In the current crypto paradigm a single secret key transforms a plaintext into a ciphertext and vice versa, or at most a different key is doing the reverse action. Attackers exposed to the ciphertext are hammering it to extract that single key and the plaintext. This paradigm is now facing an alternate setup: using a particular crypto algorithm, there are infinite number of keys that are perfectly interchangeable -- each has the same effect. Despite the fact that there are infinite number of them, they are still hard to find. And unlike regular cryptography, the best that you can hope for using this new "Family Key" cryptography, is to identify the entire infinitely large family of keys, not the actual key that executed the cryptographic action. This very fact is a cornerstone for a host of applications, mostly still to be unfolded.
Imagine a group of communicators using cryptography for secure communication. Until now they all had to share the same key. Using Family Key Cryptography, each communicator could be given his or her unique key. They will read and write to each other as if sharing a key, but do so while carrying their unique identification via their unique key. Bitcoin designers identify some powerful new payment capabilities.
Family Key cryptography enables 'Forever Key' cryptography: crashing the Shannon's limit, The Forever Key strategy will allow a single finite key to last forever. The shared secret key will be used to derive a succession of operating keys, which will be replaced before they are being compromised. Since any cryptanalysis of usage will end up with an infinite list of key candidates, there will be equal number of candidates for the shared "Forever Key", and thus there will be no erosion in the secrecy of the Forever Key regardless of its level of use.
The very idea of infinite number of interchangeable keys is so fundamentally different, that most of its applications are still unknown.