Curve25519
A Montgomery-form elliptic curve designed for fast, robust key agreement at roughly the 128-bit security level; X25519 is the Diffie-Hellman function defined over it.
Curve25519 and X25519 are often used as if they were the same name, but they refer to different layers. Curve25519 is the underlying curve; X25519 is the scalar-multiplication key-agreement function defined by RFC 7748.
Implementation Note
The safe approach is not to reimplement the curve formulas. Scalar handling, input decoding, all-zero shared-secret checks, and protocol details should follow a vetted library and the RFC contract. Key agreement also does not authenticate the peer; authentication belongs to the surrounding protocol.
X25519's engineering value is not only speed. Its deliberately narrow interface removes several parameter choices that historically created implementation mistakes.
Source
- https://datatracker.ietf.org/doc/html/rfc7748