Reed-Solomon (RS) code is one of the well-known and widely used error correction codes. Among the components of a hardware RS decoder, the key equation solver (KES) unit occupies a relatively large portion of the hardware. It is important to develop an efficient KES architecture to implement efficient RS decoders. In this paper, a novel polynomial division technique used in the Euclidean algorithm (EA) of the KES is presented which achieves the short critical path delay of one Galois multiplier and one Galois adder. Then a KES architecture with the EA is proposed which is efficient in the sense of the product of area and time.