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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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$$\nexists i,k : i \ne j \land P_{0i} \ne p E_{0i} \implies E_{0i} \ne E_{0j}$$
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$$\exists i,k : i \ne j \land P_{0i} \ne p E_{0i} \implies E_{0i} \ne E_{0j}$$
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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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