Abstract
Elliptic Curve Cryptography (ECC) is considered as one of the best candidates for public key cryptographic systems. ECC o ers equivalent security as RSA for much smaller parameter sizes. As a result, it exhibits the smaller data-paths, less memory usage and lower power consumption. Based on its computational complexity, ECC is suitable for constrained devices such as RFID tags. However, integrating ECC on RFID tags to ensure the secure information transaction is still a challenge for limited power consumption, energy and area resources. In this thesis, we propose low cost ECC engines to support the secure RFID-tag authentication protocol. The critical operation in the authentication protocol is the EC scalar multiplication. We present the arithmetic unit integrating a digit-serial multiplier, an adder, and a bit-parallel squarer. The proposed circular shift register can eciently reduce the complexity of input selection of our arithmetic unit. Based on the Montgomery ladder algorithm over binary elds, we also present the optimal operation scheduling using integer linear programming (ILP) technique that can further minimize the latency of EC scalar multiplication with little control overhead. In order to find the trade-off on digit size, we evaluate sixteen digit sizes, ranging from 1 to 16 bits of multiplier in our ECC engine. Finally, the synthesis result using TSMC 65nm CMOS technology shows that our ECC engine with digit size of 2 implemented with 10,504 gates, total power around 4.68 μW at 273 KHz within 250 ms and the energy consumption 1.17 μJ for one EC calar multiplication is the best between power, area, and energy consumption among current low cost design.