International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Byungheup Jun

Publications

Year
Venue
Title
2003
CRYPTO
2003
EPRINT
A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem
Jung Hee Cheon Byungheup Jun
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.

Coauthors

Jung Hee Cheon (2)