FUNDAMENTALS OF LINEAR ALGEBRA AND THEIR PRACTICAL APPLICATIONS IN CRYPTOGRAPHIC SYSTEMS
Keywords:
Linear algebra, cryptography, encryption, cryptanalysis, Hill cipher, AES, RSA, security, matrices, vectors. Linear algebra, cryptography, matrix operations, vector spaces, vertex encryption, lattice-based cryptography, post-quantum systems.Abstract
This article analyzes the application of linear algebra methods in cryptographic systems. Mathematics has a major role in cryptography, data security and encryption, especially linear algebra methods. The article shows how the basics of linear algebra - concepts such as vectors, matrices, determinants, inversions and linear equations - can be used in the implementation of cryptographic algorithms, encryption and decryption processes.
References
Katz, J., & Lindell, Y. (2014). Introduction to Modern Cryptography. Second Edition. Springer.
Stinson, D. R. (2005). Cryptography: Theory and Practice. Third Edition. CRC Press.
Rosen, K. H. (2012). Discrete Mathematics and Its Applications. Seventh Edition. McGraw-Hill.
Garner, H. L. (2005). Matrix Methods in Cryptography. Journal of Cryptographic Engineering, 1(1), 9-18.
Menezes, A. J., van Oorschot, P. C., & Vanstone, S. A. (1996). Handbook of Applied Cryptography. CRC Press.
Schneier, B. (2007). Cryptography Engineering: Design Principles and Practical Applications. Wiley
Carter, L. M., & Wegman, M. N. (2007). Cryptography and Network Security: Principles and Practice. Prentice Hall.
