# Design of MixColumn Transformation in AES

Why is the multiplication in MixColumn Transformation particularly by 2,3,1,1 cyclically? Why not some other numbers?

• These numbers make the encryption direction cheap; to compute the transform of the column $(A, B, C, D)$, you compute $2 \times A, 2 \times B, 2 \times C, 2 \times D)$, and then do a bunch of byte-wise xor's.
• These numbers make the decryption direction moderately cheap, to compute the inverse transform of the column $(A, B, C, D)$, you compute $2 \times A, 4 \times A, 8 \times A, 2 \times B,$ $4 \times B, ..., 8 \times D$ (doable with 12 doublings), and then do a bunch of byte-wise xor's.