## CryptoDB

### Paper: Diffie-Hellman Problems and Bilinear Maps

Authors: Jung Hee Cheon Dong Hoon Lee URL: http://eprint.iacr.org/2002/117 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2002-11640,
title={Diffie-Hellman Problems and Bilinear Maps},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / Diffie-Hellman, Bilinear Diffie-Hellman, Bilinear map},
url={http://eprint.iacr.org/2002/117},
note={ jhcheon@icu.ac.kr 11911 received 11 Aug 2002},
author={Jung Hee Cheon and Dong Hoon Lee},
year=2002
}