1. Classical Encryption techniques
Symmetric Ciphers
Classical Encryption techniques

2. AES - Finite Field Algorithm
In AES, all operations are performed on 8-bit bytes
the arithmetic operations of addition, multiplication, and division are performed over the finite
Field GF(28)
There are a total of 2n different polynomials
For n=3, 23=8the polynomials in the set are

3. AES - Finite Field Algorithm
Arithmetic follows the ordinary rules of polynomial arithmetic using the basic rules of algebra with the following two refinements.
Arithmetic on the coefficients is performed modulo 2. This is the same as the XOR operation
If multiplication results in a polynomial of degree greater than n-1, then then the polynomial is reduced modulo some irreducible polynomial m(x) of degree n
Ex: finite field GF(23)
x3+x2+1
x3+x+1
AES => GF(28)
x8+x4+x3+x1+1

5. AES Encryption Process

6. AES Encryption Process

7. AES Data Structure

8. AES Data Structure

9. The AddRoundKey stage is, in effect, a form of Vernam cipher and by itself would not be formidable. The other three stages together provide confusion, diffusion, and nonlinearity, but by themselves would provide no security because they do not use the key.We can view the cipher as alternating operations of XOR

10. Ecryption

11. AES - Substitution

12. AES – S-BOX

13. AES – ShiftRows Transformation

14. MixColumns Transformation

15. MixColumns Transformation

16. AES - AddRoundKey

17. Inputs for Single AES Round

19. AES Example

20. AES Example

21. Reference books
Cryptography and Network Security Principles and Practices
William Stallings
Network Security PRIVATE Communication in a PUBLIC World
Chalie Kaufman, Radia Perlman, Mike Speciner