Can we encrypt data using Elliptic Curves?

From time to time, I hear people saying that Elliptic Curve Cryptography (ECC) cannot be used to directly encrypt data, and you can only do key agreement and digital signatures with it. This is a common misconception, but it’s not actually true: you can indeed use elliptic curve keys to encrypt arbitrary data. And I’m not talking about hybrid-encryption schemes (like ECIES or HPKE): I’m talking about pure elliptic curve encryption, and I’m going to show an example of it in this article. It’s true however that pure elliptic curve encryption is not widely used or standardized because, as I will explain at the end of the article, key agreement is more convenient for most applications.