Soundness (interactive proof)

Soundness is a property of interactive proof systems that requires that no prover can make the verifier accept for a wrong statement except with some small probability. The upper bound of this probability is referred to as the soundness error of a proof system.

More formally, for every prover , and every :

The above definition uses the somewhat arbitrary soundness error 280. As long as the soundness error is bounded by a polynomial fraction of the potential running time of the verifier (i.e. ), it is always possible to amplify soundness until the soundness error becomes negligible relative to the running time of the verifier. This is achieved by repeating the proof and accepting only if all proofs verify. After repetitions, a soundness error will be reduced to .[1]

See also

References

  1. Goldreich, Oded (2002), Zero-Knowledge twenty years after its invention, ECCC TR02-063.


This article is issued from Wikipedia - version of the 1/1/2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.