Paper 2021/220
A New Twofold Cornacchia-Type Algorithm
Bei Wang; Yi Ouyang; Songsong Li; 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)
- 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
-
CC BY