Modified aes algorithm using multiple s boxes, AES, Cryptography

1. 1
Modified AES Algorithm Using Multiple S-Boxes
Instructor: Truong Tuan Anh, PhD
S: Chu Xuân Tình - 1870583

2. 2
Modified AES Algorithm Using Multiple
S-Boxes
1. Introduction
2. Advance Encryption Standard (AES)
3. Modified AES Algorithm
4. Avaluation
AES - Modifier

3. 3
AES - introdution
Ø In 2000, the NIST formally adopted the AES
encryption algorithm and published it as a federal
standard under the designation FIPS-197.
Ø It was chosen because of its security,
performance, efficiency, implement ability, and low
memory requirements.
• Rijndael was selected as the AES
– Designed by Vincent Rijmen and Joan Daemen
in Belgium

4. 4
AES - introdution
Ø The AES Cipher - Rijndael
• An iterative
– processes data as block of 4 columns of 4 bytes
(128 bits)
– operates on entire data block in every round
• Rijndael design:
– simplicity
– has 128/192/256 bit keys, 128 bits data
– resistant against known attacks
– speed and code compactness on many CPUs
• The MixColumn function in the AES algorithm is
an important property of the cipher

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AES - introdution
Ø The MixColumn function in the AES algorithm
is an important property of the cipher
ü It provides strength against differential and linear
attacks due to the complexity of its mathematical
operations.
ü Require computational resources in software
implementation.
ü Replacing the MixColumn function, the speed
performance of the AES algorithm will be
improved.
ü Propose for a modified AES algorithm using
multiple S-Boxes.

6. 6
AES - Classfication

7. AES - Basic
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AES
Plaintext (128 bits)
Ciphertext (128 bits)
Key (128-256 bits)
AES Conceptual Scheme

8. AES - Basic
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Ø Multiple rounds
• Rounds are (almost) identical
– First and last round are a little different

9. High Level Description
No MixColumns

10. AES - Overall Structure

11. AES - Cipher

12. AES -128-bit values
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• Data block viewed as 4-by-4 table of bytes
• Represented as 4 by 4 matrix of 8-bit
bytes.
• Key is expanded to array of 32 bits words
1 byte

13. AES - Data Unit

14. AES - Unit Transformation

15. AES - Changing Plaintext to State

16. AES -Details of Each Round

17. AES- SubBytes: Byte Substitution
• A simple substitution of each byte
– provide a confusion
• Uses one S-box of 16x16 bytes containing a permutation of all 256
8-bit values
• Each byte of state is replaced by byte indexed by row (left 4-bits) &
column (right 4-bits)
– eg. byte {95} is replaced by byte in row 9 column 5
– which has value {2A}
• S-box constructed using defined transformation of values in Galois
Field- GF(28)

18. AES - SubBytes and InvSubBytes

19. AES - SubBytes Operation
• The SubBytes operation involves 16 independent byte-
to-byte transformations. • Interpret the byte as two hexadecimal
digits xy
• SW implementation, use row (x) and
column (y) as lookup pointer
S1,1 = xy16
x’y’16

20. AES - SubBytes Table
• Implement by Table Lookup

21. AES - InvSubBytes Table

22. Sample SubByte Transformation
• The SubBytes and InvSubBytes
transformations are inverses of each other.

23. AES - ShiftRows
• Shifting, which permutes the bytes.
• A circular byte shift in each each
– 1st row is unchanged
– 2nd row does 1 byte circular shift to left
– 3rd row does 2 byte circular shift to left
– 4th row does 3 byte circular shift to left
• In the encryption, the transformation is
called ShiftRows
• In the decryption, the transformation is
called InvShiftRows and the shifting is to
the right

24. AES - ShiftRows Scheme

25. AES - ShiftRows and InvShiftRows

26. AES - MixColumns
• ShiftRows and MixColumns provide diffusion to
the cipher
• Each column is processed separately
• Each byte is replaced by a value dependent on
all 4 bytes in the column
• Effectively a matrix multiplication in GF(28) using
prime poly m(x) =x8+x4+x3+x+1

27. AES -MixClumns Scheme
The MixColumns transformation operates at the column level; it
transforms each column of the state to a new column.

