1suppose alice, bob, and carol want to use secret key technology to authenticate each other. if they all used the same secret key k, then bob could impersonate carol to alice (actually any of the three can impersonate the other to the third). suppose instead that each had their own secret key, so alice uses ka, bob uses kb and carol uses kc. this means that each one to prove his or her identity responds to a challenge with a function of his or her secret key and the challenge. is this more secure than having them all use the same secret key k?

Explained

Explanation:

Alice need to know the secret key of carol to verify the carol's answer to Alice challenges.

Similarly it needs the secret key of Bob to verify bob's answer  to Alice challenge (actually any of the three need others secret key for verify answer to challenge).

So, Bob could impersonate Carol to Alice as he should know the secret key of Carol to answer Carol's challenge. Hence it is no more secure than having all use the same secret key.

So, it is no more secure than having them all use the same secret key K.

this is true

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i looked it up

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what

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