Inherent Resistance of Efficient ECC Designs against SCA Attacks

The Montgomery kP algorithm using Lopez-Dahab projective coordinates is a time and energy efficient way to perform the elliptic curve point multiplication. It even can provide resistance against simple power analysis attacks. Nevertheless, straight forward implementations of this algorithm are not resistant against differential power analysis attacks. But highly-efficient designs i.e. designs in which different functional units are operating in parallel can increase the resistance of ECC implementations against DPA. In this paper we demonstrate this fact on the examples of our 6 implementations of the Montgomery kP algorithm. We perform horizontal DPA attacks to demonstrate the fact that the resistance of the kP algorithm against side channel analysis attacks can be increased through its implementation as an efficient design.