How do special curves make ECC run faster?
The initials ECC stand for “elliptic curve cryptosystem.” An elliptic curve is a complicated mathematical object consisting of points that can be “added” to one another. An elliptic curve cryptosystem is formed from a field F, an elliptic curve E and a point P on the elliptic curve. Encryption and decryption require repeated addition of P to itself P+P+…+P. (This is analogous in some ways to RSA encryption, which requires repeated multiplications g*g*…*g. However, RSA multiplications are much simpler than elliptic curve “additions”.) There are certain special types of fields F and elliptic curves E for which the addition operation can be performed especially efficiently. Some of these special types have been found to be insecure (e.g. “supersingular” elliptic curves, Galois fields with many subfields), but there are other special types that appear to be secure and that offer some speed advantages. Using ECC thus requires choosing one of the following two options: Fix one elliptic c
