A New Side Channel Resistant Scalar Point Multiplication Method for Binary Elliptic Curves

In this paper, a new novel LSB scalar point multiplication algorithm resistant to several side channel attacks is presented. This method is based on a similar invariant principle to Montgomery's Ladder but it can use pre-computation to halve the total runtime and achieve a speedup of l(A + D
¹
)/(lA + D
²
). Using D
²
≈ 1.5D
¹
and D
¹
≈ A, then the proposed method achieves 2lA/((l + 1.5)A) or a speedup of 2 as l, the number of scalar point multiplications on an identical base point, approaches infinity. This performance was achieved by applying the reduced complexity Montgomery Invariant point addition equation along with y-coordinate recovery to generate the point Q equal to kP. Finally, the LSB Invariant method is adapted to projective coordinates to achieve a further performance increase when the penalty for performing a field inversion operation is greater than 4 multiplications.