A security policy requires passwords to be exactly $12$ characters long. Each character may be an uppercase letter (26 choices), a lowercase letter (26 choices), a digit (10 choices), or one of $12$ special symbols. The policy also mandates that every password contain 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, what is the minimum time in years required to exhaust the entire password space? (Give your answer rounded to two significant figures.)

Question

A security policy requires passwords to be exactly $12$ characters long. Each character may be an uppercase letter (26 choices), a lowercase letter (26 choices), a digit (10 choices), or one of $12$ special symbols. The policy also mandates that every password contain 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, what is the minimum time in years required to exhaust the entire password space? (Give your answer rounded to two significant figures.)

Accepted Answer

a) $74^{12} - 64^{12} - 62^{12} + 52^{12}$ ≈ 1.9×10^22 passwords; b) ≈ 6.1×10^5 years

City Guilds Model Questions Vol1 2025 Information Technology Question 19

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