A new approach and an idea for exploration are presented to the concurrent deniable authentication based on witness-indistinguishable(WI)within the framework of universally composable(UC)security.A definition of an ideal functionality for deniable authentication is formulated.A new deniable authentication protocol is proposed based on two primitives of the verifiably smooth projective Hashing(VSPH)and non-committing encryptions(NCE).This new approach is practically relevant to VSPH based on the Decisional Diffie-Hellman (DDH)assumption and NCE based on the decisional composite residuosity(DCR)assumption.Compared with a timing constraint and public directory model,simulation of the concurrent protocols is not needed to restrict an adversary capability in a common reference string(CRS)model.The protocols are forward deniable and UC security against adaptive adversaries.Unlike previous proposals with the CCA2 public-key cryptosystem or multi-trapdoor commitments paradigm,the new paradigm leads to more efficient protocols.