Cryptographic Protocol

Definition

• A protocol is a Pair of Probabilistic, Interactive Turing Machine $(P,V)$
• $P$ is denoted as the prover
• $V$ is denoted as the verifier

Alternate Definition

A protocol is a Tuple $\pi =({\mu }_1,\dots ,{\mu }_n)$ is a protocol if:

• Every ${\mu }_i$ has a caller of ${\mu }_j$, ${\mu }_j$ is a Subroutine Machine of ${\mu }_i$
• Every ${\mu }_i$ that is a Subroutine Machine of identity ${\text{ID}}_j$, if some ${\mu }_j$ has identity ${\text{ID}}_j$, then ${\mu }_j$ is a Caller Machine of ${\mu }_i$
• If there is no such ${\mu }_j$ then ${\mu }_i$ is the main machine (entry point) of $\pi$, and ${\text{ID}}_j$ is an external identity (its floating in the Aether)