On the Black-Box Impossibility of Multi-Designated Verifiers Signature Schemes from Ring Signature Schemes

From the work by Laguillaumie and Vergnaud in ICICS’04, it has been widely believed that multi-designated verifiers signature scheme (MDVS) can be constructed from ring signature schemes in general. However, in this article, somewhat surprisingly, we prove that it is impossible to construct an MDVS scheme from a ring signature scheme in a black-box sense (in the standard model). The impossibility stems from the difference between the definitions of unforgeability of the two schemes. To the best of our knowledge, existing works demonstrating the constructions do not provide formal reductions from an MDVS scheme to a ring signature scheme, and thus, the impossibility has been overlooked for a long time.