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| '''Soundness''' is a property of [[interactive proof system]]s that requires that no prover can make the verifier accept for a wrong statement <math>y \not\in L</math> except with some small probability. The upper bound of this probability is referred to as the soundness error of a proof system.
| | My name is Peggy and I am studying Occupational Therapy and Philosophy at Lodz / Poland.<br><br>Look at my website; [http://sunquestlivingmd.com football] |
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| More formally, for every prover <math>(\tilde{\mathcal{P}})</math>, and every <math>y \not\in L</math>:
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| : <math>\Pr[(\perp,(\text{accept}))\gets (\tilde{\mathcal{P}})(y) \leftrightarrow (\mathcal{V})(y)] < 2^{-80}.</math>
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| The above definition uses the somewhat arbitrary soundness error 2<sup>−80</sup>.
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| As long as the soundness error is bounded by a polynomial fraction of the potential running time of the verifier (i.e. <math>\leq1/\mathrm{poly}(|y|)</math>), 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 <math>\ell</math> repetitions, a soundness error <math>\epsilon</math> will be reduced to <math>\epsilon^\ell</math>.<ref>{{citation|first=Oded|last=Goldreich|authorlink=Oded Goldreich|title=Zero-Knowledge twenty years after its invention|year=2002|id={{ECCC|2002|02|063}}}}.</ref>
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| ==See also==
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| * [[Interactive proof system]]
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| * [[Proof of knowledge]]
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| * [[Zero-knowledge proof]]
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| ==References==
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| <references/>
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| [[Category:Proof theory]]
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| {{Crypto-stub}}
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Latest revision as of 03:40, 7 December 2014
My name is Peggy and I am studying Occupational Therapy and Philosophy at Lodz / Poland.
Look at my website; football