ADVANCED ENCRYPTION TECHNIQUE USING BISYMMETRIC RHOTRIX AND DNA CODES WITH ELLIPTIC CURVE CRYPTOGRAPHY
By
1Shalini Gupta, 2Ruchi Narang, 3Gajendra Pratap Singh, 4Kritika Gupta and
5Kamalendra Kumar
1,2,4Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, India-171005
3School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India-110067
5Department of Basic Science, Shri Ram Murti Smarak, College of Engineering and Technology Bareilly, India-243202
Email: shalini.garga1970@gmail.com, ruchinarang8878@gmail.com, gajendra@gmail.jnu.ac.in, kritika993@gmail.com, kamlendra. 14kumar@gmail.com
(Received: October 09, 2024; In format: December 07, 2024; Revised: May 28, 2025; Accepted: July 13, 2025)
DOI: https://doi.org/10.58250/jnanabha_SI.2025.55101
Abstract
Within cryptography, various methods like DES (Data Encryption Standard), IDEA (International Data Encryption Algorithm), and Blow sh are employed to enhance security during encryption and decryption processes. In today's scenario, rhotrices assume a pivotal role in cryptography, utilizing mathematical algorithms for encrypting and decrypting confidential messages. This paper explores the utilization of bisymmetric rhotrix alongside elliptic curve cryptography, and uses DNA Codes to devise a secure and robust encryption and decryption algorithm. Here, the message is divided into blocks of 24 characters each. Using a DNA code sequence, we combine the string of the first message block with a 128-bit random integer and the private key coordinates to derive an elliptic curve point for encryption. Encryption transforms each message point into a pair of cipher points, authenticated with a digital signature to ensure data integrity. Decryption reverses this process and veri es the signature. This method guarantees secure message exchange, mutual authentication, and data integrity, making it suitable for various cryptographic applications. Additionally, we have implemented this scheme in Python and, through rigorous testing, measured the time required for encryption and decryption, demonstrating our cryptographic approach's e ciency and practical feasibility.
2020 Mathematical Sciences Classification: 12E20; 94A60
Keywords and Phrases: Elliptic curve cryptography, finite field, maximum distance separable rhotrix, DNA codes