Serious Cryptography

12ELLIPTIC CURVES

The introduction of elliptic curve cryptography (ECC) in 1985 revolutionized the way we do public-key cryptography. ECC is more powerful and efficient than alternatives like RSA and classical Diffie–Hellman (ECC with a 256-bit key is stronger than RSA with a 4096-bit key), but it’s also more complex.

Like RSA, ECC multiplies large numbers, but unlike RSA it does so in order to combine points on a mathematical curve, called an elliptic curve (which has nothing to do with an ellipse, by the way). To complicate matters, there are many different types of elliptic curves—simple and sophisticated ones, efficient and inefficient ones, ...