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There is a vast market for cryptography, in which one of the major design concerns is to speed up the execution of encryption and decryption. It is known that the quality (in terms of speed and area) of the cryptography systems is determined by how the inversion/division operators are implemented efficiently. In this paper, we propose a new arithmetic computation architecture for Elliptic Curve Cryptography (ECC) system, which increases efficiency for inverse multiplier/divider. Specifically, we propose a new architectural design approach for inversion/division operators of ECC, which is suitable for portable embedded cryptography systems, by placing the minimization of circuit area as the primary design objective. From experiments using a set of benchmark design, it is shown that our approach is effective and efficient using less circuit area (20% for inverter/37% for divider) than that of the architecture produced by conventional methods.