Multi-segment GF (2 m ) multiplication and its application to elliptic curve cryptography
Dongho Lee, Jong-Soo Oh · 2007
Scalar multiplication is the most time consuming computation in elliptic curve cryptography (ECC). ECC coprocessors provide computational support for the scalar multiplication algorithm. In this paper, we propose an efficient multi-segment GF(2m) multiplication method and discuss its application for ECC. The proposed method is particularly effective when the underlying technology provides an efficient realization of dual-port RAM block structures. We implemented ECC coprocessors in FPGA development environments to compare the resource usages of the ECC processors which use the proposed multi-segment multipliers and others using the digit-serial multipliers. The experimental results show that the proposed multi-segment multiplication method requires significantly less FPGA resources for the same multiplication performance in ECC implementations.