In this paper we introduce a structure iterated by the rule A of Skipjack and show that this structure is provably resistant against differential or linear attacks. It is the main result of this paper that the upper bound of r-round (r ≥ 15) differential(or linear hull) probabilities are bounded by p ⁴ if the maximum differential (or linear hull) probability of a round function is p, and an impossible differential of this structure does not exist if r ≥ 16. Application of this structure which can be seen as a generalized Feistel structure in a way to block cipher designs brings out the provable security against differential and linear attacks with some upper bounds of probabilities. We also propose an interesting conjecture.