(Which attack may take the longest amount of time to achieve success?

A brute-force attack exhaustively tries every possible key or password candidate until the correct one is found. Because it explores the full search space (or a very large portion of it), brute force is often the slowest method, especially when strong keys, long passwords, rate limits, and slow password hashing (bcrypt/Argon2) are used. By contrast, a dictionary attack reduces work by trying only common or likely passwords, often succeeding quickly against weak human-chosen secrets. Rainbow table attacks shift work into precomputation; once a table exists, lookup can be faster than brute-force—though salt and modern hashing defeat them. Birthday attacks are about finding collisions, not necessarily recovering a specific secret, and their expected work is about 2^(n/2) for an n-bit hash, which can be less than brute-force key search in many contexts. Therefore, among the listed options, brute-force generally takes the longest to succeed because it makes the fewest assumptions and does the most total work.