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Can an attacker learn some bits of a using this information? No. In the case of multiplication modulo a prime, we have, for any possible value of $a$, there is a unique value of $b$ that makes $a \cdot b \bmod p$ give any particular value of $c$ in the range $(1, p-1)$. That is, even if we knew all the bits of $c$, no particular value of $a$ are any ...

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