What is elliptic-curve cryptography?
- Author
- CRYPTO PORT Editorial
- Published
- Updated
- Reading time
- 5 min
In short
Elliptic-curve cryptography builds public-key cryptography out of point addition on a curve. It reaches the strength of RSA with far shorter keys, which is why blockchains — where every byte is stored forever — adopted it. Despite the name, it has nothing to do with ellipses.
Key points
- 256 bits is considered comparable to 3072-bit RSA
- The private key is an integer, the public key a curve point
- Bitcoin-family chains use the secp256k1 curve
- A practical quantum computer would undermine it
Definition
Public-key cryptography based on arithmetic over points of an elliptic curve defined on a finite field, secured by the hardness of finding how many times a point was added to itself.
Adding two points on the curve by a fixed rule yields another point on the curve. Add the generator G to itself k times and you get P: computing P from k is fast, but recovering k from P has no known shortcut beyond brute force. That k is the private key and P the public key.
For equal strength, elliptic-curve keys are roughly a tenth the length of RSA keys. That is why Bitcoin and Ethereum addresses fit in a few dozen characters — data every node stores forever. The same maths secures TLS connections and the chips in modern passports.
Each network fixes its curve. Bitcoin and Ethereum use secp256k1, while many web standards and Solana's Ed25519 signatures use different ones. Different curve, different address from the same secret, so keys are not portable across chains just because the numbers look alike.
Watch out for
- · Avoid implementations that invent their own curve parameters; non-standard curves get far less scrutiny
- · Post-quantum signature research is active, but no major chain has migrated as of now
- · The same secret does not necessarily produce the same address on another chain