24 Suppose that Trudy has a dictionary of 21 passwords and t

24. Suppose that Trudy has a dictionary of 21 passwords and the probability that a given password is in her dictionary is p. If Trudy obtains a file containing a large number of salted password hashes, show that the expected work to recover a password is bounded by 2^n-1(1+2(1 - p)/p). Hint: As in Section 7.3.5, Case IV, ignore the highly improbable case where none of the passwords in the file appears in Trudy\'s dictionary. Then make use of the fact that Sigma infinity k=0 x^k = 1/(1 - x) and also Sigma infinity k = 1 kx^k = x/(1 - x)^2, provided |x|

Solution

x