§ 01
Definition
Curve25519 was published in 2006 and standardised for key agreement in RFC 7748. It was designed to be fast and to avoid common implementation mistakes, such as timing leaks, that affected older curves.
§ 02
How it works
Each side picks a random 32-byte private key and computes a public key. Exchanging public keys lets both sides compute the same shared secret, an elliptic-curve Diffie-Hellman exchange. WireGuard uses X25519 for both its long-term keys and its per-session ephemeral keys.
§ 03
Why it matters
X25519 is now the default key exchange in most modern encrypted connections. It is not resistant to large quantum computers, which is why providers are adding hybrid post-quantum key exchange such as ML-KEM alongside it.