The judge doesn't really understand a hash well. They say things like "Google assigned a hash" which is not true, Google calculated the hash. Also I'm surprised the 3rd-party doctrine doesn't apply. There's the "private search doctrine" mentioned but generally you don't have an expectation of privacy for things you share with Google
Google at some point decided how to calculate that hash and that influences what the value is right? Assigned seems appropriate in that context? Either way I think the judge's wording makes sense.
Once the hashing algorithm was assigned, individual values are computed or calculated.
I don't think the judge's wording is all that bad but the word "assigned" is making it sound like Google exercised some agency when really all it did was apply a pre-chosen algorithm.