Differential probability for a component in non-linear function of K2 v2.0

Authors propose a method which can evaluate an accurate differential probability for multi-byte arithmetic addition with S-boxes. The 8-bit truncated differential probability for 32-bit arithmetic addition with AES S-boxes were compared to the conventional evaluation (replacing S-box with XOR). It was found that there are 1937 paths that the probabilities increase compared to the probabilities by the conventional evaluation. Among them, 1512 paths were ignored in the conventional evaluation. There were 18 peculiar paths that the 8-bit truncated differential probabilities were the same with that of 32-bit arithmetic addition without S-boxes even though the output differences are non-zero.