Last Attempt Introduction-to-Cryptography Questions

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.

In AES, the number of rounds is explicitly tied to the key length. AES-128 uses 10 rounds, AES-192 uses 12 rounds, and AES-256 uses 14 rounds. The purpose of additional rounds is to increase diffusion and confusion, strengthening resistance against cryptanalysis as the key schedule and state transformations iterate more times. Although key length primarily affects brute-force resistance, AES’s designers and standardization parameters link longer keys with more rounds to maintain security margins across variants, especially considering differences in the key schedule structure. Thus, as key length increases from 128 to 192 to 256 bits, the number of rounds increases correspondingly from 10 to 12 to 14. This relationship is fixed by the AES specification and does not vary dynamically at runtime. Therefore, the correct correlation is that the number of rounds increases as the key length increases.

One-way client authentication is the method where the client (customer) proves its identity to the server (web service). In cryptographic terms, this is commonly implemented through client credentials such as client TLS certificates (mTLS from the server’s perspective) or through authentication protocols layered over TLS (for example, signed tokens), but the defining direction is that the client is the party being authenticated. In a strict TLS certificate-authentication framing, client authentication occurs when the server requests a client certificate during the handshake and the client demonstrates possession of the corresponding private key (via signature in handshake messages). The server then validates the client certificate chain and authorization policy. One-way server authentication, by contrast, authenticates only the server to the client and does not identify the customer. Mutual authentication authenticates both sides simultaneously; while it includes client authentication, it is broader than what the question asks. “End-to-end authentication” describes assurance between endpoints across intermediaries, but it is not the specific “customer authenticates to service” method in certificate-based terminology. Therefore, the best answer is one-way client authentication.