We found a 32nd-order differential characteristic of MISTY1 without FL functions, which makes the differential of upper 7bit of 64-bit output of the 5th round be zero. By using this characteristic and a linearization technique, we show that 6-round MISTY1 without FL functions can be attacked with 235:5 of chosen plaintexts and 234:3 of computations of FO function. We demonstrate this 6-round attack by a computer simulation. CPU time for the simulation is 2 hours and 35 minutes. This attack reduces the plaintexts to 2:3:5 and the computations to 2:14:9 compared to conventional 6-round attack. We also show that 7-round MISTY1 without FL functions can be attacked with 236:5 of the plaintexts and 2112:0 of the computations by using a combination of the 6-round attack and exhaustive search. This 7-round attack reduces the computations to 2:13:1 although the plaintexts increase 224:6 times. These drastic reductions of the computational costs come from counting up the number of occurrences of ciphertexts, and omitting the ciphertexts occurring even number of times from computation.