This paper presents a novel design methodology for the hardware implementation of non-linear bijective functions, commonly used in most symmetric-key cryptographic algorithms and known as substitution boxes (S-boxes). The proposed technique thwarts a particularly relevant class of side-channel attacks against cryptographic hardware, that of differential power analysis attacks (DPA). In the proposed approach, the cost of the countermeasure is kept low in terms of silicon process overheads (standard CMOS gates used), area requirement, power consumption and latency, when compared to existing countermeasures. Its effectiveness is proven by showing resistance to simulated DPA attacks using power curves derived with SPICE simulation.