fpga implementation of binary edwards curve usingternary representation
Elliptic curve cryptography (ECC) has proven its superiority, since it was proposed in the domain of Public-Key Cryptography [1]. Further, Edwards curve adds a new paradigm to ECC in terms of speed and security against exceptional point attacks. This curve has been recently extended to Binary Edwards Curves (BEC), due to efficiency of implementation in GF (2 m ) fields and to harvest the advantages of a unified and complete scalar point multiplication on the family of BEC. In spite of achieving the unification, it introduces more challenges to the designer to reduce the computation time and trade-off the area in efficient way. This work reports an implementation of BEC processor with an effort to better utilize the look-up table (LUT) of the FPGA. The design further implements the ternary algorithm to increase the efficiency. However, to the best of our knowledge there exists no previous implementations of BEC on FPGA platform. The proposed design has been implemented for state-of-the-art GF (2 233 ) fields. The performance of the design has been found to compare favorably with the existing designs on standard cell ASIC libraries, in spite of being implemented on FPGA platform.
fpga elliptic curve cryptography (ecc) binary edwards curve (bec)