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"Elliptic curve encryption" is somewhat popular wording; one better be specific like ElGamal encryption with a group of points on elliptic curve. So, start with ElGamal to understand what kind of group is expected. Try ElGamal with multiplicative group modulo a (large) prime. At last, consider objects named points on a curve as an unusual set with highly ...

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In RSA, $\phi(N)$ is hidden and this is why nobody could calculate private key. For a prime modulus, order of multiplicative group is not a secret. Well, this question looks like encouraging your own thinking of RSA and related arithmetic, so please keep digging in.

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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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