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Definition
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.
Theory
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...
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Recommended Reading
Cramer R, Damgård I, Schoenmakers B (1994) Proofs of partial knowledge and simplified design of witness hiding protocols. In: DeSnedt YG (ed) Advances in cryptology – crypto’94. Lecture notes in computer science, vol 839. Springer, Berlin, pp 174–187
Feigel U, Shamir A (1990) Witness indistinguishable and witness hiding protocols.” In: Silverman JH (ed) Proceedings of 22nd symposium on theory of computing (STOC’90). ACM Press, New York, pp 416–426
Goldreich O (2001) Foundations of cryptography – basic tools. Cambridge University Press, Cambridge
Okamoto T (1993) Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell EF (ed) Advances in cryptology – crypto’92. Lecture notes in computer science, vol 740. Springer, Berlin, pp 31–53
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Schoenmakers, B. (2011). Witness Hiding. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_15
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