The paper presents an efficient architecture for a one-way function using Two Predecessor Single Attractor Cellular Automata (TPSA CA). Most of the widely used key establishment algorithms employ one-way functions based on modular exponentiation that are computationally very expensive. However, the implementation of the proposed architecture shows that the TPSA based one-way algorithm can be implemented very efficiently with very less consumption of computational resources like power, area and clock cycles. Such a one-way function can be an ideal replacement of modular exponentiation based one-way functions and thus help to develop fast and secure key establishment protocols.