This paper deals with improving Montgomery’s algorithm. We improve mongomery’s algorithm such that modular multiplications can be executed two times faster. Each iteration in our algorithm requires only one addition, while that in Montgomery’s requires two additions. We then propose a cellular array to implement modular exponentiation for the Rivest–Shamir–Adleman cryptosystem. It has approximately 2n cells, where n is the word length. The cell contains one full-adder and some controlling logic. The time to calculate a modular exponentiation is about 2n2 clock cycles.