In this paper, we propose new methods for calculating fast VLSI arithmetic
algorithms for secure data encryption and decryption in the Elliptic Curve
Cryptosystem (ECC), and also verify the proof-of-concepts by numerical expr
essions and through the use of HDL (Hardware Description Language). We have
developed a fast finite field multiplier that utilizes a new concept, and
a finite field divider with an improved internal structure, as well as a no
vel fast algorithm for calculating kP, which is the most time-consuming ope
ration in the ECC data encryption scheme. The proposed multiplier features
a higher throughput per cost ratio than any other existing Galois Field (GF
) multiplier that can be used in the large prime finite field. Furthermore,
our improved divider shows better extensibility. The developed algorithm f
or point multiplication decreases the steps required for iteration by half
compared to that of the traditional double-and-add algorithm. It also reduc
es the number of field multiplications by about 19% and that of field divis
ions by about 9%.