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Consider Shamir's secret sharing. The idea is you need $k$ out of $n$ parts of a key to recover some secret $S$. Then, if you "summarize" a key and encrypted text without providing at least $k$ par...
Answer
#1: Initial revision
Consider [Shamir's secret sharing](https://en.wikipedia.org/wiki/Shamir%27s_secret_sharing). The idea is you need $k$ out of $n$ parts of a key to recover some secret $S$. Then, if you "summarize" a key and encrypted text without providing at least $k$ parts of the key, you effectively lose all of the information in the encrypted text. But this example is quite convoluted and I'm not quite sure if it's what you're looking for.