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A high performance elliptic curve coprocessor is developed, which is optimized for a binary field recommended by NIST. The architecture uses a field multiplier capable of performing a field multiplication over the extension field with degree 163 in 0.060 μsec. The coprocessor uses Lopez and Dahab's projective coordinate system and is optimized specifically for Koblitz curves. An efficient implementation of Itoh and Tsujii's method for inversion with performance comparable to the extended Euclidean algorithm is used. A prototype of the processor has been implemented for the binary extension field with degree 163 on a Xilinx XCV2000E FPGA. The prototype runs at 66 MHz and performs an elliptic curve scalar multiplication in 0.233 msec on a generic curve and 0.075 msec on a Koblitz curve.