Theorem. Audit-before-commit bounds contaminated commits [ftip-00D4]
Theorem. Audit-before-commit bounds contaminated commits [ftip-00D4]
Use the audit of Definition [ftip-00D3] and commit a proposal only when its audit returns \(\mathsf {pass}\). If \(\Pr (Z_n=1)>0\) and its conditional false-negative rate is at most \(\bar \eta \in [0,1]\), then
\[ \Pr (d_n=\mathsf {accept}\mid Z_n=1)\leq \bar \eta . \]Proof. Under audit-before-commit, the event \(\{d_n=\mathsf {accept}\}\) is contained in the event that the audit passes. Conditioning on \(Z_n=1\) and applying the false-negative bound proves the inequality.
This statement bounds one declared admission channel. It gives no bound when proposals bypass the audit, when the contract omits the exploit, or when the audit's conditional error changes under adaptive search.