Witness hiding is a property attributed to an interactive proof or an interactive argument, similar in nature to the zero-knowledge property. If an interactive proof is zero-knowledge, it is also witness hiding, but the converse does not necessarily hold. For many applications, witness hiding protocols are sufficiently secure and more efficient than zero-knowledge protocols.
Loosely speaking, an interactive proof is witness hiding if an arbitrarily cheating verifier, after engaging in many executions of the protocol with an honest prover, is not able to compute a witness unless the verifier is able to compute one anyway, without interacting with the prover at all. In this context, a witness may be thought of as a private key, corresponding to a public key. If an interactive proof is witness hiding, it is not excluded that a cheating verifier learns some fraction of the bits of a witness. However, knowledge of such a fraction of the bits cannot be feasibly extended to knowing all of the...
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References
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Schoenmakers, B. (2005). Witness Hiding. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_461
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