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They had me until this part . . .

    Authentication requires that you play a round of the game —
    but this time, your 30-letter sequence is interspersed with 
    other random 30-letter sequences.
Which makes it sound to me like your password could be deduced from a single (failed) login attempt, and then reproduced after a session in the trainer.



Their discussion of that attack, from the paper itself:

    If the attacker is allowed multiple authentication 
    attempts — iterating the extraction and test phases, 
    alternating between the two — then the protocol may 
    become insecure.  The reason is that during an 
    authentication attempt the attacker sees the three 
    sequences k0; k1; k2 and could memorize one of them (30 
    symbols). He would then train offline on that sequence so 
    that at the next authentication attempt he would have a 
    1/3 chance in succeeding. If the attacker could memorize 
    all three sequences (90 symbols), he could offline 
    subject a trained user to all three sequences and 
    reliably determine which is the correct one and then 
    train himself on that sequence. He is then guaranteed 
    success at the next authentication trial.

    We note that this attack is non-trivial to pull off 
    since it can be difficult for a human attacker to 
    memorize an entire sequence at the speed the game is 
    played.
. . . which isn't all that reassuring, given that if I were trying to break in using this technique, I wouldn't be memorizing, I'd be recording.

But it sounds like the system is designed to only give an attacker one trial (notionally opening a trap door under his feet if he fails even once), and it does seem much more secure in that context.




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