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Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4

Manoj Kumar1 , Ankur Kumar2

Section:Research Paper, Product Type: Journal Paper
Volume-7 , Issue-5 , Page no. 1330-1337, May-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7i5.13301337

Online published on May 31, 2019

Copyright © Manoj Kumar, Ankur Kumar . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: Manoj Kumar, Ankur Kumar, “Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4,” International Journal of Computer Sciences and Engineering, Vol.7, Issue.5, pp.1330-1337, 2019.

MLA Style Citation: Manoj Kumar, Ankur Kumar "Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4." International Journal of Computer Sciences and Engineering 7.5 (2019): 1330-1337.

APA Style Citation: Manoj Kumar, Ankur Kumar, (2019). Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4. International Journal of Computer Sciences and Engineering, 7(5), 1330-1337.

BibTex Style Citation:
@article{Kumar_2019,
author = {Manoj Kumar, Ankur Kumar},
title = {Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {5 2019},
volume = {7},
Issue = {5},
month = {5},
year = {2019},
issn = {2347-2693},
pages = {1330-1337},
url = {https://www.ijcseonline.org/full_paper_view.php?paper_id=4409},
doi = {https://doi.org/10.26438/ijcse/v7i5.13301337}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i5.13301337}
UR - https://www.ijcseonline.org/full_paper_view.php?paper_id=4409
TI - Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4
T2 - International Journal of Computer Sciences and Engineering
AU - Manoj Kumar, Ankur Kumar
PY - 2019
DA - 2019/05/31
PB - IJCSE, Indore, INDIA
SP - 1330-1337
IS - 5
VL - 7
SN - 2347-2693
ER -

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Abstract

In this present approach, some efficient computing techniques of Ancient Indian Vedic Mathematics for elliptic curve cryptography (ECC) over the Ring A4 has been studied, in which, it has been observed that the applications of AIVM Techniques or Sutras decrease the number of multiplications and squares which occur in point doubling and point addition in ECC over the Ring A4. This paper described the use of AIVM Sutras, Urdhva-Tiryagbhyam for multiplication and Dvandva-Yoga for the square of any number in the ECC over the Ring A4. The results proved that AIVM based scheme shows better performance in speed, processing time and power consumption of multipliers compared to conventional method. The effect of some AIVM techniques over ECC was investigated and the obtained results are explained in the form of tables and graphs.

Key-Words / Index Term

Cryptography, Dvandva-Yoga, Elliptic Curve, Finite Field, Point Addition, Point Doubling, Ring A4, Scalar Multiplication, Urdhva-Tiryagbhyam, Vedic Mathematics

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