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ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudorandom generators, and other tasks. they can be used for encryption by combining the key agreement with an asymmetric encryption scheme.

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Finding if two points on elliptic curve are related

No you can't. I'll make the argument over the integers, it directly transfers to ECC points. Suppose you have two integers $c,e\in\mathbb Z$. You can now prove for every $a\in\mathbb Z$ that $c$ and …
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How to calculate elliptic curve parameters?

It is possible to find the desired values in an acceptable amount of time. TL;DR: Find the curve order, factor it, select a (random) point until you have one with the desired order and calculate the c …
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