28. AES-MixColumn & InvMixColumn

29. AES - AddRoundKey
• XOR state with 128-bits of the round key
• AddRoundKey proceeds one column at a
time.
– adds a round key word with each state
column matrix
– the operation is matrix addition
• Inverse for decryption identical
– since XOR own inverse, with reversed keys
• Designed to be as simple as possible

30. AES - AddRoundKey Scheme

31. AES Round

32. AES Key Scheduling
• takes 128-bits (16-bytes) key and expands
into array of 44 32-bit words

33. AES -Key Expansion Scheme

34. AES -Key Expansion submodule
• RotWord performs a one byte circular left shift on a word
For example:
RotWord[b0,b1,b2,b3] = [b1,b2,b3,b0]
• SubWord performs a byte substitution on each byte of
input word using the S-box
• SubWord(RotWord(temp)) is XORed with RCon[j] – the
round constant

35. AES Security
• AES was designed after DES.
• Most of the known attacks on DES were already tested
on AES.
• Brute-Force Attack
– AES is definitely more secure than DES due to the larger-size
key.
• Statistical Attacks
– Numerous tests have failed to do statistical analysis of the
ciphertext
• Differential and Linear Attacks
– There are no differential and linear attacks on AES as yet.

36. AES ALGORITHM USING MULTIPLE S-BOXES
vPROPOSED MODIFIED 128-AES ALGORITHM
USING MULTIPLE S-BOXES
Ø The MixColumns function is perceive to be
requiring more computational resources in
software implementation as compared to the
other functions
Ø Propose for a modified version of the 128-AES
algorithm using two substitution boxes
ü The first S-Box is the Rijndael S-Box
ü The second S-Box is constructed using XOR
operation and affine transformation

37. AES ALGORITHM USING MULTIPLE S-BOXES

38. AES - CONSTRUCTION OF THE NEW S-BOX
vThe second S-Box is derived from the
original S- Box as designed in the AES
ØExclusive OR Operation
§ each cell in the AES-Rijndael will be
XORed with 7F
AES-Rijndael[x,y] XOR (7F)
§ The Key[i] shall be any hexadecimal value
between 00 to FF (Table 1. AES-
2SboxXOR7F)

39. AES - CONSTRUCTION OF THE NEW S-BOX

40. AES - CONSTRUCTION OF THE NEW S-BOX
vThe second S-Box is derived from the
original S- Box as designed in the AES
ØExclusive OR Operation
ØAffine Transform Operation
ü After creating the initial values of AES-
2SboxXOR
ü Scramble the bits in each byte value, we next
apply the following transformation to each bit bi
as stored in the initial AES-2SboxXOR7F:

41. AES - CONSTRUCTION OF THE NEW S-BOX
ØAffine Transform Operation
ü For the inverse AES-2SboxXOR, the following
transformation to each bit was used for bit
scrambling:

42. AES - CONSTRUCTION OF THE NEW S-BOX

43. EVALUATION RESULTS

44. EVALUATION RESULTS

45. EVALUATION RESULTS

46. CONCLUSION
üModified AES algorithm using multiple
S-boxes.
üWe observed that the speed performance
greatly increased in the modified AES
algorithm using multiple S-Boxes, while
the security side has slightly weakened.
üEasily implemented using cheap
processors and a minimum amount of
memory.
üVery efficient
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47. Referents
• [1] National Institute of Standards and
Technology, Advanced Encryption Standard,
FIPS 197 (2011).
• [2] Paper “Modified AES Algorithm Using
Multiple S-Boxes”
• [3] Wiki & slide & Internet.
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Thanks for your attention!