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

Authors:
Reza Ebrahimi Atani
Shahabaddin Ebrahimi Atani
Sattar Mirzakuchaki
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URL: http://eprint.iacr.org/2007/391
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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.
BibTeX
@misc{eprint-2007-13671,
  title={A novel public key crypto system based on semi-modules over quotient semi-rings},
  booktitle={IACR Eprint archive},
  keywords={Public key cryptography, Diffie-Helman protocol, One-way trapdoor functions, Semi group actions, Quotient semi-rings},
  url={http://eprint.iacr.org/2007/391},
  note={Published in "International Mathematical Forum" rebrahimi@iust.ac.ir 13788 received 30 Sep 2007, last revised 2 Oct 2007},
  author={Reza Ebrahimi Atani and Shahabaddin Ebrahimi Atani and Sattar Mirzakuchaki},
  year=2007
}