Abstract
We present a new approach to designing public-key cryptosystems based on covers and logarithmic signatures of non-abelian finite groups. Initially, we describe a generic version of the system for a large class of groups. We then propose a class of 2-groups and argue heuristically about the system’s security. The system is scalable, and the proposed underlying group, represented as a matrix group, affords significant space and time efficiency.
Article PDF
Similar content being viewed by others
References
T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31, 469–472 (1985)
G. Higman, Suzuki 2-groups. Ill. J. Math. 7, 79–96 (1963)
B. Huppert, Endliche Gruppen I (Springer, Berlin, 1967)
B. Huppert, N. Blackburn, Finite Groups II (Springer, Berlin, 1982)
S.S. Magliveras, A cryptosystem from logarithmic signatures of finite groups. In Proceedings of the 29th Midwest Symposium on Circuits and Systems (Elsevier, Amsterdam, 1986), pp. 972–975
S.S. Magliveras, N.D. Memon, The algebraic properties of cryptosystem PGM. J. Cryptol. 5, 167–183 (1992)
S.S. Magliveras, D.R. Stinson, T. van Trung, New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups. J. Cryptol. 15, 285–297 (2002)
P. Nguyen, Editor, New Trends in Cryptology, European project “STORK—Strategic Roadmap for Crypto”—IST-2002-38273. http://www.di.ens.fr/~pnguyen/pub.html#Ng03
P. Shor, Polynomial time algorithms for prime factorization and discrete logarithms on quantum computers. SIAM J. Comput. 26(5), 1484–1509 (1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Stefan Wolf
This work was partially supported by a Federal Earmark grant for Research in Secure Telecommunication Networks (2004-05).
Rights and permissions
About this article
Cite this article
Lempken, W., van Tran, T., Magliveras, S.S. et al. A Public Key Cryptosystem Based on Non-abelian Finite Groups. J Cryptol 22, 62–74 (2009). https://doi.org/10.1007/s00145-008-9033-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00145-008-9033-y