Exponent-inversion Signatures and IBE under Static Assumptions

Boneh-Boyen signatures are widely used in many advanced cryptosystems. It has a structure of “inversion in the exponent”, and its unforgeability against q chosen-messages attack is proven under the non-static q-Strong Diffie-Hellman assumption. It has been an open problem whether the exponent-inversion signature, and its various applications, can be proved based on a weaker static assumption. We propose a dual-form Boneh-Boyen signature and demonstrate how to prove the security for the exponent-inversion signature structure in the standard model under static assumptions. We apply our proof technique to a number of related cryptosystems employing similar structure, including anonymous credentials, identity-based encryption (IBE) and accountable authority IBE. Our results give the first exponent-inversion IBE in the standard model under static assumption. Our anonymous credentials and accountable authority IBE are also better than existing schemes in terms of both security and efficiency.