Short undeniable signatures without random oracles: The missing link

We introduce a new undeniable signature scheme which is existentially unforgeable and anonymous under chosen message attacks in the standard model. The scheme is an embedding of Boneh and Boyen's recent short signature scheme in a group where the decisional Diffie-Hellman problem is assumed to be difficult. The anonymity of our scheme relies on a decisional variant of the strong Diffie-Hellman assumption, while its unforgeability relies on the strong Diffie-Hellman assumption.