Paper 2002/117
Diffie-Hellman Problems and Bilinear Maps
Jung Hee Cheon and Dong Hoon Lee
Abstract
We investigate relations among the discrete logarithm (DL) problem, the Diffie-Hellman (DH) problem and the bilinear Diffie-Hellman (BDH) problem when we have an efficient computable non-degenerate bilinear map $e:G\times G \rightarrow H$. Under a certain assumption on the order of $G$, we show that the DH problem on $H$ implies the DH problem on $G$, and both of them are equivalent to the BDH problem when $e$ is {\it weak-invertible}. Moreover, we show that given the bilinear map $e$ an injective homomorphism $f:H\rightarrow G$ enables us to solve the DH problem on $G$ efficiently, which implies the non-existence a {\it self-bilinear} map $e:G\times G \rightarrow G$ when the DH problem on $G$ is hard. Finally we introduce a sequence of bilinear maps and its applications.
Metadata
- Available format(s)
- PS
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Diffie-HellmanBilinear Diffie-HellmanBilinear map
- Contact author(s)
- jhcheon @ icu ac kr
- History
- 2002-08-12: received
- Short URL
- https://ia.cr/2002/117
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2002/117,
author = {Jung Hee Cheon and Dong Hoon Lee},
title = {Diffie-Hellman Problems and Bilinear Maps},
howpublished = {Cryptology {ePrint} Archive, Paper 2002/117},
year = {2002},
url = {https://eprint.iacr.org/2002/117}
}
