Consider a replacement for Facebook which is a distributed hash table, using cryptographic signatures to manage identity and read permission; the details still need to be worked out, though the design principle is no single central entity controls everyone's information.
Is it possible to untag yourself from a picture for such a system? My first thought is, of course not, because it is very difficult to delete anything from a robust distributed hashtable.
The simplest third party tags consists of someone else inserting a piece of data into the DHT consisting of a pair: the hashcode of the picture and your unique identifier, possibly cryptographically signed by them. Such a tag cannot be easily deleted.
We thwart such tagging by avoiding ever giving out a globally unique identifier for yourself. Each of your friends knows you by a different identifier, and that identifier is only useful if one has the friend's private key. It's sort of a graph duality: the edges between nodes carry labels, not the nodes themselves. I don't know how to make this work. It seems it might not work because, even if you don't give out a globally unique identifier, there's no stopping someone else from forcefully creating one for you.
Another untagging mechanism might be chaff: whenever you tag yourself, you create a private key with which you can, later, produce countless fake tags of yourself, very difficult to distinguish from the original, effectively untagging yourself.
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