Efficient Elliptic Curve Point Multiplication Using Digit-Serial Binary Field Operations

This paper details the design of a new high-speed point multiplier for elliptic curve cryptography using either field-programmable gate array or application-specified integrated circuit technology. Different levels of digit-serial computation were applied to the data path of Galois field (GF) multiplication and division to explore the resulting performances and find out an optimal digit size. We provide results for the five National Institute of Standards and Technology recommended curves, outperforming the previous published results. In
GF
(2
¹⁶³
), we achieve a point multiplication in 19.38 μs in Xilinx Virtex-E. Using the modern Xilinx Virtex-5, the point multiplication times in
GF
(2
m
) for
m
= 163, 233, 409, and 571 are 5.5, 17.8, 33.6, 102.6, 384μs, respectively, which are the fastest figures reported to date.