what is the impact of smaller bit size sbox

Question

There are multiple S-boxes type, as DES uses 4 bit S-box and AES uses 8 bit S-box. I want to know how this effect the security?? If we use 4 bit or 8 bit. apart from the DC attack. Both provides confusion then why 4 bit and 8 bit different size

Answer 1

the differential property , linear property , algebraic order is larger for 8 bit s-boxes compared to 4 bit s-boxes.

The optimal differential/linear probability is 2^-6 for 8-bit s-box while it is 2^-2 for 4-bit s-boxes, therefore less number of active s-boxes needed (less rounds) to achieve minimum differential/linear security bound using 8-bit s-boxes.

However, 4-bit s-boxes are good for light implementation and threshold masking to resist side channel analysis.