[xxceylpf] Gradually learning a longer password

Let a password interface provide a way for the user to gradually learn longer passwords over time.  Application is unlock PIN for mobile phones.  It starts out with a very short password, perhaps one digit.  After the user is seen to have successfully mastered it, the phone extends the password by one more digit, allows the user to practice it, and proceed onward.  If the user forgets, he or she can use already mastered prefix plus brute forcing one extra digit.  Over time, the user learns through repeated use a long password, hopefully secure against attackers.

Because the phone is picking each new digit randonly, the long password has a lot of entropy.