In this paper, we newly define the notion of edge regular power fuzzy graph, based on the properties of edge regular fuzzy graph and power fuzzy graph (PFG). Totally edge regular power fuzzy graph is presented as a special case of edge regular power fuzzy graph. General formulas are derived to calculate the degree of edges for a total power fuzzy graph when it is edge regular and total degree of edges when it is totally edge regular. Further, this concept is applied in the encryption method to decipher data by authorised persons.