Paper 2021/220
A New Twofold CornacchiaType 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 4GLV decompositions. The algorithm consists of two subalgorithms, 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 subalgorithm can be replaced by another Euclidean domain $\mathbb{Z}[\omega]$ $(\omega=\frac{1+\sqrt{3}}{2})$. As a consequence, we design a new twofold Cornacchiatype 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)
 Category
 Publickey cryptography
 Publication info
 Preprint. MINOR revision.
 Keywords
 Elliptic curves4GLV decompositionsTwofold Cornacchiatype algorithm
 Contact author(s)
 wangbei @ mail ustc edu cn
 History
 20210304: last of 3 revisions
 20210302: received
 See all versions
 Short URL
 https://ia.cr/2021/220
 License

CC BY
BibTeX
@misc{cryptoeprint:2021/220, author = {Bei Wang and Yi Ouyang and Songsong Li and Honggang Hu}, title = {A New Twofold CornacchiaType 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} }