Bypassing the characteristic bound in logUp

Liam Eagen; Ulrich Haböck

Paper 2024/2067 Original: eprint.iacr.org/2024/2067 ↗

Bypassing the characteristic bound in logUp

Liam Eagen

Ulrich Haböck

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.
History: 2025-02-20: last updated; 2024-12-23: published
Short URL: https://ia.cr/2024/2067
License: https://creativecommons.org/licenses/by-sa/4.0/

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}
}