This paper describes a scalable unified architecture for Montgomery multiplication over either of the finite fields GF(p) and GF(2n). This architecture has the advantage of possessing a new redundant binary adder that supports carry-save additions under either of the Galois Fields without the need for an external control signal to specify which field is to be used. Its main advantage over previously reported dual field multiplier is that a control signal which is broadcast to all cells to suppress carries under GF(2n) is not needed. Consequently, larger multipliers can be synthesised whose pipelined speed is independent of the buffering required for the control signal.