A system requires passwords of length 8. Each character can be an uppercase letter (26), a lowercase letter (26), a digit (10) or one of 10 special symbols, giving a total character set of 72. The policy mandates that a password must contain at least one uppercase letter, at least one digit, and at least one special symbol.

(a) How many distinct passwords satisfy the policy?

(b) If an attacker can test $10^{9}$ passwords per second, how many years (to two decimal places) would be required to exhaust the entire password space?

(c) The security guideline requires a minimum resistance of 100 years. Does the policy meet this requirement? Answer "Yes" or "No" and give the computed time.

Question

A system requires passwords of length 8. Each character can be an uppercase letter (26), a lowercase letter (26), a digit (10) or one of 10 special symbols, giving a total character set of 72. The policy mandates that a password must contain at least one uppercase letter, at least one digit, and at least one special symbol.

(a) How many distinct passwords satisfy the policy?

(b) If an attacker can test $10^{9}$ passwords per second, how many years (to two decimal places) would be required to exhaust the entire password space?

(c) The security guideline requires a minimum resistance of 100 years. Does the policy meet this requirement? Answer "Yes" or "No" and give the computed time.

Accepted Answer

No; about 0.01 years (≈3.7 days)

City Guilds Model Questions Vol1 2022 Information Technology Question 11

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