Jim Miller says:

Does DES (or name your favorite encryption algorithm) produce as output all possible cyphertexts of length L, given all possible conbinations of keys and plaintexts of length L?

DES defines a family of fucntions defined by the keys, call them E_k, that map the 64 bit integers one to one into the 64 bit integers. That is, no two plaintexts produce the same cyphertext. Therefore, you don't need all possible combinations of keys -- any key will produce all possible cyphertexts if you chain through all possible plaintexts.

Since there are more combinations of key and plaintext than there are possible cyphertexts outputs of length L, you know there must be some combinations of key and plaintext that produce the same cyphertext.

Given any two distinct keys, k_1 and k_2, it is pretty much guaranteed that there are at the very least plenty of cyphertexts C_1=E_k_1(P_1) such that there is a C_2=E_k_2(P_2) with C_1 = C_2 and P_1 != P_2. Perry