Existing privacy preserving schemes have attained maximum privacy level either using the exponential modular operations or the strong intractability assumptions. But they failed to guarantee the following challenges till date namely (1) computationally bounded single database scheme with non-trivial communication (2) inbuilt integrity support (3) only linear encryption operations. We have proposed a single database Oblivious Transfer (OT) or Symmetric Private Information Retrieval (SPIR) schemes using the quadratic residuosity as the underlying cryptographic primitive. In this paper, we have constructed a new quadratic residuosity based concurrently executing recursive 2-bit encryption function which fulfill all the above mentioned challenges. This recursive 2-bit encryption functions receive Quadratic Residuosity Assumption (QRA) based queries and produce the reasonable communication bits as the response bits. The greatest advantages of the proposed schemes is that they operate on the plain database and the concurrently executing recursive 2-bit encryption functions involve only linear number of modular multiplications.