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This is a reduction showing that if you can compute $g^{a^2}$ given $g^a$, then you can solve the computational Diffie Hellman problem. Here is the reduction. Let $A$ be an adversary that given $g^a$ for a random $a$, outputs $g^{a^2}$ with probability $\epsilon$. We construct $A'$ who receives $u=g^a$ and $v=g^b$ and works as follows. $A'$ runs $A$ three ...

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