The Implementations and Applications of Elliptic Curve Cryptography

14 pages•Published: March 21, 2024

Meilin Liu, Kirill Kultinov and Chongjun Wang

Abstract

This paper introduces two distinct new software implementations of ECC over the finite field GF(p) utilizing character arrays and bit sets. Our novel implementations operate on ECC curves of the form y2 = x3 + ax + b (mod p). We have optimized the point addition operation and scalar multiplication on a real SEC (Standards for Efficient Cryptography) ECC curve over a prime field. Furthermore, we have tested and validated the Elliptic Curve Diffie-Hellman key exchange on a real SEC ECC curve using two different implementations of big integer classes. We then proceeded to compare and analyze the performance of these two distinct implementations. Elliptic Curve Cryptography (ECC) represents a promising public-key cryptography system due to its ability to achieve the same level of security as RSA with a significantly smaller key size. ECC stands out for its time efficiency and optimal resource utilization.

Keyphrases: ecc, ecdh, elgamal, elliptic curve, elliptic curve cryptography, point operations

In: Ajay Bandi, Mohammad Hossain and Ying Jin (editors). Proceedings of 39th International Conference on Computers and Their Applications, vol 98, pages 89-102.

Links:	https://easychair.org/publications/paper/zJLs
	https://doi.org/10.29007/gbsb

BibTeX entry

@inproceedings{CATA2024:Implementations_Applications_Elliptic_Curve,
  author    = {Meilin Liu and Kirill Kultinov and Chongjun Wang},
  title     = {The Implementations and Applications of Elliptic Curve Cryptography},
  booktitle = {Proceedings of 39th International Conference on Computers and Their Applications},
  editor    = {Ajay Bandi and Mohammad Hossain and Ying Jin},
  series    = {EPiC Series in Computing},
  volume    = {98},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/zJLs},
  doi       = {10.29007/gbsb},
  pages     = {89-102},
  year      = {2024}}

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