In point multiplication a point P on the elliptic curve is multiplied with a scalar k using elliptic curve equation to

obtain another point Q on the same elliptic curve i.e. KP=Q.

Point multiplication is achieved by two basic Elliptic curve operations

• Point addition, adding two points J and K to obtain another point L i.e., L = J + K.

• Point doubling, adding a point J to itself to obtain another point L i.e. L = 2J.

Eg : k = 23 then kP = 23.P = 2(2(2(2P) + P) + P) + P.

Input: Binary representation of k and point P

k = (kn-1….k1k0)2

Output: kP

Return R

point Validation

The validation of the elliptic curve domain parameters can be simplified into two categories; validating an Elliptic Curve, and validating a Base Point.