Generalized Diffie-Hellman Modulo a Composite is
not Weaker than Factoring
Eli Biham, Dan Boneh and Omer Reingold
The Diffie-Hellman key-exchange protocol may naturally be
extended to k>2 parties. This gives rise to the generalized
Diffie-Hellman assumption (GDH-Assumption).
Naor and Reingold have recently shown an efficient construction
of pseudo-random functions and reduced the security of their
construction to the GDH-Assumption.
In this note, we prove that breaking this assumption modulo a composite
would imply an efficient algorithm for factorization.
Therefore, the security of both the key-exchange protocol and
the pseudo-random functions can be reduced to factoring.
Keywords: Diffie-Hellman Assumption, Factoring, Key-Exchange,
, gzipped Postscript .
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