1. A Modified Rijndael Algorithm and it’s Implementation on FPGA
Information Engineering & Technology
German University In Cairo
Department of Electronics and Electrical Engineering
A Modified Rijndael Algorithm and it’s Implementation on FPGA
Ahmed Abou-Bakr Mohamed
Electronics Dept.,
Information Engineering & Technology
German University in Cairo (GUC)
Dr. Ahmed Hasan Madian
Assistant Professor, Electronics Dept.,

2. Outline Introduction Rijndael Algorithm Implementation
Modified Rijndael
Implementation results
Conclusion
Dr. Ahmed H. Madian

3. Introduction In 1998 the DES has been expired as security algorithm
National Institute of Standards and Technology (NIST) initiates a process to develop an Advanced Encryption Standard (AES)
On November 26, 2001 NIST announced that the Rijndael encryption algorithm became the AES 3

4. Rijndael
Developed by two Belgian cryptographers where it’s based on SP-Networks.
The ciphering process is divided into three stages:
Key Expansion
Rounds
Final Round
C. Chitu and M. Glesner, An FPGA implementation of the AES-Rijndael
in OCB/ECB modes of operation, Microelectronics Journal 36 (2005)
139146, 21 October, 2004.
RIJNDAEL BLOCK DIAGRAM

5. 1- Substitution
It’s a non linear operation were 128 bit data is broken down into 16 chunks, 8 bits each, each of which is used as the address for S-box look up table.

6. 1- Substitution (cont’d)
Substitution Simulation

7. 2- Inverse Substitution
Inverse Substitution Simulation

8. 3- Shift Rows
Cyclically permutes the rows of the input data to the left.

9. 3- Shift Rows (cont’d)
Shift Rows Simulation

10. 4- Inverse Shift Rows
Cyclically permutes the rows of the input data to the right.

11. 4- Inverse Shift Rows (cont’d)
Inverse Shift Rows Simulation

12. 5- Mixing Columns P • S S’ =
Computes a new matrix S' by multiplying two matrices together the current matrix S by the polynomial matrix P. 2 3 1
S11
S12
S13
S14
S21
S22
S23
S24
S31
S32
S33
S34
S41
S42
S43
S44
S’ =

13. 5- Mixing Columns (cont’d)
Multiplication By ‘1’:
The Data remains the same.
Multiplication By ‘2’:
The 8 bit data is left shifted by 1 bit.
The least significant bit is replaced by 0.
Then the most significant bit of the original data is used for comparison
(a) If it is 0, then the left shifted data is the result.
(b) If it is 1, then the left shifted value is XORed with the reduction polynomial, which in our case is , to generate the result.

14. 5- Mixing Columns (cont’d)
Multiplication By 2 Simulation
Multiplication By ‘3’:
We simply XOR the original input with the result of multiplication by 2.

15. 5- Mixing Columns (cont’d)
Mixing Columns Simulation

16. 7- Key Expansion
One of the functions that ensures that a cryptography algorithm is not vulnerable.
Generates ten matrices using the round constant matrix.
The key expansion process is divided mainly into three operations:
Rotation
Substitution
Xoring

17. 7- Key Expansion (cont’d)
Rotation:
Rotates a 32 bit input one byte to the left.
Substitution:
Similar to the one described above.
Xoring:
Bit wise xor operation of corresponding bits.

18. 7- Key Expansion (cont’d)
Row 6 contains the results from xoring row 5 and row 2 together.
To get row 5, row 4 is rotated, substituted and the xored with row 1 of the round constant matrix. Finally the output of such an operation is then xored with row 1 to get row 5.

19. 7- Key Expansion (cont’d)
During the implementation only one matrix was generated, due the delay that will be caused since that each new row depends on the previous one.
Key Expansion Simulation

20. 8- Round Key Addition
It simply performs a bit wise xor operation of the expanded round key with another input.

21. 8- Round Key Addition (cont’d)
Round Key Addition Simulation

22. Modified Rijndael Algorithm

23. 9- Proposed Stage Of Modified Rijndael
Mirror
Inverse Mirror
Doesn’t require any arithmetical or logical operations thus routing was used during implementation.

24. 9- Proposed Stages for Rijndael Modification (cont’d)
Mirror Simulation
Inverse Mirror Simulation

25. 10- Encryption / Decryption

26. 10- Encryption / Decryption (cont’d)
Encryption / Decryption FSM

27. 10- Encryption / Decryption (cont’d)

28. Implementation results
Category
Used
Total Available
% Used
Slice Flip Flops
3658
18816
19%
Slices
7148
9408
75%

29. Conclusion Modified Rijndeal algorithm has been presented
The modification done with adding new stage mirror stage which doesn’t require bigger hardware area.
The system has been simulated and implemented on FPGA with total area of 75% and max. frequency of 44MHz.

30. Thanks