A Related-Key Attack against Multiple Encryption based on Fixed Points
In order to alleviate the burden of short keys, encrypting a multiple times has been proposed. In the multiple encryption mode, there may be encryptions under the same or different keys. There have been several attacks against this encryption mode. When triple encryption is based on two keys, for instance, Merkle and Hellman proposed a subtle meet-in-the-middle attack with a complexity similar to breaking a single encryption, requiring nearly all the codebook. In the case of triple encryption with three keys, Kelsey, Schneier, and Wagner proposed a related-key attack with complexity similar to breaking a single encryption.