Suppose that you have n accounts, each of which requires a password. Trudy has a dictionary and the probability that a password appears in Trudy’s dictionary is p.

a. If you use the same password for all n accounts, what is the probability that your password appears in Trudy’s dictionary?

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b. If you use distinct passwords for each of your n accounts, what\ is the probability that at least one of your passwords appears in Trudy’s dictionary? Show that if n = 1, your answer agrees with your answer to part a.

c. Which is more secure, choosing the same password for all accounts, or choosing different passwords for each account? Why?

Suppose that Alice uses two distinct passwords—one strong password for sites where she believes security is important (e.g., her online bank), and one weak password for sites where she does not care much about security (e.g., social networking sites).

a. Alice believes this is a reasonable compromise between security and convenience. What do you think?

b. What are some practical difficulties that might arise with such an approach?

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