Elliptic Curve Cryptography implementation on FPGA using Montgomery multiplication for equal key and data size over GF(2m) for Wireless Sensor Networks

Abstract

In public key cryptography, RSA algorithm has been used for a long time, but it does not meet the constraints of WSNs. Elliptic Curve Cryptography(ECC) has been employed recently because of its high security for same length bit. ECC point multiplication operation is time consuming which affects the speed of encryption and decryption of data. In this paper, we propose the point multiplication using Montgomery multiplication technique that achieves considerable speed and with reduced area utilization. The ECC is first simulated on different FPGA devices, with key length 112 and 163 bits and the area-speed tradeoff is compared. ECC algorithm is implemented with software and hardware choosing Artix 7 XC7a100t-3csg324 FPGA which supports key lengths of 112 and 163 bits. The proposed ECC algorithm is modeled using VHDL and synthesized on Spartan 3 and 6, Virtex 4, 5 and 6 and Artix 7 before the hardware implementation on Atrix 7. The design satisfies the needs of resource constrained WSNs devices with equal key length and data size, the device utilization is within 13 percentage.