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, Pseudo-Random Function.

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