Patent ID: 8542820

Claim:
An apparatus for calculating a result of a scalar multiplication of a reference number with a reference point on an elliptic curve, comprising: a point selector configured to select randomly or pseudo-randomly an auxiliary point on the elliptic curve, wherein the reference point and the auxiliary point are different points on the elliptic curve, wherein the point selector is configured to select the auxiliary point independent from the reference point or wherein the auxiliary point is selected based on a mixing function applied to the reference point; and a processor configured to calculate the result of the scalar multiplication with a double-and-always-add process using the auxiliary point, wherein the processor is configured to calculate the result of the scalar multiplication based on a loop, which, per execution, operates on an intermediate point, and configured to set the intermediate point equal to the auxiliary point prior to a first execution of the loop, wherein the loop is executed N-times, wherein N is a number of bits comprised by the reference number in a binary representation, wherein the processor is configured to calculate the result of a subtraction of the auxiliary point from the intermediate point, wherein the subtraction is a part of the loop.