Cryptology ePrint Archive: Report 2007/391

A novel public key crypto system based on semi-modules over quotient semi-rings

Reza Ebrahimi Atani, Shahabaddin Ebrahimi Atani, Sattar Mirzakuchaki

Abstract: In A generalization of the original Diffie-Hellman key exchange in (ℤ/pℤ)* found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. Maze, Monico and Rosenthal extend such a generalization to the setting of a Semi-group action on a finite set, more precisely, linear actions of abelian semi-rings on semi-modules. In this paper, we extend such a generalization to the linear actions of quotient semi-rings on semi-modules. In fact, we show how the action of quotient semi-rings on a semi-module gives rise to a generalized Diffie-Hellman and ElGamal protocol. This leads naturally to a cryptographic protocol whose difficulty is based on the hardness of a particular control problem, namely the problem of steering the state of some dynamical system from an initial vector to some final location.

Category / Keywords: Public key cryptography, Diffie-Helman protocol, One-way trapdoor functions, Semi group actions, Quotient semi-rings

Publication Info: Published in "International Mathematical Forum"

Date: received 30 Sep 2007, last revised 2 Oct 2007

Contact author: rebrahimi at iust ac ir

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Version: 20071014:181731 (All versions of this report)

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