Welcome to the resource topic for 2002/117
Title:
Diffie-Hellman Problems and Bilinear Maps
Authors: Jung Hee Cheon, 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.
ePrint: https://eprint.iacr.org/2002/117
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