Paper 2021/220

A New Twofold Cornacchia-Type Algorithm

Bei Wang, Yi Ouyang, Songsong Li, and Honggang Hu

Abstract

We focus on exploring more potential of Longa and Sica's algorithm (ASIACRYPT 2012), which is an elaborate iterated Cornacchia algorithm that can compute short bases for 4-GLV decompositions. The algorithm consists of two sub-algorithms, the first one in the ring of integers $\mathbb{Z}$ and the second one in the Gaussian integer ring $\mathbb{Z}[i]$. We observe that $\mathbb{Z}[i]$ in the second sub-algorithm can be replaced by another Euclidean domain $\mathbb{Z}[\omega]$ $(\omega=\frac{-1+\sqrt{-3}}{2})$. As a consequence, we design a new twofold Cornacchia-type algorithm with a theoretic upper bound of output $C\cdot n^{1/4}$, where $C=\frac{3+\sqrt{3}}{2}\sqrt{1+|r|+|s|}$ with small values $r, s$ given by the curve. Besides, we give some applications of our new algotithm in some cuvres not considered in Longa and Sica's algorithm.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. Minor revision.
Keywords
Elliptic curves4-GLV decompositionsTwofold Cornacchia-type algorithm
Contact author(s)
wangbei @ mail ustc edu cn
History
2021-03-04: last of 3 revisions
2021-03-02: received
See all versions
Short URL
https://ia.cr/2021/220
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/220,
      author = {Bei Wang and Yi Ouyang and Songsong Li and Honggang Hu},
      title = {A New Twofold Cornacchia-Type Algorithm},
      howpublished = {Cryptology ePrint Archive, Paper 2021/220},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/220}},
      url = {https://eprint.iacr.org/2021/220}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.