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Public key cryptography based on semigroup actions


Maze, G; Monico, C; Rosenthal, J (2007). Public key cryptography based on semigroup actions. Advances in Mathematics of Communications, 1(4):489-507.

Abstract

A generalization of the original Diffie-Hellman key exchange in ∕* found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general.
In Section 5 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

Abstract

A generalization of the original Diffie-Hellman key exchange in ∕* found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general.
In Section 5 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Public key cryptography, Diffie-Hellman protocol, one-way trapdoor functions, semigroup actions, simple semirings.
Language:English
Date:2007
Deposited On:02 Nov 2009 12:13
Last Modified:05 Apr 2016 13:23
Publisher:American Institute of Mathematical Sciences
ISSN:1930-5338
Additional Information:First published in Advances in Mathematics of Communication in vol. 1, no. 4 (2007), published by the American Institute of Mathematical Sciences and Shandong University
Publisher DOI:https://doi.org/10.3934/amc.2007.1.489
Related URLs:http://arxiv.org/abs/cs/0501017v4

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