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.