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
Creative Commons Attribution
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}
}
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