Final answer:
In Quantum Cryptography, if Alice and Bob have matching extensions, it signifies a successful Quantum Key Distribution process, validating secure communication without interference from eavesdroppers.
Step-by-step explanation:
In Quantum Cryptography, specifically within the realm of Quantum Key Distribution (QKD), when Alice and Bob have the same values for their extensions, it indicates that their process of key generation is synchronized and successful. This is a desired outcome. For example, when using the BB84 protocol, Alice and Bob have to compare a subset of their keys to check for eavesdroppers. If the extensions (the subset of comparing keys) are identical, they can be confident that there was no interference and hence, they can use the remaining, unshared part of their keys for secure communication. If their keys did not match, this would indicate potential eavesdropping, and they would then discard the keys and restart the key distribution. Therefore, the correct answer is d) They authenticate each other's identities for secure communication.