Definition
Elliptic Curve Cryptography is a public-key cryptography approach based on the algebraic structure of elliptic curves over finite fields. Proposed independently by Neal Koblitz and Victor Miller in 1985, ECC has gradually become the dominant approach for new asymmetric cryptographic deployments because it provides the same security as RSA at far smaller key sizes — a 256-bit ECC key is roughly equivalent in strength to a 3072-bit RSA key.
Why It Matters for VPNs
Smaller keys mean faster handshakes, smaller certificates, and lower bandwidth overhead — which matters especially on mobile devices where the VPN must reconnect frequently as the network changes. Modern VPN protocols rely heavily on ECC: WireGuard uses Curve25519 for key exchange and Ed25519 for signatures, IKEv2 commonly uses NIST P-256 or P-384, and TLS 1.3 strongly prefers ECDHE for key exchange.
Curves to Know
The most common curves in production are NIST P-256, P-384, and P-521 (used by U.S. government systems and most commercial TLS), and Curve25519 / Ed25519 (designed by Daniel J. Bernstein, used in WireGuard, Signal, and modern SSH). Curve25519 was designed specifically to be fast, side-channel-resistant, and free of suspect parameters, and has become the preferred choice for new protocols.