Cut-and-Choose Protocols
A cut-and-choose protocol is a two-party protocol in which one party tries to convince another party that some data he sent to the former was honestly constructed according to an agreed upon method. Important examples of cut-and-choose protocols are interactive proofs [4], interactive arguments [1], zero-knowledge protocols [1, 3, 4] and witness indistinguishable and witness hiding protocols [2] for proving knowledge of a piece of information that is computationally hard to find. Such a protocol usually carries a small probability that it is successful despite the fact that the desired property is not satisfied.
The very first instance of such a cut-and-choose protocol is found in the protocol of Rabin [5] where the cut-and-choose concept is used to convince a party that the other party sent him an integer n that is a product of two primes p, q, each of which is congruent to 1 modulo 4. Note that this protocol was NOT zero-knowledge.
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References
Brassard, G., D. Chaum, and C. Crépeau (1988). “Minimum disclosure proofs of knowledge.” JCSS, 37, 156–189.
Feige, U. and A. Shamir (1990). “Witness indistinguishable and witness hiding protocols.” Proceedings of the 22nd Annual ACM Symposium on the Theory of Computing, Baltimore, MD, May 1990, ed. Baruch Awerbuch. ACM Press, New York, 416–426.
Goldreich, Oded, Silvio Micali, and Avi Wigderson (1991). “Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems.” Journal of the Association for Computing Machinery, 38 (3), 691–729.
Goldwasser, Shafi, Silvio Micali, and Charles Rackoff (1989). “The knowledge complexity of interactive proof systems.” SIAM Journal on Computing, 18 (1), 186–208.
Rabin, M.O. (1977). “Digitalized signatures.” Foundations of Secure Computation. Papers presented at a 3 day workshop held at Georgia Institute of Technology, Atlanta, October 1977, eds. Richard A. DeMillo et al. Academic Press, New York, 155–166.
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Crépeau, C. (2005). Cut-and-choose protocol. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_92
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