Introduction to Cryptography

1. In a one-time pad, if a message m of length l(lamba) is is encrypted with a key k = 0^l (i.e., k consists of all 0s) then enck(m) = m. That is why, it is sometimes suggested to prohibit this key. In other words, the keyspace is restricted to strings which are all not zeros. Is the resulting cryptosystem perfectly secure?