What Is Elliptic Curve Cryptography (ECC)?

In ECC, the private key is a very large random number. The public key is obtained by multiplying a fixed starting point on the curve (the generator point) by this number. This operation can be computed easily, but reversing it, that is, finding the private key from the public key, is practically impossible with today's computers because of the elliptic curve discrete logarithm problem.

ECC's main advantage is that it provides a similar level of security with much shorter keys than older methods such as RSA; a 256-bit ECC key offers security equivalent to roughly a 3072-bit RSA key. This means smaller signatures and less storage. Bitcoin and Ethereum use the secp256k1 curve; networks such as Solana and Cardano rely on Ed25519 signatures, while Ethereum's Proof of Stake layer relies on BLS signatures on the BLS12-381 curve.

ECC's security depends on correct implementation: weak random number generation or faulty libraries can lead to keys being leaked. In addition, because sufficiently powerful quantum computers are expected to be able to break ECC with Shor's algorithm, options for moving to quantum-resistant cryptography are being researched.