A Fast and Compact FPGA Implementation of Elliptic Curve Cryptography Using Lambda Coordinates

Elliptic curve cryptography (ECC) provides high security with shorter keys than other public-key cryptosystems and it has been successfully used in security critical embedded systems. We present an FPGA-based coprocessor that communicates with the host processor via a 32-bit bus. It implements ECC over an elliptic curve that offers roughly 128-bit security. It is the first hardware implementation that uses the recently introduced lambda coordinates and the Galbraith-Lin-Scott (GLS) technique with fast endomorphisms. One scalar multiplication requires 65,000 clock cycles with a maximum clock frequency of 274 MHz on a Xilinx Virtex-5 FPGA, which gives a computation time of 0.24 ms. The area utilization is 1552 slices and 4 BlockRAMs. Our coprocessor compares favorably to other published works both in terms of speed and area, which makes it a good choice for embedded systems that require high-security public-key cryptography.