Paper 2002/113 Original: eprint.iacr.org/2002/113 ↗
A Note on the Bilinear Diffie-Hellman Assumption
Abstract
Abstract. The Bi-linear Diffie-Hellman (BDH) intractability assumption is required to establish the security of new Weil-pairing based cryptosystems. BDH is reducible to most of the older believed-to-be-hard discrete-log problems and DH problems, but there is no known reduction from any of those problems to BDH. Let the bilinear mapping be e:G1 X G1->G2, where G1 and G2 are cyclic groups. We show that a many-one reduction from any of the relevant problems to BDH has to include an efficient mapping \phi:G2 ->G1 where \phi(g^{x})=f(x)P. Here g, and P are generators of the corresponding cyclic groups. The function \phi must be used in the reduction either before or after the call to oracle BDH. We show that if f(x)=ax^n+b for any constants a,b,n, then \phi could be used as an oracle for a probabilistic polynomial time solution for Decision Diffie-Hellman in G2. Thus such a reduction is unlikely.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2002-08-10: last updated
- 2002-08-10: published
- Short URL
- https://ia.cr/2002/113
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2002/113,
author = {Yacov Yacobi},
title = {A Note on the Bilinear Diffie-Hellman Assumption},
howpublished = {Cryptology {ePrint} Archive, Paper 2002/113},
year = {2002},
url = {https://eprint.iacr.org/2002/113}
}