This paper is about a new efficient method for the implementation of convolvers and correlators using the Fermat Number Transform (FNT) and the inverse (IFNT). The latter present advantages compared to Inverse Fast Fourier Transform (IFFT). An efficient state space method for implementing the Inverse FNT (IFNT) over rectangular windows is proposed for the cases where there is a large overlap between the consecutive input signals. This is called Inverse Generalized Sliding Fermat Number Transform (IGSFNT) and is useful for reducing the computational complexity of finite ring convolvers and correlators. This algorithm uses the technique of Generalized Sliding associated to matricial calculation in the Galois Field. The computational complexity of this method is compared with that of standard IFNT.