeprint:2022/1105,
author = {Anthony Hart and Morgan Thomas},
title = {Arithmetization of Σ¹₁ relations with polynomial bounds in Halo 2},
howpublished = {Cryptology ePrint Archive, Paper 2022/1105},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1105}},
url = {https://eprint.iacr.org/2022/1105}
}

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