Well let's analyze it using the game from the paper. An attacker could do the following I believe: 1. Take something compressible like x0=AAAA... 2. Compress

Well let's analyze it using the game from the paper. An attacker could do the following I believe: 1. Take something compressible like x0=AAAA... 2. Compress to get y0. 3. Take x1=y0. Compress to get y1. Now most likely y0=y1 meaning that decompressing y1 doesn't give x1, so you lost. But if y1 != y0, then 4. Take x{i+1} = y{i} and compress. Eventually there will be a collision. Preventing this is why the author's scheme is so complex.