A General Framework of Side-Channel Atomicity for Elliptic Curve Scalar Multiplication

Simple power attack (SPA) is a type of side-channel attack (SCA). In the literature, many SPA-resistant scalar multiplication algorithms have been proposed, but most are inefficient and not interoperable with other coding methods. To prevent SPA, Chevallier-Mames et al. proposed a technique called side-channel atomicity for pure binary number systems. Using their method, extra costs for preventing SPA can be limited. Even though many researchers have extended this technique to other number systems, their algorithms are for specific cases and few provide implementation results. In this paper, we generalize the atomicity technique to protect nearly all existing fast coding methods/number systems. Our general framework provides security and flexibility while its efficiency is coupled to that of the coding methods. Moreover, we utilize our framework to protect the known fastest scalar multiplications by exploring application on the GLV method for GLS curves. Proof of concept programs are written in the C language along with assembly for fast field operations and run on AMD Athlon X2 245-based hardware.