ALGEBRAIC BRAID GROUP PUBLIC KEY CRYPTOGRAPHY
By
Kamakhya Paul1, Pinkimani Goswami2 and Madan Mohan Singh3
1Department of Mathematics, North Eastern Hill University, Shillong-793022, Meghalaya, India
2Department of Mathematics, University of Science and Technology Meghalaya, Ri-Bhoi-793101, Meghalaya, India
3Department of Basic Sciences & Social Sciences, North Eastern Hill University, Shillong-793022, Meghalaya, India
Email: kamakhyapaul4@gmail.com, pinkimanigoswami@yahoo.com, mmsingh2004@gmail.com
(Received : October 12, 2022 ; In format : November 02, 2022; Revised: November 14, 2022; Accepted: November 15, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52225
Abstract
The braid group cryptography arises with the involvement of the braid group, which is an infinite non-commutative group arising from geometric braids. In this paper, we have proposed a new public key cryptosystem based on braid group. The security of our proposed scheme is based on two hard problems on braid group, conjugacy search problem and p-th root problem on braid group. We also checked the one-wayness, semantic security and efficiency of our proposed scheme, and found it to be computationally secured.
2020 Mathematical Sciences Classification: 94A60, 20F36
Keywords and Phrases: Public key cryptography, Braid group; Conjugacy search problem; p-th root problem.