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

Notes: