For post quantum cryptography lattice based systems are among the most widely used and safest systems. One of the difficult problems on lattice based systems are based Learning With Errors (LWE) problem. LWE based protocols, because of the definition of the LWE problem, it contains matrix vector product. These multiplications in the protocols take a lot of time. Because, size of matrices used are very large. Therefore, these multiplications need to be accelerated, optimized and made with an acceptable time. In this study, FrodoKEM, Lizard, Emblem, Lotus key encapsulation mechanishms using LWE problem and matrix vector product in FrodoKEM are focused. A efficient matrix vector product library was created based on the productions in the FrodoKEM protocol and applied to other protocols and the results were examined.