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
Creative Commons Attribution
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}
}
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