The system has several potential flaws. and the possible solutions mentioned in the comments below the second article all introduce new problems.
Several people suggest adding a timestamp to the "name" (actually, identifier) to be tested; this would introduce a flaw that completely destroys and accountability; all the Evil Government has to do, is change the timestamp by a few seconds to change the output of the algorithm.
This, of course, assumes that the timestamp involved is the time the algorithm is executed for the passenger in question, meaning the exact moment the TSA agent scans or enters the information on their passport.
Also, I would say the whole system depends on the key size. If the keysize is small, an adversary would only need a few observations of the algorithm (known input and known output) to determine the key. On the other hand, if the key is sufficiently large, the Evil Government could just select whoever they want, and figure out which key would generate the selection of that particular day.
Alternatively, the algorithm could include the number of the passport, serial number of the ticket, or a social security number (or foreign equivalent). In any case, it has to be something the Evil Government can't choose or manipulate on that particular day.
On the other hand, the algorithm would have to include something that even the Evil Government can't predict, simply because they know, in advance, who will be flying on a particular day, first decide who must be searched, and then decide what their "secret key" will be that particular day.
If there would be a way to prove that the secret key really was chosen by a fair random method, I guess it might just work.
Another way to make it work would be to publish a hash value of the secret key in advance (before the flights are booked, and thus before the government can know who will be flying that day), as a commitment to that particular key.
In short: I think that either the commitment should be made a long time in advance (maybe several weeks or even months), or it should include something the government can't predict or manipulate, but the passenger can verify.
Maybe we should just ask the passenger to pick a number, and use that in the algorithm (along with many other, verifiable factors, of course).
The die roll is also inherently flawed; it would be trivial to include a small magnet or ferromagnetic material on the side opposite the "go through invasive screening" side, and an electromagnet in the table, so the agent or an automated system can force that particular outcome. In case of a magnet, the automated system could also force a "clear" outcome, for certain people who are decided to be more equal than others.