On the security of multiple encryption

Double encryption has been suggested to strengthen the Federal Data Encryption Standard (DES). A recent proposal suggests that using two 56-bit keys but enciphering 3 times (encrypt with a first key, decrypt with a second key, then encrypt with the first key again) increases security over simple double encryption. This paper shows that although either technique significantly improves security over single encryption, the new technique does not significantly increase security over simple double encryption. Cryptanalysis of the 112-bit key requires about 2 56 operations and words of memory, using a chosen plaintext attack. While DES is used as an example, the technique is applicable to any similar cipher.