How exactly is a specific message sent in ECC

Question

I tried to think about it and came up with no answer. I read how the Elliptic curve cryptography works, I understand that Bob and Alice have their own key which they multiply the generator of the elliptic curve points (which is a group), and then do it again after they switch the messages and get finally the same point on the elliptic curve. What is hard for me to understand is how the final point helps Bob to secure a real message (for example if Bob want to send the number 2 to Alice, How can he do that?). for me it is not trivial.

Answer 1

What you had described is the Elliptic Curve version of the Diffie-Hellman Key Exchange. So you exchanged the keys, now what?

While there are some works on how to encrypt messages with Elliptic Curves the more standard approach is Elliptic Curve Integrated Encryption Scheme (ECIES).

Basically, it is a hybrid cryptosystem. With ECDH ( Elliptic Curve Diffie-Hellman) you exchange the keys, then use a Key Derivation Function (KDF) to derive a key for the symmetric cipher like AES, or ChaCha. Now, you can encrypt messages with modern encryption modes like, AES-GCM or ChaCha20-Poly1305 (Authenticated Encryption modes that provide you confidentiality integrity and mutual authentication.

You can see the details on Wikipedia page.

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Note: If one really wants to encrypt with Elliptic Curves, they can use ElGamal encryption ( generalized ElGamal), however, point embedding in ECC is not perfect.