Secret key formed by the combination of several keys I think there exists an algorithm to create a key from the combination of a group of keys in such a way that if I encrypt a message using the key formed from the combination, I should be able to decrypt it using any one of the keys from the group. Any idea?
A trivial solution would be to encrypt the message under all the different keys and concatenate the ciphertexts. However, this obviously has a large blow-up in terms of ciphertext length. 

An idea to decrease the blowup would be to encrypt the message under a new short key $k'$ to get a ciphertext $c$, then encrypt $k'$ under all the IDs $k_1,...,k_n$ individually and concatenate the results to $c$ and broadcast the concatenation.

This may not be great in practice but it has an asymptotic rate of $1$, which is better than the trivial solution's rate of $1/n$.

One caveat for both the above solutions is that there would have to be some ordering on the stations, and the stations would have to know their place in the ordering.