The Elliptic-Curve Diffie-Hellman (ECDH) is an important Memorandum of Understanding that allows two parties, each with a pair of public-private keys with an elliptical curve, to create a common secret on an uncertain channel.    This common secret key can be directly used as a key or derive another key. The key or derived key can then be used to encrypt subsequent communication with a chiphiffre key. It is a variant of the Diffie-Hellman protocol with elliptical cryptography. Ed25519 has the advantage of being able to use the same key to sign a key agreement (normally you wouldn`t). I`m not familiar enough with mathematics to say if it`s a feature of the fact that it`s an Edwards curve, although I know it`s converted to a Montgomery coordinate system (effective in Curve25519) for the key chord… Ed25519 is more than a curve, there is also, among other things, the deterministic key generator (z.B. hashing), which is worth keeping an eye on. This is a frustrating thing about DJB implementations, as happens, as they need to be treated differently to maintain interoperability. ECDH is a variant of the Diffie-Hellman algorithm for elliptical curves. It is actually a key memorandum of understanding, more than an encryption algorithm. This essentially means that the ECDH defines (to some extent) how keys should be generated and exchanged between the parties.
How we encrypt data with such keys depends on us. However, note that the contexts of use are quite different. Cryptography is little more than calculating elliptical curves; the “key life cycle” must be taken into account. Simply put, you don`t want to handle turnkeys and signature keys with the same procedures. For example, if you lose your key agreement key (your dog eats your smart card — don`t laugh, it really happens), then you can no longer decipher the data that has been encrypted in relation to that key (z.B. encrypted emails sent to you, and stored in an encrypted format). From a business perspective, the loss of a key can also be the loss of an employee (the employee was fired and was run over by a bus or retired, or whatever). As a result, encryption keys (including agreement keys) often need to be crushed (for example. B, a copy of the private key is printed and stored in a safe). On the other hand, the loss of a signature key does not mean a loss of data; Previously issued signatures can still be verified; Recovering such a loss is as easy as creating a new pair of keys. However, the existence of a fiduciary system tends to automatically remove signatures from any legal value that might be attributed to them.
Elliptical curves apply to key chords, digital signatures, random pseudo-generators and other tasks.