Paper 2003/019 Original: eprint.iacr.org/2003/019 ↗
A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem
Abstract
We propose the first polynomial time algorithm for the braid Diffie-Hellman conjugacy problem (DHCP) on which the braid key exchange scheme and the braid encryption scheme are based~\cite{KLCHKP01}. We show the proposed method solves the DHCP for the image of braids under the Lawrence-Krammer representation and the solutions play the equivalent role of the original key for the DHCP of braids. Given a braid index $n$ and a canonical length $\ell$, the complexity is about $2^{-2}\ell^3 n^{4\tau+2}\log n$ bit operations, where $\tau=\log_27\approx 2.8$ (Theoretically, it can be reduced to $O(\ell^3 n^{8.3}\log n)$ using $\tau=2.376$). Further, we show that the generalization into the decomposition problem causes only 8 times of the complexity.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2003-04-08: last updated
- 2003-01-30: published
- Short URL
- https://ia.cr/2003/019
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2003/019,
author = {Jung Hee Cheon and Byungheup Jun},
title = {A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2003/019},
year = {2003},
url = {https://eprint.iacr.org/2003/019}
}