Advanced Encryption Standard (AES)

Advanced Encryption Standard, a symmetric key algorithm, implemented in C++. All the parties use the same key for encryption and decryption. It has superseded DES, another symmetric key algorithms.

About

Rijndael was selected by NIST (National Institute of Standards and Technology) as AES. Unlike Rijndael in which block length and key length can be specified to any multiple of 32 bits, AES fixes block length to 128 bits and key length to (128 or 192 or 256) bits.

Description

The total number of rounds with key of 128 bits is 10. There are four subroutine that are performed in each rounds.

Byte Substitution Transformation

Each element of state is non-linearly mapped to corresponding element in the s-bx. ¹

Byte_Sub

Shift Rows

Rows are cyclically shifted to the left with offset of 0, 1, 2, 3 for rows of 1, 2, 3 and 4 respectively. ²

Shift_Rows

Mix columns ³

Each new column (ro, r1, r2, r3) is generated from old column (a0, a1, a2, a3).

Here, r0 = {2 . a0} + {3 . a1} + {1 . a2} + {1. a3} r1 = {1 . a0} + {2 . a1} + {3 . a2} + {1. a3} r2 = {1 . a0} + {1 . a1} + {2 . a2} + {1 . a3} r3 = {3 . a0} + {1 . a1} + {1 . a2} + {2 . a3}

Add Round Key

For each round, subkey is combined with the state matrix using biwise XOR.

Key Generation

Initial key is described as a state matrix.

Co	C1	C2	C3
a₀₀	a₀₁	a₀₂	a₀₃
b₁₀	b₁₁	b₁₂	b₁₃
c₂₀	c₂₁	c₂₂	c₂₃
d₃₀	d₃₁	d₃₂	d₃₃

The last column is cyclically rotated to move the last block to the top.

Co	C1	C2	C3
a₀₀	a₀₁	a₀₂	d₃₃
b₁₀	b₁₁	b₁₂	a₀₃
c₂₀	c₂₁	c₂₂	b₁₃
d₃₀	d₃₁	d₃₂	c₂₃

The last column is then mapped with the corresponding element of the s-box.

C3		C3^'
a₀₀	–>	a₀₂
b₁₀	–>	b₁₂
c₂₀	–>	c₂₂
d₃₀	–>	d₃₂

New column C₀ is generated by XORing previous C₀ with the new column.

C0		C3^'
a₀₀	⊕	a₀₂
b₁₀	⊕	b₁₂
c₂₀	⊕	c₂₂
d₃₀	⊕	d₃₂

Similarly all new coulumns are generated by XORing with pervious columns.

details — code

http://goo.gl/lfkNI ↩
http://goo.gl/j8YGJ ↩
Understanding AES Mix-Columns Transformation Calculation by Kit Choy Xintong ↩