Suppose that when a fingerprint is compared with one other (nonmatching) fingerprint, the chance of a false match is 1 in 1010 , which is approximately the error rate when 16 points are required to determine a match (the British legal standard). Suppose that the FBI fingerprint database contains 107 fingerprints.
a. How many false matches will occur when 100,000 suspect fingerprints are each compared with the entire database?
b. For any individual suspect, what is the chance of a false match?
For password cracking, generally the most realistic situation is Case IV of Section 7.3.5. In this case, the amount of work that Trudy must do to determine a password depends on the size öf the dictionary, the probability that a given password is in the dictionary, and the size of the password file. Suppose Trudy’s dictionary is of size 2™, the probability that a password is in the dictionary is p, and the password file is of size M. Show that if p is small and M is sufficiently large, then Trudy’s expected work is about 2″/p.
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