Elliptic-curve cryptography (ECC) is the most important tool in modern public-key cryptography. Implementations of prime-order curve group are usually incomplete or have a variable-time addition formulas. Usually implementers use Elliptic-curve groups with composite order such as Edwards curves, twisted Edwards curves, Jacobi quartics and Montgomery curves. The order of this curves is h·q for some large prime q and small positive integer h. The cofactor h for Edwards curves, twisted Edwards curves, Jacobi quartics and Montgomery curves is divisible by 4.
