The threat of digital counterfeiting and forgery of integrated circuits is growing at an alarming rate. At the same time, the functionalities of integrated circuits are becoming much more complex. This paper presents a design for cryptographic applications using Physically Unclonable Functions (PUFs) that can be implemented on an FPGA taking advantage of its unique architecture. The first part of the research involves development of techniques for the generation of uniquely distinguishable responses from ROPUFs taking advantage of the unique architecture of the FPGA and the latter part involves development of error correction technique using Artificial Neural Networks. The proposed design is implemented on several Xilinx Spartan FPGAs and the Hamming distances for the responses are computed and analyzed. The uniqueness of the responses is found to be 49.0625%. It is also found that the results of the proposed ECC also prove to be computationally efficient than the conventional BCH codes.