What the X stands for in the front of Elliptic curve names like X25519

Question

I have seen Curve25519 and X25519, Curve448 and X448. I've seen a small note in this answer

(Historical note: Originally, X25519 was called Curve25519, but now Curve25519 just means the elliptic curve and X25519 means the cryptosystem.)

• Is it a standard to say CurveABC is the Elliptic Curve and XABC is the cryptosystem?
• Or, it is just a convention between the Elliptic Curve Cryptographers.

Answer 1

It is an open standard by IETF.org

We can find the details in the mail archive of IETF, D. J. Bernstein's response;

It has become increasingly common for "Curve25519" to refer to an elliptic curve, while the original paper defined "Curve25519" as an X-coordinate DH system using that curve. "Ed25519" unambiguously refers to an Edwards-coordinate signature system using that curve.

Kenny and others in Toronto recommended changing terminology to clearly separate these three items. Let me suggest the following terminology:

• "X25519" is the recommended Montgomery-X-coordinate DH function.
• "Ed25519" is the recommended Edwards-coordinate signature system.
• "Curve25519" is the underlying elliptic curve.

All relevant coordinate systems already have standard names in the literature, and I would suggest sticking to those names whenever it's necessary to discuss the coordinate systems per se: [...]

Bolds are mine.