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.

Note: This is an example to show how to ask a question for this broad question — kelalaka, Oct 08 '20 at 15:12

score 16 · Accepted Answer · edited Oct 09 '20 at 06:55

16

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.

edited Oct 09 '20 at 06:55

Community

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answered Oct 08 '20 at 15:31

kelalaka

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Thanks to Squeamish Ossifrage for directing the link. – kelalaka Oct 08 '20 at 15:40
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I thought before reading this answer, that X stood for the X as in DH Key eXchange, since X25519 is the cryptosystem developed using that particular curve Curve25519 !!! – Aravind A Oct 08 '20 at 19:01
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@VivekanandV Schrödinger's cat. Until the author's intent is not known all are valid :). X X-coordinate, Ed Edwards-coordinate. consistent. But revealed. The cat is living :) – kelalaka Oct 08 '20 at 19:32
@kelalaka thanks for the answer, it is the kind of insight I was looking for in in the broad question you linked in your comment. – ams Oct 09 '20 at 13:45
@ams hope you got my point. A good question has your (single or very related) problem(s), what you see here and there (wiki, or the www) then your understanding/confusion,... correct tags and a good title ( not broad one, too), then post and wait. – kelalaka Oct 09 '20 at 17:08

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

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