Alice, Bob, and Carol want to use secret key cryptography to authenticate each other. Compare the security of having a single shared secret that they all share, with the security of having each of them use their own secret (Alice authenticates to either Bob or Carol by proving knowledge of KA, Bob with KB, and Carol with KC).

Assume a cryptographic algorithm that is linear in the length of the key to perform "good guy operations," e.g., encryption, decryption, key generation, integrity check generation, and integrity check verification; and that it is exponential in the length of the key to perform "bad guy operations," e.g., brute force breaking.

In a well-crafted document, fully discuss the following items. Provide details and justifications for each item. This should be a 4- to 6-page Microsoft Word document. Cite your sources, wherever required.

Advances in computation make computers an order of magnitude faster. Does this work to the advantage of the good guys, the bad guys, or neither? Justify your answer with reasoning.

Assuming a very large message and public keys user, describe what information would need to be included in each of the following:
Bob sending an unencrypted, signed message to Alice.

Bob sending an unencrypted, signed message to multiple recipients (Alice and Carol).

Bob sending an encrypted, signed message to Alice.

Bob sending an encrypted, signed message to Alice and Carol.

Explain efficiency issues and alternate methods that would work but be less efficient.

Analyze whether it will be easier to have nonrepudiation with the use of public or private user keys. How about plausible deniability?