Lattice-based cryptography (LBC) is a promising and efficient public key cryptography scheme whose theoretical foundation lies in Learning with Error (LWE) problem and its variant such as Ring-LWE (R-LWE) is the most studied cryptosystem which allows for more efficient implementation while maintaining the hardness of an original problem. Polynomial multiplication is the bottleneck of R-LWE, that can either be done using Number Theoretic Transform (NTT) or schoolbook polynomial multiplication (SPM) algorithm, the use of SPM is wider and possible for all parameters of R-LWE schemes. This work proposes an efficient and parallel strategy for SPM in R-LWE; by successfully reducing its time complexity from n2 to n2/4 (making it 1.8× faster and 1.4× hardware efficient). Furthermore, by adjusting the bit width for the error terms, the polynomial multiplication and addition blocks are reused for both encryption and decryption modules resulting in 16.30% reduced area and 1.7× better throughputincomparison to state-of-the-art SPM based R-LWE designs.