SECURITY OF PUBLIC KEY ENCRYPTION USING DICKSON POLYNOMIALS OVER FINITE FIELD WITH 2k
By
Kamakhya Paul1, Pinkimani Goswami2 and Madan Mohan Singh3
1Department of Mathematics, North Eastern Hill University, Shillong, Meghalaya, India-793022
2Department of Mathematics, University of Science and Technology Meghalaya,Ri-Bhoi, Meghalaya, India-793101
3Department of Basic Sciences & Social Sciences, North Eastern Hill University, Shillong,
Meghalaya, India-793022
Email: kamakhyapaul4@gmail.com, pinkimanigoswami@yahoo.com, mmsingh2004@gmail.com
(Received : May 16, 2023; In format : May 27, 2023; Revised : August 09, 2023, Accepted: August 30, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53209
Abstract
The application of Dickson polynomial in public key cryptography is observed due to its permutation behaviors and semi-group property under composition. Here we have mostly concentrated on checking the one-wayness and semantic security of our scheme. The proposed scheme is based on Dickson polynomial over a finite field with 2k, whose security depends on the Integer Factorization Problem(IFP) and the Discrete Dickson Problem(DDP), which is as difficult as solving discrete logarithmic Problem (DLP). Our proposed cryptosystem is computationally secured with one wayness and semantic security, it also reduces the complexity of many other proposed schemes.
2020 Mathematical Sciences Classification: 94A60, 11T06
Keywords and Phrases: Dickson Polynomial, Integer Factorization Problem, Discrete Dickson Problem, Discrete logarithm Problem, Encryption Scheme.