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The motivation, to me, is that in reality you can consider any router on the internet to be successfully executing an "intruder-in-the-middle" attack just by forwarding messages unchanged. After a successful execution of the identification scheme, Bob knows that someone on the channel is Alice, which is all the protocol was hoping to achieve. It was ...


2

Without a sign the verifier learns that the number he received is a QR modulo n. Whether a number is a QR is a hard problem as he does not know the factors of n.


2

In context of interactive proof systems (including zero-knowledge proofs) completeness means the same as the term correctness as used for many other (interactive) cryptographic schemes or protocols. I guess that's mainly due to historical reasons (there are even some people that use correctness instead of completeness in context of zero-knowledge proofs). ...


1

A straightforward way to prove this when you can prove AND as well as OR statements about discrete logarithms is to take all the $K=\binom{M}{N}$ subsets $A_i=\{A_{i_1},\ldots,A_{i_N}\}$ with $N$ elements of points from the set of your $M$ points and prove the statement $$PK\{(\alpha_1,\ldots,\alpha_N): \bigvee_{j\in K} \big( \bigwedge_{A_{j_i}\in A_j} ...


1

You may be aware of the fact that zero-knowledge proofs for any language in $NP$ can be constructed if you have a zero-knowlege proof for any $NP$-complete language. Then you can reduce your original language to the $NP$-complete one in polynomial time and you are done (more precisely you reduce the instance and the corresponding witness). As the ...



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