ADVANCED ENCRYPTION STANDARD [AES]
BY
Dr SAPNA P J
WHY AES?
A drawback of DES is the use of 64-bit block size.
For reasons of both efficiency and security, a larger
block size is desirable.
As a replacement, Advanced Encryption Standard
was proposed
NIST specified that AES must be a symmetric
block cipher with a block length of 128 bits and
support for key lengths of 128, 192, and 256 bits.
NIST selected Rijndael as the proposed AES
algorithm
RIJNDAEL
Rijndael was designed to have the following characteristics:
● Resistance against all known attacks
● Speed and code compactness on a wide range of platforms
● Design simplicity
The input to the encryption and decryption algorithms is a single 128-bit block.
This block is depicted as a square matrix of bytes
key is expanded to array of words
Four transformations in the rounds:
Byte substitution (1 S-box used on every byte)
Shift rows (permute bytes between groups/columns)
Mix columns (uses matrix multiplication of groups)
Add round key (XOR state with key material)
BYTE SUBSTITUTION
The Substitute bytes stage uses an S-box to
perform a byte-by-byte substitution of the block.
There is a single S-box used on every byte.
This S-box is a permutation of all 256 8-bit values,
constructed using a transformation which treats the
values as polynomials in GF(28)
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}
SHIFT ROWS
A circular byte shift in 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
Decrypt inverts using shifts to right
Since state is processed by columns, this
step permutes bytes between the
columns
MIX COLUMNS
Each column is processed separately
Each byte is replaced by a value dependent on all 4 bytes in the column
Each byte of a column is mapped into a new value that is a function of all four bytes in that
column.
It is designed as a matrix multiplication
Addition is the bitwise XOR operation and that multiplication can be performed according to the
rule. In particular, multiplication of a value by x (i.e., by {02}) can be implemented as a 1-bit
left shift followed by a conditional bitwise XOR with (0001 1011) if the leftmost bit of the
original value (prior to the shift) is 1.
MixColumns transformation on the first column
ADD ROUND KEY
Add Round Key stage which is a simple bitwise XOR of the current block with a
portion of the expanded key
Note this is the only step which makes use of the key and obscures the result, hence
MUST be used at start and end of each round, since otherwise could undo effect of
other steps.
But the other steps provide confusion/diffusion/non-linearity.
Thus you can look at the cipher as a series of XOR with key then scramble/permute
block repeated.
This is efficient and highly secure
In the forward add round key transformation, called AddRoundKey, the 128 bits of State are
bitwise XORed with the 128 bits of the round key
The operation is viewed as a columnwise operation between the 4 bytes of a State column and one
word of the round key; it can also be viewed as a byte-level operation.The following is an example of
AddRoundKey:
The inverse add round key transformation is identical to the forward add round key
transformation, because the XOR operation is its own inverse.
AES KEY EXPANSION
Expansion of the key into 11 partial keys which are used in initial round , 9 main rounds and final round
The AES key expansion algorithm takes as input a 4-word (16-byte) key and produces a linear array of
44 words (176 bytes).
RotWord performs a one-byte circular left shift on a word. This means that an input word [b0,b1, b2, b3] is
transformed into [b1, b2, b3, b0].
Subbytes performs a byte substitution on each byte of its input word, using the S-box
The result of steps 1 and 2 is XORed with a round constant and the column four positions earlier
This result is Xored with 2nd column . This result is Xored with third column . This will result in round key 1
