Encryption using semigroup action

Authors

  • Indira Devi Anooja Department of Mathematics, CMS College Kottayam (Autonomous), Kottayam 686 001 Ker- ala, India; anoojai@gmail.com.
  • Sivadasan Vinod Department of Mathematics, Government College for Women, Thiruvananthapuram, Kerala, India; wenod76@gmail.com.
  • Gopinadhan Sathikumari Biju Department of Mathematics, College of Engineering, Thiruvananthapuram-695016, Kerala, India; gsbiju@cet.ac.in.

DOI:

https://doi.org/10.23755/rm.v41i0.649

Keywords:

semigroupaction, enciphering, plaintext, ciphertext, cryptosystem

Abstract

Anencipheringtransformationisafunctionf thatconvertsanyplaintext message into a ciphertext message and deciphering transformation is a function f−1, which reverse the process. Such a set-up is calledacryptosystem. Inthispaper,weextendageneralizationofthe original Diffie-Hellman key exchange and ElGamal cryptosystem in (Z/pZ)∗ by constructing a semigroup action on a finite dimensional vector space T over F2.

Author Biographies

  • Indira Devi Anooja, Department of Mathematics, CMS College Kottayam (Autonomous), Kottayam 686 001 Ker- ala, India; anoojai@gmail.com.

     

     
  • Sivadasan Vinod, Department of Mathematics, Government College for Women, Thiruvananthapuram, Kerala, India; wenod76@gmail.com.

     

     
  • Gopinadhan Sathikumari Biju, Department of Mathematics, College of Engineering, Thiruvananthapuram-695016, Kerala, India; gsbiju@cet.ac.in.

    Department of Mathematics

    Associate professor

References

Iris Anshel, Michael Anshel, and Dorian Goldfeld. An algebraic method

for public key cryptography. Mathematical Research Letters, 6(3–

:287–291, 1999.

Gilbert Baumslag, Benjamin Fine, and Xiaowei Xu. Cryptosystems

using linear groups. Applicable Algebra in Engineering,

Communication and Computing, 17(3):205–217, 2006.

Simon R Blackburn and Steven Galbraith. Cryptanalysis of two

cryptosystems based on group actions. In International Conference

on the Theory and Application of Cryptology and Information

Security, volume 3531, pages 52–61. Springer, 1999.

Whitfield Diffie and Martin Hellman. New directions in cryptography.

IEEE transactions on Information Theory, 22(6):644–654, 1976. Taher ElGamal. A public key cryptosystem and a signature scheme

based on discrete logarithms. IEEE transactions on information

theory, 31(4):469–472, 1985.

Ki Hyoung Ko, Sang Jin Lee, Jung Hee Cheon, Jae Woo Han, Ju-

sung Kang, and Choonsik Park. New public-key cryptosystem using

braid groups. In Annual International Cryptology Conference,

pages 166–183. Springer, 2000.

Neal Koblitz. Algebraic methods of cryptography. Berlin Heidelberg

New York: Springer, 1998. PH Kropholler, SJ Pride, WAM Othman, KB Wong, and PC Wong. Properties of certain semigroups and their

potential as platforms for cryptosystems. In Semigroup Forum,

volume 81, pages 172–186. Springer, 2010. RogerCLyndonandPaulESchupp. Combinatorialgrouptheory.

BerlinHeidelberg New York: Springer, 1977.

G´erard Maze, Chris Monico, and Joachim Rosenthal. Public key

cryptography based on semigroup actions. Advances of

Mathematics of Communications, 1 (4):489–507, 2007.

Alfred J Menezes, Paul C Van Oorschot, and Scott A Vanstone.

HandbookAppliedCryptography.DiscreteMathematicsandItsApplications. CRCpress, New York, 1996.

Vladimir Shpilrain and Alexander Ushakov. Thompsons group and

public key cryptography. In International Conference on Applied

Cryptography and Network Security, pages 151–163.

Springer,2005.

Vladimir Shpilrain and Gabriel Zapata. Combinatorial group theory

and public key cryptography. Applicable Algebra in Engineering,

Communication and Computing, 17(3):291–302, 2006.

Keith R Slavin. Public key cryptography using matrices. 2007. US

Patent 10260818, http://www.patentstorm.us/patents/7184551-

fulltext.html.

Akihiro Yamamura. Public-key cryptosystems using

the modular group. In

International Workshop on Public Key Cryptography, pages 203–

Springer, 1998.

Downloads

Published

2021-12-31

Issue

Vol. 41 (2021)

Section

Volume 41-2021

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.