Current public-key cryptography systems are vulnerable to quantum computing based attacks. Post-quantum cryptographic (PQC) schemes, based on mathematical paradigms such as lattice-based hard problems, are under consideration by NIST as quantum-safe alternatives. Profiling of several latticebased cryptography algorithms reveals that polynomial multiplication and random number generation are the most time consuming components. The nature of these computations and challenges in vectorizing them are discussed in this paper. Vectorization of the identified time-consuming primitives results in 52% and 83% improvement in performance for the CRYSTALS-Kyber KEM SHA3 variant and AES variant, respectively.