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Needham–Schroeder refers to both, a symmetric key or a public key authentication protocol.
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When would you increment a nonce and when not?
K is the shared key for encryption known by _Alice and _Bob. $N_A$ is a nonce created by Alice. The function f is the increment by 1 function.
(1) Alice -> Bob: $E_K(N_A)$
So Alice encrypts a nonce wi …