New Extensions of Pairing-based Signatures into Universal (Multi) Designated Verifier Signatures

TL;DR

This paper introduces new efficient pairing-based short signatures for universal designated verifier signatures, with security based on standard cryptographic assumptions, suitable for constrained devices, and extends these schemes to multi-user settings.

Contribution

It proposes novel pairing-based short signature schemes for universal designated verifier signatures, with security proofs and multi-user extensions, improving efficiency and applicability.

Findings

Security based on strong Diffie-Hellman and bilinear Diffie-Hellman assumptions

Pairing-free signing and designation for constrained devices

Extensions to multi-user settings for broader applicability

Abstract

The concept of universal designated verifier signatures was introduced by Steinfeld, Bull, Wang and Pieprzyk at Asiacrypt 2003. These signatures can be used as standard publicly verifiable digital signatures but have an additional functionality which allows any holder of a signature to designate the signature to any desired verifier. This designated verifier can check that the message was indeed signed, but is unable to convince anyone else of this fact. We propose new efficient constructions for pairing-based short signatures. Our first scheme is based on Boneh-Boyen signatures and its security can be analyzed in the standard security model. We prove its resistance to forgery assuming the hardness of the so-called strong Diffie-Hellman problem, under the knowledge-of-exponent assumption. The second scheme is compatible with the Boneh-Lynn-Shacham signatures and is proven unforgeable, in the random oracle model, under the assumption that the computational bilinear Diffie-Hellman problem is untractable. Both schemes are designed for devices with constrained computation capabilities since the signing and the designation procedure are pairing-free. Finally, we present extensions of these schemes in the multi-user setting proposed by Desmedt in 2003.