Affine Coordinate Binary Edwards Curve Scalar Multiplier with Side Channel Attack Resistance
Apostolos P. Fournaris, Odysseas Koufopavlou · 2015
Taking into account the high regularity and completeness of Binary Edwards Curves (BEC), BEC point operation efficient implementation in hardware becomes a need especially since such curves tend to be more resistant against side channel attacks than the classical Weierstrass Elliptic Curves. However, BECs require more GF(2k) operations for a single scalar multiplication. This constitutes a deterring factor for their wide adoption and standardization. In this paper, a design methodology, hardware architecture and implementation is proposed on the efficient implementation of BEC scalar multiplication accelerators. To achieve that, a parallelism approach is introduced on affine coordinate representation BECs supporting fast GF(2k) inversion through a GF(2k) inversion algorithm capable of realizing also GF(2k) multiplication. The resulting architecture using 4 parallel operating GF(2k) arithmetic units when implemented in FPGA technology provide better results than similar Weierstrass Curves following parallelism techniques, indicated that BECs support parallelism better than their Weierstrass equivalent.