KASUMI is a block cipher which has been adopted as a standard of 3GPP. In this paper, we study the pseudorandomness of idealized KASUMI type permutations for adaptive adversaries. We show that • the four round version is pseudorandom and • the six round version is super-pseudorandom. Key words: Cryptography, block cipher, KASUMI, pseudorandomness, provable security. ∗ A preliminary version of this paper appears in The Eighth Australasian Conference on Information Security and Privacy, ACISP 2003 [5].