Some analysis on conjugacy search problem for Diffie-Hellman protocol
DOI:
https://doi.org/10.15282/daam.v3i2.8936Keywords:
Diffie-Hellman protocol, Nonabelian group , Conjugacy search problemAbstract
The field in nonabelian group-based cryptosystem have gain attention of the researchers as it expected to offers higher security when confronted with quantum computational due to more complex algebraic structures. Hence, this paper intents to give an overview on Diffie-Hellman protocol considering the mathematically hard problem such as the conjugacy search problem in a group G. In this paper we provide examples for G of non abelian group particularly the group of SL(2,3).
ARTICLE HISTORY
Received: 20/07/2022
Revised: 20/09/2022
Accepted: 30/09/2022
Published: 30/09/2022
References
A. Shamir, New Directions in Croptography. Berlin, Germany: Springer, 2001, pp. 159.
G. Baumslag, B. Fine and X. Xu, “Cryptosystems using linear groups,” Applicable Algebra in Engineering, Communicationand Computing, vol. 17, no. 3–4, pp. 205–217, 2006.
N. Rahman and V. Shpilrain, “MAKE: A matrix action key exchange,” Journal of Mathematical Cryptology, vol. 16, no. 1,pp. 64–72, 2022.
T. Lin, “A Study of Non-Abelian Public Key Cryptography,” International Journal of Network Security, vol. 20, no. 2, pp.278–290, 2018.
G. H. J. Lanel, T. M. K. K. Jinasena and B. A. K. Welihinda, “A Survey of Public-Key Cryptography over Non-AbelianGroups,” International Journal of Computer Science and Network Security, vol. 21, no. 4, pp. 289-300, 2021.
C. Mullan, “Some results in group-based cryptography,” Ph.D. dissertation, Department of Mathematics, University of London, Surrey, England, 2011.
S. R. Blackburn, C. Cid and C. Mullan, Group Theory in Cryptography. Somerset, United Kingdom: University in Bath, 2011 pp. 133–149.
E. T. Whittaker, “The Mathematical Association,” Mathematical Gazette, vol. 10, no. 145, pp. 17–19, 1920.
J.J Rotman, An Introduction to the Theory of Groups. Illinois, United States of America: Springer, 1995.
C.C. Pinter, A Book of Abstract Algebra. New York, United States of America: Courier Corporation, 2010.
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