135
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Cryptography using generalized Fibonacci matrices with Affine-Hill cipher

ORCID Icon &
Pages 2341-2352 | Received 01 Mar 2020, Published online: 11 Mar 2021

References

  • Aumasson, J.-P. Serious Cryptography: A Practical Introduction to Modern Encryption. No Starch Press, 2017.
  • Daras, N. Applications of mathematics and informatics in military science, vol. 71. Springer Science & Business Media, 2012.
  • Dummit, D. S., and Foote, R. M. Abstract algebra, vol. 3. Wiley Hoboken, 2004.
  • Elgamal, T. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE transactions on information theory 31, 4 (1985), 469–472. doi: 10.1109/TIT.1985.1057074
  • Gould, H. W. A history of the fibonacci q-matrix and a higher-dimensional problem. Fibonacci Quart 19, 3 (1981), 250–257.
  • Grillet, P. A. Abstract algebra, vol. 242. Springer Science & Business Media, 2007.
  • Grimaldi, R. P. Fibonacci and Catalan numbers. Wiley Online Library, 2012.
  • Gupta, I., Singh, J., and Chaudhary, R. Cryptanalysis of an extension of the hill cipher. Cryptologia 31, 3 (2007), 246–253. doi: 10.1080/01611190701202465
  • Honsberger, R. Mathematical gems iii, dolciani math, 1985.
  • Johnson, R. C. Fibonacci numbers and matrices. manuscript available at http://www.dur.ac.uk/bob.johnson/fibonacci (2008).
  • Koshy, T. Fibonacci and Lucas numbers with applications. John Wiley & Sons, 2019.
  • Koukouvinos, C., Lappas, B., and Simos, D. Encryption schemes using orthogonal arrays. Journal of Discrete Mathematical Sciences and Cryptography 12, 5 (2009), 615–628. doi: 10.1080/09720529.2009.10698260
  • Mao, W. Modern cryptography: theory and practice. Pearson Education India, 2003.
  • Paar, C., and Pelzl, J. Understanding cryptography: a textbook for students and practitioners. Springer Science & Business Media, 2009.
  • Stallings, W. Cryptography and network security: principles and practice, 7th Ed. Pearson Education Limited, 2017.
  • Stinson, D. R. Cryptography: theory and practice, 3rd Ed. Chapman and Hall/CRC, Taylor & Francis Group, 2006.
  • Stothers, A. J. On the complexity of matrix multiplication. The University of Edinburgh (2010).
  • Sundarayya, P., and Vara Prasad, G. A public key cryptosystem using affine hill cipher under modulation of prime number. Journal of Information and Optimization Sciences 40, 4 (2019), 919–930. doi: 10.1080/02522667.2018.1470751
  • Thilaka, B., and Rajalakshmi, K. An extension of hill cipher using generalized inverses and mth residue modulo n. Cryptologia 29, 4 (2005), 367–376. doi: 10.1080/0161-110591893933
  • Viswanath, M., and Kumar, M. R. A public key cryptosystem using hill’s cipher. Journal of Discrete Mathematical Sciences and Cryptography 18, 1-2 (2015), 129–138. doi: 10.1080/09720529.2014.962856

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.