1. A method in an elliptic curve cryptographic system comprising: computing a plurality of coefficients of a polynomial representing a carry-less product of two input operands according to a graph-based single iteration multiplication routine that is computed according to an input operand length to reduce an amount of multiplications required to compute the carry-less product of the two input operands; reducing the carry-less product modulo a programmable polynomial that defines the elliptic curve cryptographic system by performing division using two multiplications.