Cryptographic Algorithm Using Matrix Inversion as Data Protection

Authors

  • Peter B. Zirra Department of Mathematical Sciences Adamawa State Universiti Mubi, Nigeria
  • G.M. Wajiga Department of Mathematics and Computer Science, Federal Universiti of Technology Yola, Nigeria

DOI:

https://doi.org/10.32890/jict2011.10.4

Keywords:

Cryptographic algorithms, Delta encoding, Newton’s method, Inversion matrix, Non-linear equations, Decryption key, Cryptanalyst

Abstract

This study aimed at providing algorithms to secure sensitive information in store or in transit via unsecure channels from the hands of the Internet criminals by scrambling the sensitive information into a set of linear equations in matrix form and deciphering by solving the systems of the linear equations in conjunction with the principles of the delta encoding scheme, a formula and a lookup alphanumeric position table. The algorithms were tested with samples of real data and the result practically demonstrated how systems of non-linear equations turned into linear equations are indeed of relevance in providing strong and complex encryption and decryption keys to protect sensitive information in store or in transit via unsecure channels. The proposed algorithms ensured that unauthorized users do not have access to sensitive and classified documents stored or transmitted to an intended recipient without a secret key. This means that, there is confidentiality, non-repudiation and integrity of our sensitive and classified information from the hands of unauthorized users on the Internet because of the robustness of the proposed algorithms.

 

References

Beekman, G. (1999). Computer confluence. Calfonia: Addison-Wesley.

Biazar, J., & Ghanbary, B. (2008). A new approach for solving systems of non-linear equations. International Mathematical Forum, 3(38), 1885–1889.

Biazar, J. & Ghanbary, B. (2009). A modification on Newton’s method for solving systems of non-linear equations. World Academy of Science, Engineering and Technology, 58, 897–901.

Boneh, D. (1999). Twenty years of attack on the RSA cryptography. Notices American Mathematic Society, 46(1), 203–213.

Buchmann, J. (2005). Introduction to cryptograph (2nd ed.). New York: Springer-Verlag.

Burden, R. J., & Faires, J. D. (2001). Numerical analysis (7th ed.). USA: Brooks/Cole.

Crina, G., & Ajith, A. (2008). A new approach for solving non-linear equations system. IEEE Transaction on Systems, Man, and Cybernetic, 38(3), 698–714.

Diaa, S. A. M., Hatem, M. A. K., & Mohiy, M. H. (2010). Evaluating the performance of symmetric encryption algorithms. International Journal of Network Security, 10(3), 213–219.

Discoverthenetwork.Org. (2010). A guide to the political left. Retrieved from www.discoverthenetworks.org. Journal of ICT, 10, pp: 67–

Figg, B. (2004). Cryptography and network security. Retrieved from http:/ www.homepages.dsu.edu/figgw.

Goh, E. (2007). Encryption schemes from bilinear maps (Unpublished doctoral dissertation). USA: Stanford University.

Kahate, A. (2008). Cryptography and network security (2nd ed.). New Delhi: Tata McGraw Hill.

Kak, A. (2009). Classical encryption techniques. Lecture notes on “Computer and Network Security”. Purdue University.

Kessler, G. C. (2010). Handbook on local area networks: An overview of cryptography. United Kingdom: Auerbach. Retrieved from http://www. garykessler.net/library.

Koblitz, N. (1994). A course in number theory and cryptography (2nd ed.). Berlin: Springer Verlag.

Laudan, C. K., & Traver, C. G. (2004). E-commerce. Business. Technology. Society (2nd ed.). New York: Pearson Education.

Menezes, A., Ooschot, P.V., & Vanstone, S. (1996). Handbook of applied cryptography. New York: CRS Press.

Murdoch, M. (2001). Introduction to cryptography, Part 1: The broad view.

Murphy S. (1990). The cryptanalysis of FEAL-4 with 20 chosen plaintexts. Journal of Crytology, 2(1), 145–154.

Moore, G. W. (2001). Cryptography mini-tutorial. Lecture notes University of Maryland School of Medicine. Retrieved from http://www. medparse.com.

Obi, G. M. M. (2000). A generalization of the RSA algorithm. Proceedings of Computer Association of Nigeria Conference Series, 11(1), 203–207.

Olaoye, B. (2011). ICT security training scholarship to university. A letter of Invitation.

Potdar, V., & Chang, E. (2004). Disguising text cryptography using image cryptography. International Network Conference. United Kingdom: Plymouth. Journal of ICT, 10, pp: 67–

Rudolf, D. (2000). Development and analysis of block cipher and DES system. Retrieved from http://www.cs.usask.ca.

Schneier, B. (1996). Applied cryptography. New York: John Wiley and Sons.

Schneier, B. (2003). Practice cryptography. New York: John Wiley and Sons.

Stallings, W. (2006). Cryptography and network security (4th ed.). Englewood (NJ): Prentice Hall.

Steven, W.S. (2007). The scientist and engineer’s guide to digital signal processing. Califonia: Technical Publishing.

Stroud, K.A., and Dexter, J.B. (2007). Engineering mathematics (6th ed.). New York: Palgrave Macmillan.

Su, N., Zobel, R.N. & Iwu, F.O. (2003). Simulation in cryptographic protocol design and analysis. Proceedings of 15th European Simulation Symposium. University of Manchester, UK.

Talbot, J., & Welsh, D. (2006).Complexity and cryptography: An introduction New York: Cambridge University Press.

The Times of India. (2011). Retrieved from http://www.timesofindia. indiatimes.com.

Young, A., & Yung, M. (2004). Malicious cryptography-exposing crypto virology. New York: John Wiley & Sons.

Yusuf, M. A. (2007). Data security: Layered approach algorithm (Unpublished master’s thesis). Abubakar Tafawa Balewa University, Bauchi, Nigeria.

Wang, H. (2002). Security architecture for the teamdee system (Unpublished master’s thesis). Polytechnic Institution and State University, Virginia, USA.

Wiener, M. (1990). Cryptanalysis of short RSA secret exponents. IEEE Transaction Information Theory, 36(1), 553–558.

William, H. C. (1982). A p+1 method of factoring. Mathematic of Computation, l39 (3), 225–234.

Downloads

Published

18-04-2011

How to Cite

Zirra, P. B., & Wajiga, G. (2011). Cryptographic Algorithm Using Matrix Inversion as Data Protection. Journal of Information and Communication Technology, 10, 67-83. https://doi.org/10.32890/jict2011.10.4

Research impact

Harvested 2026-09-22
0 citations recorded so far

Counts differ between services because each indexes a different body of literature. None of them is the whole picture.

Identifiers DOI 10.32890/jict2011.10.4