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De-Identification Through Encryption
Encryption is reporting the value g(f(x)) instead of f(x)
g is 1-1 so it has an inverse (though the inverse may not be known)
g should be totally private; otherwise it can be compromised
g is a derangement function if it has no fixed point, i.e.,
Derangement alone is not enough
- Need to avoid short periods: g(g(x)) = x
- Also want g to be computationally one-way. g(x) = x+1 is no good
Whether g has a fixed point is undecidable. Generalized SHA?
Question: when is g(f(x)) totally private?
There exists a totally private derangement function g and a totally private f such that g(f(x)) is determined everywhere