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This q pairs work because when the oracle selects b=0:
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This q pairs work because when the oracle selects b=0:
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There will be no colisions:
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There will be no colisions:
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$$\forall i,k : i \ne j \and P_0[i] \neq p E_0[i] \implies E_0[i] \neq E_0[j]$$
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$$\forall i,k : i \ne j \and P_0\[i\] \neq p E_0\[i\] \implies E_0\[i\] \neq E_0\[j\]$$
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there if you don't find any colissions you can assume that the the oracle selected b=0
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there if you don't find any colissions you can assume that the the oracle selected b=0
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if the oracle selects b=1:
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if the oracle selects b=1:
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If q is big enough, there will be colissions:
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If q is big enough, there will be colissions:
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$$\exists i,k : i \ne j \and P\[i\] \eq P\[j\] \and R\[i\] = R\[j\] \implies E_1\[i\] = E_1\[j\]$$
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$$\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\[j\]$$
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where $R$ is the list of random values generated for each pair
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where $R$ is the list of random values generated for each pair
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\subsection*{4.3}
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\subsection*{4.3}
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