On strict estimation method of provable security against differential and linear cryptanalysis

Abstract

We give stricter upper bounds to the probabilities of differential and linear hull of DES-like ciphers than the previous results. The previous results in [6, 7] said that every r-round differential (or linear hull) with r ≽ 4 is bounded by 2p ² (or 2q ²) where p (or q) is the maximum probability of a non-trivial differential (or linear hull) of the function which is used in each round. Using our new estimation method of provable security it is shown that these bounds change depending on the number of rounds. This change gives a decrease function of the number of rounds with the limit value. Moreover, our estimation gives 2p ²-p ³ (or 2q ²-q ³) for 4 and 5 rounds so our method is stricter than the previous one. The bounds converge to about p ²(or q2) for an increasing number of rounds.