Modular exponentiation and modular multiplication are the cornerstone computations performed in public-key cryptography systems such as RSA cryptosystem. The operations are time consuming for large operands. Much research effort is directed towards an efficient hardware implementation of both operations. This paper describes the characteristics of two architectures: the first one implements modular multiplication using a systolic version of the fast Montgomery algorithm and the other to implement the parallel binary exponentiation algorithm. The latter uses two Montgomery modular multipliers. Results in terms of space and time requirements for an FPGA prototype are given.