AES Guest Lecturer

AES Algorithm - MixColumns
• This with shift rows provides diffusion
• The columns are considered polynomials over
GF(2 8 ) and multiplied modulo x 4 +1 with a(x)
where a(x) = {03}x 3 + {01}x 2 + {01}x + {02}
NOTE: x 4 +1 is relatively prime to a(x)
a ’ j (a j *a(x))mod(x 4 +1)
• This can also be written as matrix multiplication.
a ’ 0
02 03 01 01
a 0
a ’ 1
a ’ 2
=
01 02 03 01
01 01 02 03
a 1
a 2
a ’ 3
03 01 01 02
a 3