Question: In practice, it is often the case that good block ciphers such as AES ( or some carefully designed hashes such as SHA 2 5

In practice, it is often the case that good block ciphers such as AES (or some carefully designed hashes such as SHA256) are assumed to be a PRF. However, block cipher, by name, works on a fixed length of blocks, e.g., AES works on 128-bit messages only. The followings are two possible ways to adjust the input/output length of a PRF, prove that the constructions are still PRF according to the above definition.

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