# Application of linear algebra in cryptography

What is the application of linear algebra in cryptography? Application of linear algebra in cryptography. Linear algebra is widely used in many engineering applications. The most common examples are: network solving, chemical equation balancing, engineering economy and in network security. With the advancement in technology, we prefer to communicate via network these days. Sending text messages, voice notes, online banking are the applications that demand to send/receive information without being hacked. The purpose of hacking is to retrieve the information being send between sender and receiver. In order to avoid hacking messages are encrypted/ encoded with different encoding schemes. One of them is cryptography.

## What is the cryptography?

Cryptography is a technique of encoding our actual information with a proper “key” that is supposed to be known to both: the sender and receiver. The message is encoded using this key. Hence the original information is transformed into another form and then transferred to the receiver. Upon receiving that message, the receiver decrypts that message using the same key. Hence the communication is secured.

### Cryptography example

In this example lets say a sender wants to send a message “good morning”. In order to send the message, all the alphabets are numbered starting from 0 to 25. Then the blank is assigned value=26 and so on as shown in the figure below. Then using a given key these messages are encoded. The example shows the complete detail of the work.

Also watch here

https://www.youtube.com/watch?v=X2Cb4GcXdi0&t=2s

## Other Topics of Linear Algebra

- what are the row spaces, column spaces and null spaces in Linear Algebra?
- How to solve system of linear equations in Linear Algebra?
- what is the vector space in linear algebra? vector space example
- How to test the given vectors are linearly independent or not?
- What are the matrices and their types ?
- Finding Eigen Values and Eigen Vectors using MATLAB
- How to diagonalize a matrix? Example of diagonalization
- What are the shortcuts for finding the determinant of a matrix?
- What are the Block Matrices?
- what are the examples of scalar and vector quantities?
- How to perform similar matrices transformation?
- How to find the basis of a vector space V?
- what are the eigen values and eigen vectors? explain with examples
- What are the nodal incidence matrices?
- What is the span of a vector space?