Im havirng a had time understanding ECC. For example, I have the equation below:

Equation : y^2 = x^3 - 4x + 1
Initial Points : 

    A = (2, 1)

    B = (-2, -1)

N or number of iteration : 10

Final Point or Location : ?

I know that ECC has got to do something with private keys and public keys. But I know Im missing something important. My question is how to actually encrypt a message using ECC. For example, the sentence : "Shalom !".

What is the actual encrypted text, and how to get the private key and public key from it? Please help.


Elliptic curve cryptography usually implies Elliptic Curve Diffie-Hellman (and/or digital signatures).

Diffie-Hellman is a key agreement algorithm, rather than a public-key encryption algorithm. You can not use it to "directly" encrypt your message.

Diffie-Hellman allows two parties to arrive at a mutual shared secret. Once you have a shared secret, encryption is (relatively) easy: Derive an encryption key for a symmetric (authenticated) cipher using the shared secret, and then use that key for encryption.

Using public-key cryptography to share a secret, then using that for symmetric cryptography is frequently referred to as "hybrid encryption".


You could cobble together an RSA-like construction using elliptic curves. But there is no advantage to doing so.

Indeed, in many if not most situations, you don't really want "public-key encryption".

Even if you have public-key encryption (meaning you can a priori select a message rather than generating a shared secret), it's usually a better idea to use it to encapsulate a key and use that for symmetric encryption than it is to use the public-key encryption algorithm to send your message.

| improve this answer | |
  • $\begingroup$ Thanks, but do you know how to use and what is the shortcut function use to arrive at a final location when the private key is already known and the two initial points? $\endgroup$ – alyssaeliyah Feb 4 '19 at 8:13
  • $\begingroup$ What is the final location and why there are two points? $\endgroup$ – kelalaka Feb 4 '19 at 13:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.