done 6.1
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Andre Henriques 2023-11-07 17:26:25 +00:00
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@ -135,13 +135,13 @@
This q pairs work because when the oracle selects b=0:
There will be no colisions:
$$\forall i,k : i \ne j \and P_{0i} \neq p E_{0i} \implies E_{0i} \neq E_{0j}$$
$$\forall i,k \nexists i,k : i \ne j \and P_{0i} \ne p E_{0i} \implies E_{0i} \ne E_{0j}$$
there if you don't find any colissions you can assume that the the oracle selected b=0
if the oracle selects b=1:
If q is big enough, there will be colissions:
$$\exists i,k : i \ne j \and P_{1i} \eq P_{1j} \and R_i = R_j \implies E_{1i} = E_{1j}$$
$$\exists i,k : i \ne j \and P_{1i} \eq P_{1j} \and R_i = R_j \implies E_{1i} \eq E_{1j}$$
where $R$ is the list of random values generated for each pair
\subsection*{4.3}