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 expressions 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 novel fast algorithm for calculating kP, which is the most time-consuming operation 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 for point multiplication decreases the steps required for iteration by half compared to that of the traditional double-and-add algorithm. It also reduces the number of field multiplications by about 19% and that of field divisions by about 9%.