A compact FPGA-based architecture for elliptic curve cryptography over prime fields

This paper proposes an FPGA-based application-specific elliptic curve processor over a prime field. This research targets applications for which compactness is more important than speed. To obtain a small datapath, the FPGA´s dedicated multipliers and carry-chain logic are used and no parallellism is introduced. A small control unit is obtained by following a microcode approach, in which the instructions are stored in the FPGA´s Block RAM. The use of algorithms that prevent Simple Power Analysis (SPA) attacks creates an extra cost in latency. Nevertheless, the created processor is flexible in the sense that it can handle all finite field operations over 256-bit prime fields and all elliptic curves of a specified form. The comparison with other implementations on the same generation of FPGAs learns that our design occupies the smallest area.