Rubik's Attack

Let ENC and DEC be cipher encryption and decryption steps, not necessarily respectively. Consider the operation

  c=ENC(k,p)
  c'=c XOR mask
  p'=DEC(k,c')

or the operation

  c=ENC(k,p)
  k'=k XOR mask
  p'=DEC(k',c)

where c, p, c', p', and mask are all known. Can k be recovered with enough examples?

This is named after many Rubik's cube operations are of the form AXA^-1; that is, first do a preparation, then do something, then undo the preparation.