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# Is there an extension of the definition of zero knowledge proof to different information quantities?

a zero-knowledge proof is a method by which a prover proves to a verifier that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true

Is there a definition of proof in which the prover conveys no more than X information (where X can be 2 bits for example)? If yes, is it a field of research?

Hi! Can you not can just send the \$x\$ bits of information along the proof, and additionally prove that those bits are indeed part of the witness?
Hi Ruben, I didn't understand your comment. My question is whether we can define x-bit knowledge proof, which means proof in which no more than x bits of information are conveyed to the verifier.
I wonder if Knowledge Tightness (Oded Goldreich, Foundation of Cryptography, section 4.4.4.2) matters in someway...
Isn't this the point of [secure two-party computation](https://en.wikipedia.org/wiki/Secure_multi-party_computation)? The way it is defined can be thought of as extending the formulation of (honest-verifier) zero-knowledge by providing the simulator with the output (see Goldreich's chapter).
@baro77 and ckamath Thanks! I'm pretty new to this topic so I'll read more in order to understand your comments :)
I sit in a Tesla and translated this thread with Ai:

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