• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: 20, Pages: 2074-2078

Original Article

Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers

Received Date:10 April 2024, Accepted Date:28 April 2024, Published Date:14 May 2024


Background/Objectives: Elliptic Curve Cryptography (ECC) is a public-key encryption method that is similar to RSA. ECC uses the mathematical concept of elliptic curves to achieve the same level of security with significantly smaller keys, whereas RSA's security depends on large prime numbers. Elliptic curves and their applications in cryptography will be discussed in this paper. The elliptic curve is formed by the extension of a Diophantine pair of Centered Hexadecagonal numbers to a Diophantine triple with property D(8). Method: The Diffie–Hellman key exchange, named for Whitfield Diffie and Martin Hellman, was developed by Ralph Merkle and is a mathematical technique for safely transferring cryptographic keys over a public channel. Based on the Diffie–Hellman key exchange, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography. The generation of keys, encryption and decryption are the three main operations of the ElGamal cryptosystem. Findings: Given the relative modesty of our objectives, the fundamental algebraic and geometric characteristics of elliptic curves shall be delineated. Then the behaviour of elliptic curves modulo p: ultimately, there is a fairly strong analogy between the structure of the points on an elliptic curve modulo p and the integers modulo n will be studied. In the end, elliptic curve ElGamal encryption analogues of Diffie–Hellman key exchange will be created. Novelty: Elliptic curves are encountered in a multitude of mathematical contexts and have a varied and fascinating history. Elliptic curves are very significant in number theory and are a focus of much recent work. The earlier research works in Elliptic Curve Cryptography has concentrated on computer algorithms and pairing – based algorithms. In this paper, the concept of polygonal numbers and its extension from Diophantine pair to triples is encountered, thus forming an elliptic curve and perform the encryption-decryption process. MSC Classification Number: 11D09, 11D99,11T71,11G05.

Keywords: Elliptic curves, Cryptography, Encryption, Decryption, Centered polygonal numbers


  1. Somanath M, Kannan J, Shanthi PV, Mahalakshmi M, . Contemporary Research Trends in Mathematics (1). (pp. 1-175) Multi Spectrum Publications. 2023.
  2. Sangeetha V, Anupreethi T, Somanath M. Construction of Special dio — triples. Indian Journal Of Science And Technology. 2023;16(39):3440–3442. Available from: https://dx.doi.org/10.17485/ijst/v16i39.1735
  3. Yan Y. The Overview of Elliptic Curve Cryptography (ECC) In: The International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2022), Journal of Physics: Conference Series. (Vol. 2386, pp. 1-8) IOP Publishing. 2022.
  4. Stallings W. Cryptography and Network Security: Principles and Practice (8). (pp. 1-767) London. Pearson Education Inc. 2023.
  5. Somanath M, Kannan J, Raja K. Encryption Decryption Algorithm Using Solutions of Pell equation. Int. J. Math. And Appl. 2022;10(1):1–8.
  6. Miret JM, Sadornil D, Tena JG. Pairing-Based Cryptography on Elliptic Curves. Mathematics in Computer Science. 2018;12(3):309–318. Available from: https://dx.doi.org/10.1007/s11786-018-0347-3
  7. Ullah S, Zheng J, Din N, Hussain MT, Ullah F, Yousaf M. Elliptic Curve Cryptography; Applications, challenges, recent advances, and future trends: A comprehensive survey. Computer Science Review. 2023;47. Available from: https://dx.doi.org/10.1016/j.cosrev.2022.100530


© 2024 Sangeetha et al.  This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


Subscribe now for latest articles and news.