CyberGlossary

Cryptography

Elliptic Curve Cryptography (ECC)

Also known as: ECC

Definition

A family of public-key algorithms based on the algebraic structure of elliptic curves over finite fields, offering equivalent security to RSA with much smaller keys.

Elliptic Curve Cryptography (ECC) builds public-key primitives — key exchange (ECDH), digital signatures (ECDSA, EdDSA), and encryption (ECIES) — on the group of points of an elliptic curve over a finite field. Its security relies on the elliptic-curve discrete logarithm problem (ECDLP), which is currently exponentially hard. Because ECDLP is harder than the integer-factorization problem for keys of comparable size, ECC delivers strong security with much shorter keys: a 256-bit ECC key (e.g., curve P-256 or Curve25519) provides roughly the same security as RSA-3072. ECC is therefore preferred for TLS 1.3, SSH, modern mobile and IoT devices, and most blockchain systems. Like RSA, ECC is vulnerable to large-scale quantum computers, motivating migration to post-quantum schemes.

Examples

  • Curve25519 powers WireGuard, Signal, and modern SSH key exchanges.
  • Bitcoin and Ethereum use the secp256k1 curve for ECDSA signatures.

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