Related-key attack against triple encryption based on fixed points

Triple encryption was proposed to increase the security of single encryption when the key is too short. In the past, there have been several attacks in this encryption mode. When triple encryption is based on two keys, Merkle and Hellman proposed a subtle meet-in-the-middle attack which can break it at a price similar to breaking single encryption (but with nearly all the code book). When triple encryption is based on three keys, Kelsey, Schneier, and Wagner proposed a related-key attack which can break it at a price similar to breaking single encryption.