The document discusses the application of matrix multiplication in cryptography. It explains that cryptography involves encrypting a message into a coded form using a matrix multiplication with a non-singular matrix, and decrypting by multiplying the encoded matrix with the inverse of the encryption matrix. Encryption converts text to numbers in a matrix and decryption recovers the original text matrix using the inverse matrix. Matrix cryptography can be used for secure communication, secret sharing of data, and access control.

1.  Name: Mohammad Waqas
 Roll Number: 19CH18
 Subject: Liner Algebra Analytical Geometry (LAAG)
 Date: 27/07/2020
1

2. Presentation Topic
Application of matrix multiplication
(Cryptography)
2

3. What is Cryptography
 A cryptogram is a message written according to a secret code (the Greek word
kryptos means “hidden”). This section describes a method of using matrix
multiplication to encode and decode messages.
 Cryptography mainly consist of encryption and decryption
Encryption
 Convert the plain data into numerical by giving A to 1,B to 2,C to 3 and so on.
 Place the numerical in to matrix M of order mn ≥ L.
 Multiply the matrix M with a non-singular matrix A to get the encoded matrix X.
 The determinate of (non singular matrix) A must be equal to ±1.
 Convert the resultant, the encrypted message matrix in to a text message of
length L and that will be send to the receiver.
3

4. Decryption
 Receiver can form a matrix with the encrypted message.
 Multiply the encoded matrix X with 𝐴−1
to get back the message matrix M.
 Encryption and decryption require the use of some secret information usually referred
as a key.
 This first matrix , used by sender is called the encryption matrix (encoding matrix) and
its inverse is called decryption matrix (decoding matrix) , which is used by the receiver.
 Begin by assigning a number to each letter in the alphabet (with 0 assigned to a blank
space), as follows
4

5. 5Application of cryptography
 Secure communication:
 To prevent eavesdropping war time communication and business transactions
 Secret Sharing / data hiding:
 Hide something that has been written.
 Access Control:
 Regulate access to satellite and cable TV.
 Cell phones:
 Prevent people from stealing cell phone . Access code or evadropping

6. 6

7. 7

8. 8

9. References
 Book Name: Elementary Linear Algebra
 Author name: Howard Antion and Chris Rorrers
 Edition Number: 11th edition
 Publisher year: 2014
 www.synopsys.com. C.J.R.Berges
9

10. 10