An arrangement is provided for performing modular exponentiations. A modular exponentiation may be performed by using multiple Montgomery multiplications. A Montgomery multiplication comprises a plurality of iterations of basic operations (e.g., carry-save additions), and is performed by a Montgomery multiplication engine (MME). Multiple MMEs of smaller sizes may be chained together to perform modular exponentiations of larger sizes. Additionally, a single MME of a smaller size may be scheduled to perform modular exponentiations of larger sizes. Moreover, the process of performing a Montgomery multiplication may be pipelined both horizontally and vertically. Furthermore, processes of performing two Montgomery multiplications may be interleaved and performed by the same MME or chained MMEs.