Bypassing the characteristic bound in logUp

Liam Eagen; Ulrich Haböck

Paper 2024/2067

Bypassing the characteristic bound in logUp

Liam Eagen, Alpen Labs, Polygon Labs

Ulrich Haböck, Polygon Labs

Abstract

In this informal note, we describe how to bypass the characteristic bound in logUp [eprint 2022/1530] by abstracting the notion of (pole) multiplicity. The method applies as well to the GKR-variant from Papini and Haböck [eprint 2023/1284], and it moreover unlocks fractional decomposition lookups over binary fields.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Lookup arguments permutation argument fractional decomposition
Contact author(s): liameagen @ protonmail com
ulrich haboeck @ gmail com
History: 2025-02-20: revised; 2024-12-23: received; See all versions
Short URL: https://ia.cr/2024/2067
License: CC BY-SA

BibTeX

@misc{cryptoeprint:2024/2067,
      author = {Liam Eagen and Ulrich Haböck},
      title = {Bypassing the characteristic bound in {logUp}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/2067},
      year = {2024},
      url = {https://eprint.iacr.org/2024/2067}
}