One feature pertains to elliptic curve (EC) point multiplication for use in generating digital signatures. In one aspect, a scalar multiplier (k) of a base point (P) of order (n) is selected on an elliptic curve for use with EC point multiplication. An integer value (r) is then randomly generated from within a range of values constrained so that, regardless of the particular value of (r) obtained within the range, EC point multiplication procedures performed using the scalar multiplier (k) summed with a product of the integer multiplier (r) and the order (n) consume device resources independent of the value of the scalar multiplier (k) to thereby reduce or eliminate side-channel leakage. This may be achieved by determining the range of values for r so that the bit position of the most significant bit of k+(r*n) will be even and fixed for a particular elliptic curve.