A first group of modulo result matrices corresponding to modulo of elements of a first matrix by each of a plurality of moduli is stored. A second group of modulo result matrices corresponding to modulo of elements of a second matrix by each of the plurality of moduli is stored. It is determined whether an element operation of a multiplication of the first matrix with the second matrix can be performed using a first hardware multiplication module rather than a second hardware multiplication module. In response to a determination that the element operation can be performed using the first hardware multiplication module, the element operation is performed using the first hardware multiplication module including by multiplying one or more corresponding elements from the first group of modulo result matrices with one or more corresponding elements from the second group of modulo result matrices.