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In this paper, we present a very low power prime-field elliptic-curve cryptography (ECC) processor for use in power-limited applications. The proposed ECC processor is flexible in terms of field and curve parameters and the power consumption is minimized by simplifying the architecture of the processor and also trading off speed for power. To assess the power efficiency of the design, we have implemented the processor for 168-bit and 192-bit fields using a standard 0.13 mum CMOS technology. The simulation results show that the 168-bit and 192-bit processors consume only 23.1 muW and 26.3 muW at a 1 MHz clock respectively, which is considerably lower than the power consumptions reported for similar designs. At the standard frequency of 13.56 MHz, the hardware completes one 168-bit scalar multiplication in 0.72 seconds and one 192-bit scalar multiplication in 1.15 seconds. With these specifications, the proposed ECC processor may be used in non-time-critical applications of contact-less smart cards as well as RFID tags and wireless sensors.