Matrix Inversion over a Finite Ring in Python/NumPy | Compute the inverse of the key in Hill Cipher

Have you wondered how to compute the inverse of a matrix over a finite ring in Python using the NumPy package? How to compute the inverse of a matrix over integer ring modulo 26? How to compute the inverse of a matrix in Hill Cipher using Python? This topic has applications particularly in cryptography and Hill Cipher. In this video, we will explore these questions.

We will examine these questions from a theoretical perspective first, and then we will see how these ideas could help us in finding the inverse of a matrix over a finite ring in Python. Later, we will actually implement it in Python.

If you would like to know more about Hill Cipher or how to implement Hill Cipher in Python, then checkout this playlist:

You can find the source code used in this video here:

If you come across this video for a different reason or you know of a different approach for computing such inverses, please let me know in the comments. Feel free to ask questions or share your thoughts!

Link to the Wikipedia page mentioned in the video:

Thanks for watching :)

00:00 - Introduction
01:29 - Definition of an invertible matrix
02:48 - An equation for the inverse of a matrix
03:51 - The inverse of the determinant and examples
07:28 - Method for computing the inverse of a matrix over a finite ring
08:31 - Implementation in Python
19:40 - Changing the float matrix to integer matrix
23:43 - Concluding remarks

[paulroberts]

this really helped me with my class. you're a legend, thank you!

[kourosh]

Please do a Q&A soon I have a lot of questions