Pseudorandomness Analysis of the Lai-Massey Scheme

At Asiacrypt’99, Vaudenay modified the structure in the IDEA cipher to a new scheme, which they called as the Lai-Massey scheme. It is proved that 3-round Lai-Massey scheme is sufficient for pseudorandomness and 4-round Lai-Massey scheme is sufficient for strong pseudorandomness. But the author didn’t point out whether three rounds and four rounds are necessary for the pseudorandomness and strong pseudorandomness of the Lai-Massey Scheme. In this paper we find a tworound pseudorandomness distinguisher and a three-round strong pseudorandomness distinguisher, thus prove that three rounds is necessary for the pseudorandomness and four rounds is necessary for the strong pseudorandomness.