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3

Yes, you are right. In a proof, the soundness holds against a computationally unbounded prover and in an argument, the soundness only holds against a polynomially bounded prover. Arguments are thus often called "computationally sound proofs".


2

Sure they can, it's called the socialist millionaires problem. The most common solution is to use Yao's protocol: Alice sends a garbled circuit of the equality function to Bob, and then Alice use oblivious transfers to send the keys necessary for the evaluation of the circuit to Bob. Another option is to rely on additively homomorphic IND-CPA encryption: ...



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