Breaking the decisional Diffie-Hellman problem in totally non-maximal imaginary quadratic orders

Antonio Sanso

Paper 2024/201

Breaking the decisional Diffie-Hellman problem in totally non-maximal imaginary quadratic orders

Antonio Sanso, Ethereum Foundation

Abstract

This paper introduces an algorithm to efficiently break the Decisional Diffie-Hellman (DDH) assumption in totally non-maximal imaginary quadratic orders, specifically when $\Delta_1 = 3$, and $f$ is non-prime with knowledge of a single factor. Inspired by Shanks and Dedekind's work on 3-Sylow groups, we generalize their observations to undermine DDH security.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: class groups
Contact author(s): asanso @ ethereum org
History: 2024-02-12: approved; 2024-02-09: received; See all versions
Short URL: https://ia.cr/2024/201
License: CC BY

BibTeX

@misc{cryptoeprint:2024/201,
      author = {Antonio Sanso},
      title = {Breaking the decisional Diffie-Hellman problem in totally non-maximal imaginary quadratic orders},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/201},
      year = {2024},
      url = {https://eprint.iacr.org/2024/201}
}