In Cryptology, a cipher is group if re-encrypting a ciphertext with another key generates a new cipher text that can be decrypted to the original plaintext with a single key. If a cipher is a group, double encryption provides no greater security, as all ciphertexts can be decrypted with a single key.

It has been proven that DES is not a group. A body of plaintext was encrypted with one key and then decrypted with another key. The body of ciphertext was then brute forced and it was found that a single key did not facilitate decryption. Each block of plaintext could be decrypted by using a separate key. If a cipher is a group, a single key can be used in place of two keys.

It is unknown if many algorithms are a group, as the key length of some algorithms prevents a brute force attack.