Paper 2021/1446

Batch point compression in the context of advanced pairing-based protocols

Dmitrii Koshelev, École Normale Supérieure de Lyon
Abstract

This paper continues previous ones about compression of points on elliptic curves Eb:y2=x3+b (with j-invariant 0) over a finite field Fq of characteristic p>3. It is shown in detail how any two (resp., three) points from Eb(Fq) can be quickly compressed to two (resp., three) elements of Fq (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 Fq. As a result, for many fields Fq 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 Fq. As a by-product, it is also explained how to sample uniformly at random two (resp., three) ``independent'' Fq-points on Eb essentially at the cost of only one cubic (resp., sextic) root in . Finally, the cases of four and more points from are commented on as well.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Preprint.
Keywords
batch point compressioncubic and sextic rootselliptic curves of -invariant 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
Creative Commons Attribution
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}
}
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