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One could split both secrets into smaller parts, commit to parts and "gradually" open that commitments to each other, so that no party is better than (ahead of the other) one such part. For example, let secret be a big number split into bits. With an additively homomorphic bit commitment scheme, the other party could verify that bit commitments correspond ...

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The worker does not know $s, t(s), v_k(s), w_k(s), y_k(s)$, the workers knows only the content of the public evaluation key and the public verification key. That's to say, the worker knows only $g^s, g^{t(s)}, g^{v_k(s)}$ etc.

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My guess is, responses $\hat x_{(g,i)}..\hat x_{(1,i)}$ ($s$ in the example) are computed modulo group order that is not available to verifiers of the statement claimed. Challenge difference is always one ($1$) while rewinding for binary ($0$/$1$) challenges, and it is not expected to be one for "large" challenges. Dividing by a non-one (in other words, ...

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That can be done if and only if oblivious transfer can be done. (In that case, one could do it with a protocol that securely solves the Socialist Millionaire Problem, rather than the protocol given on wikipedia.) It would be difficult to remove the "this can be detected by the other party" allowance, since the restriction of the desired functionality to ...

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SRP does DH key exchange with authentication, and has the capability to also authenticate the server as well (though usually the server is authenticated by keeping the verifier secret). If the key is generated strictly from a password and salt, with the salt stored on the server, you can do a dictionary attack on the verifier (e.g. if the server is ...

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Having a client (ex. your web browser) use zero-knowledge proofs to authenticate itself to a server only makes sense if the server knows about the client's public key in advance, and if the client keeps the same private key forever. So you could have the client-side generate a keypair when you register your account, and the server records your public key ...

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Rough scetch, assuming Bob is standing next to you in the same room: Prepare cards with the correct numbers on them Lay down the cards according to the setup, face up Lay down the remaining cards with the correct solution, face down, so that Bob can't see them. Now you let Bob choose one column, row or sector. You pick up the cards in that row, column ...

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