Post-quantum cryptography (PQC) will be needed to secure public-key cryptosystems from quantum computers in the near future. The National Institute of Standards and Technology (NIST) is organizing the standardization of PQC algorithms, particularly those for key encapsulation and digital signatures. One candidate selected by NIST in the third round of the standardization process is the lattice-based CRYSTALS-Dilithium digital signature algorithm. We explore the integration of CRYSTALS-Dilithium in a Response-based Cryptography (RBC) protocol to enable quantum resistance. RBC utilizes un-corrected responses from Physically Unclonable Functions (PUFs) as seeds to generate cryptographic keys used for authentication between a server and client device. Authentication is achieved when the server generates a seed from its initially recorded PUF challenge that exactly matches the seed generated from the client device’s PUF response. However, there is noise inherent to PUF technology that causes the client’s response to differ from the seed recorded on the server during enrollment. The RBC protocol addresses this problem by having the server independently correct its own seed. But, the computational requirements for seed correction increase exponentially with the error rate of the PUF. Therefore, architectures such as Graphics Processing Units (GPUs) are utilized to perform this seed correction in parallel. We propose the first known CRYSTALS-Dilithium implementation on the GPU and use this implementation to develop the first reported Post-Quantum RBC protocol in the literature. We compare our GPU-Accelerated CRYSTALS-Dilithium RBC algorithm to a baseline implementation parallelized using a multi-core CPU. We find that our approach using the GPU achieves speedups of 69.03×, 82.52×, and 90.70× over the CPU for security levels 2, 3, and 5, respectively. To further accelerate the seed correction procedure, we fragment the PUF seed into sub-seeds which allows for a higher error-rate in the PUF given a fixed timing threshold.