We investigate the Misty structure with respect to the security notion of sequential indifferentiability of Mandal et al. (TCC 2012). As our main result, we prove sequential indifferentiability for 7-round Misty structures using seven independent random permutations in the rounds. We also prove insecurity for 5 rounds by exhibiting an attack. Our main result implies known-key security of 7 rounds in the sense of correlation intractability, providing the first known-key security results on Misty structures to our knowledge.