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> XOR is not a great choice here. Consider that 2 copies of a row give the same result as 0 (or 4, 6, etc).

That indeed is a major flaw. You have to use another commutative operation that doesn’t destroy entropy. Addition seems a good choice to me.

> And even without multiple copies of rows, you can force any hash you'd like

I don’t see how that matters for this problem.

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It depends on whether you are doing something security critical with the result.

Maybe you have a trusted table hash but only a user-supplied version of the table. Before you use that data for security sensitive queries, you should verify it hasn't been modified.

Basically, if you ever have to contend with a malicious adversary, things are more interesting as usual. If not, addition is likely fine (though 2^k copies of a row now leave the k lowest bits unchanged).

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