Security is a crucial requirement in the envisioned applications of the Internet of Things (IoT), where most of the underlying computing platforms are embedded systems with reduced computing capabilities and energy constraints. In this paper we present the design and evaluation of a scalable low-area FPGA hardware architecture that serves as a building block to accelerate the costly operations of exponentiation and multiplication in [Formula: see text], commonly required in security protocols relying on public key encryption, such as in key agreement, authentication and digital signature. The proposed design can process operands of different size using the same datapath, which exhibits a significant reduction in area without loss of efficiency if compared to representative state of the art designs. For example, our design uses 96% less standard logic than a similar design optimized for performance, and 46% less resources than other design optimized for area. Even using fewer area resources, our design still performs better than its embedded software counterparts (190x and 697x).