Using the Moore-Penrose Generalized Inverse in Cryptography

• Authors: Asmaa M. Kanan , Zaleekha Abu Zayd
• Languages of publication: EN

Abstracts

EN

In this work, we introduce a new method in cryptography. It is using the Moore-Penrose generalized inverse of a rectangular matrix to the cryptographic system. We use a rectangular matrix which has the Moore-Penrose generalized inverse as a key. We mean, the rectangular matrix which has full row rank, or the rectangular matrix which has full column rank, or the rectangular matrix which has full factorization.

Keywords

EN

Cipher text; Cryptography; Full Column Rank; Full Rank Factorization; Full Row Rank; Plain text; Rectangular Matrix; The Moore-Penrose Generalized Inverse

Discipline

• INFORMATICS: INFORMATICS

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World Scientific News
• Year: 2020
• Volume: 148
• Pages: 1-14

Contributors

author

Asmaa M. Kanan

• Department of Mathematics, Faculty of Science, Sabratha University, Sabratha, Libya

author

Zaleekha Abu Zayd

• Department of Mathematics, Faculty of Science, Sabratha University, Sabratha, Libya

References

• [1] J. Levine, R. E. Hartwig, Applications of the Drazin invers to the Hill Cryptographic System. Part I. Cryptologia 4(2) (1980) 71-85
• [2] J. Levine, R. E. Hartwig, Applications of the Drazin invers to the Hill Cryptographic System. Part II. Cryptologia 4(3) (1980) 150-168
• [3] R. E. Hartwig, J. Levine, Applications of the Drazin invers to the Hill Cryptographic System. Part III. Cryptologia 5(2) (1981) 67-77
• [4] R. E. Hartwig, J. Levine, Applications of the Drazin invers to the Hill Cryptographic System. Part IV. Cryptologia 5(4) (1981) 213-228
• [5] J. Levine, J. V. Brawley, Jr., Involutory commutants with some applications to algebraic cryptography. I. Journal für die reine und angewandte Mathematik 224 (1966) 20-43
• [6] J. Levine, J. V. Brawley, Jr., Involutory commutants with some applications to algebraic cryptography. II. Journal für die reine und angewandte Mathematik 227 (1967) 1-24
• [7] J. Levine, Varible matrix Substitution in Algebraic cryptography. Amer. Math. Monthly 65 (1958) 170-179
• [8] L. S. Hill, Cryptography in an algebraic alphabet. Amer. Math. Monthly 36 (1929) 306-312
• [9] J. Levine, Some elementary cryptanalysis of algebraic cryptography. Amer. Math. Monthly 68 (1961) 411-418
• [10] A. M. Kanan, A. A. Elbeleze, A. Abubaker, Applications the Moore-Penrose Generalized Inverse to linear systems of Algebraic Equations. American Journal of Applied Mathematics 7(6) (2019) 152-156
• [11] J. Z. Hearon, Generalized Inverses and solutions of linear systems. Journal of Research of the National Bureau of Standards-B. Mathematical Sciences 72B(4) (1968) 303-308
• [12] J. L. Bonilla, R. L. Vazquez, S. V. Beltran, Moore-Penrose`s inverse and solution of linear systems. World Scientific News 101 (2018) 246-252
• [13] G. B. Thapa1, P. L. Estrada, J. L. Bonilla, On the Moore-Penrose Generalized Inverse matrix. World Scientific News 95 (2018) 100-110
• [14] T. N. E. Greville, The Pseudoinverse of a rectangular singular matrix and its application to the solution of systems of linear equations. SIAM Rev. 1 (1960) 38-43
• [15] A. Saman, A. M., Solution of linearly-Dependent Equations by Generalized Inverse of Matrices. Int. J. Sci. Emerging Tech 4 (2012) 138-142
• [16] R. Penrose, A generalized inverse for matrices. Proc. Camb. Phil. Soc. 51 (1955) 406-413
• [17] A. B. Israel, Generalized Inverses of Matrices and Their Applications. Springer, (1980) 154-186
• [18] C. E. Langenhop, On Generalized Inverses of Matrices. SIAM J. Appl. Math. 15 (1967) 1239-1246
• [19] C. R. Rao, S. K. Matira, Generalized Inverses of a matrix and Its Applications. New York: Wiley (1971) 601-620.
• [20] H. Ozden, A Note On The Use of Generalized Inverse Of Matrices In Statistic. Istanbul Univ. Fen Fak. Mat. Der. 49 (1990) 39-43
• [21] R. E. Cline, T. N. E. Gerville, A Drazin Inverse For Rectangular Matrices. Linear Algebra and Its Appliations 29 (1980) 53-62

• Document Type: article