1. A method in an elliptic curve cryptographic system comprising: pre-computing, for encryption, a multiplication routine according to an input operand length using one iteration graph-based multiplication; computing, by a computing device, a first carry-less product of two input operands according to the pre-computed multiplication routine; and computing, by the computing device, a second carry-less product between the first carry-less product and a sparse polynomial by performing a number of SHIFT and Exclusive-OR operations, where the sparse polynomial comprises a plurality of coefficients and the number of coefficients of the plurality equal to one is smaller than the number of coefficients of the plurality equal to 0, and the number of SHIFT and Exclusive-OR operations is in the order of the number of coefficients of the plurality equal to I in a polynomial defining an elliptic curve binary field.