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

in flag

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?

us flag
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?
Amit Keinan avatar
in flag
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.
baro77 avatar
gd flag
I wonder if Knowledge Tightness (Oded Goldreich, Foundation of Cryptography, section matters in someway...
ckamath avatar
ag flag
Isn't this the point of [secure two-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).
Amit Keinan avatar
in flag
@baro77 and ckamath Thanks! I'm pretty new to this topic so I'll read more in order to understand your comments :)

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