We introduce a variation of coded computation that ensures data security and master's privacy against workers, which is referred to as private secure coded computation. In private secure coded computation, the master needs to compute a function of its own dataset and one of the datasets in a library exclusively shared by external workers. After recovering the desired function, the workers must not be able to know which dataset in the library was desired by the master or obtain any information about the master's own data. We propose a private secure coded computation scheme for matrix multiplication, namely private secure polynomial codes, based on private polynomial codes for private coded computation. In simulations, we show that the private secure polynomial codes achieves better computation time than private polynomial codes modified for private secure coded computation.