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The master key has to be stronger in the sense that it's more sensitive than session keys. The information used to derive session keys are not necessarily secret, so if it's easy to recover the master key, an attacker will be able to compute all the derived keys. On the other hand, recover a single session key will not help you to recover the master key ...


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how does $A$ know $g^y$ to include in the formula above? Actually, what they mean here is, in fact, $g^y \bmod p$; that is, the value that $A$ received. It wouldn't work to insert the literal values $g^x$ and $g^y$; apart from the fact that $A$ doesn't know the second one, there's also the practical difficulty that since $x$ and $y$ are (perhaps) 256 ...



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