Paper 2021/1446
Batch point compression in the context of advanced pairing-based protocols
Abstract
This paper continues previous ones about compression of points on elliptic curves $E_b\!: y^2 = x^3 + b$ (with $j$-invariant $0$) over a finite field $\mathbb{F}_{\!q}$ of characteristic $p > 3$. It is shown in detail how any two (resp., three) points from $E_b(\mathbb{F}_{\!q})$ can be quickly compressed to two (resp., three) elements of $\mathbb{F}_{\!q}$ (apart from a few auxiliary bits) in such a way that the corresponding decompression stage requires to extract only one cubic (resp., sextic) root in $\mathbb{F}_{\!q}$. As a result, for many fields $\mathbb{F}_{\!q}$ occurring in practice, the new compression-decompression methods are more efficient than the classical one with the two (resp., three) $x$ or $y$ coordinates of the points, which extracts two (resp., three) roots in $\mathbb{F}_{\!q}$. As a by-product, it is also explained how to sample uniformly at random two (resp., three) ``independent'' $\mathbb{F}_{\!q}$-points on $E_b$ essentially at the cost of only one cubic (resp., sextic) root in $\mathbb{F}_{\!q}$. Finally, the cases of four and more points from $E_b(\mathbb{F}_{\!q})$ are commented on as well.
Metadata
- Available format(s)
- Category
- Implementation
- Publication info
- Preprint.
- Keywords
- batch point compressioncubic and sextic rootselliptic curves of $j$-invariant $0$generating "independent" points
- Contact author(s)
- dimitri koshelev @ gmail com
- History
- 2023-09-21: last of 8 revisions
- 2021-10-27: received
- See all versions
- Short URL
- https://ia.cr/2021/1446
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1446, author = {Dmitrii Koshelev}, title = {Batch point compression in the context of advanced pairing-based protocols}, howpublished = {Cryptology {ePrint} Archive, Paper 2021/1446}, year = {2021}, url = {https://eprint.iacr.org/2021/1446} }