Paper 2016/1189 Original: eprint.iacr.org/2016/1189 ↗
On the Bit Security of Elliptic Curve Diffie--Hellman
Abstract
This paper gives the first bit security result for the elliptic curve Diffie--Hellman key exchange protocol for elliptic curves defined over prime fields. About $5/6$ of the most significant bits of the $x$-coordinate of the Diffie--Hellman key are as hard to compute as the entire key. A similar result can be derived for the $5/6$ lower bits. The paper also generalizes and improves the result for elliptic curves over extension fields, that shows that computing one component (in the ground field) of the Diffie--Hellman key is as hard to compute as the entire key.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2017-04-26: last updated
- 2017-01-01: published
- Short URL
- https://ia.cr/2016/1189
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2016/1189,
author = {Barak Shani},
title = {On the Bit Security of Elliptic Curve Diffie--Hellman},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/1189},
year = {2016},
url = {https://eprint.iacr.org/2016/1189}
}