The development and implementation of post-quantum cryptosystems have become pressing issues in the design of secure computing systems, as general quantum computers have become more feasible in recent years. In this paper, we introduce a set of FPGA-based post-quantum cryptographic primitives (PQCPs) consisting of four frequently used security components, i.e., public key cryptosystem (PKC), key exchange (KEX), oblivious transfer (OT), and zero-knowledge proof (ZKP). The three main contributions of this work are: (1) FPGA-tailored implementation of the hardware primitives with novel algorithmic proposals of the OT and ZKP; (2) algorithmic optimizations to reduce area and latency costs without compromising security; and (3) open-sourcing the synthesizable and fully verifiable code for the community at large. The RTL code base is fully parameterizable with an efficient, n-point Number-Theoretic Transform (NTT) module for fast polynomial multiplications. These primitives will aid researchers and designers in constructing quantum-proof secure computing systems to prepare for the post-quantum era. Implementation results, on an Zynq-7000 FPGA, show various design trade-offs and correlations between system parameters and the associated hardware cost and latency. The source code for this project is available on the ASCS Lab website at the following URL: http://ascslab.org/research/pqcp/index.html.