done 6.1
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Andre Henriques 2023-11-07 17:24:20 +00:00
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This q pairs work because when the oracle selects b=0:
There will be no colisions:
$$\forall i,k : i \ne j \and P_0\[i\] \neq p E_0\[i\] \implies E_0\[i\] \neq E_0\[j\]$$
$$\forall i,k : i \ne j \and P_{0i} \neq p E_{0i} \implies E_{0i} \neq 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_1\[i\] \eq P_1\[j\] \and R\[i\] = R\[j\] \implies E_1\[i\] = E_1\[j\]$$
$$\exists i,k : i \ne j \and P_{1i} \eq P_{1j} \and R_i = R_j \implies E_{1i} = E_{1j}$$
where $R$ is the list of random values generated for each pair
\subsection*{4.3}