There is nothing that identifies a person more precisely than their genome. It is, after all, unique to each person.
That means that by definition, anonymizing genomes is impossible. If someone tells you they will 'anonymize' your genome data, run away, they don't know what they are doing.
Much like you can't anonymize browsing history data, email metadata or financial transactions -- I suspect DNA information also cannot be satisfactorily anonymized.
de anonymizing genetic data is not that hard. Also, if your relatives opt for it, they can still get a pretty decent picture of your genome so not going for it doesn't necessarily mean you are protected.
The weird thing about DNA and genes is that the data, should you have access to it in it's original form, as samples of biological material, is never anonymous.
The techniques that effectively anonymize genetic information, typically render it as an unusable data set for practical purposes.
The only thing that makes DNA anonymous is constructing an unrelated set of hash keys as lookups, and then using these coded tokens as decoupled representational references to a remote system that mitigates requests. Even then, even without access to the direct data, the traits expressed COULD still accidentally identify certain members of the set very easily.
How many albinos are in the set? How many male albinos? How many male albinos with blood type O positive? Oh look, it's Joe and it turns out he's a carrier for this other embarrassing genotype. Whoops, secret's out and everyone knows, and there's no going back!
So phenotypes can still identify people inadvertently, and then provide opportunities for the enumeration of members, through process of elimination, inherently weakening what might become a theater of anonymity.
But more terrible still, is, let's just say they give the raw genetic data up. Say you have a juicy tidbit of information you pulled from the collection of samples, and you think you know who it is. So you surreptitiously snag a hair follicle from them. It's them all right, and you can prove it conclusively. Maybe your a nice guy and you won't misuse this sort of advantage, but is that true for everyone at large, throughout society?
With DNA, genomes and genetic evidence, you kind of just have to keep saying to yourself "this is not anonymizable, it will never be anonymous, we cannot truly de-identify anyone's DNA" and the sooner we come to terms with that, the better we'll get at dealing with this sort of data.
There's no way you can keep your genome private in the long term. Even today anyone can get DNA samples from you without your knowledge or consent, but in the near future it will be trivial to collect and sequence anyone's DNA using an iPhone.
Besides, the same knowledge that makes attacks possible also makes defense possible.
You are leaving a DNA trail in your wake, and it's only private or personal insofar as no one looked at it. But it seems like it's something that we really have no hopes of keeping private over any reasonable timeline into the future.
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