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Elliptic curve point multiplication (ECPM) is one of the most critical operations in elliptic curve cryptography. In this brief, a new hardware architecture for ECPM over GF(p) is presented, based on the residue number system (RNS). The proposed architecture encompasses RNS bases with various word-lengths in order to efficiently implement RNS Montgomery multiplication. Two architectures with four and six pipeline stages are presented, targeted on area-efficient and fast RNS Montgomery multiplication designs, respectively. The fast version of the proposed ECPM architecture achieves higher speeds and the area-efficient version achieves better area-delay tradeoffs compared to state-of-the-art implementations.