Abstract
This paper presents a power analysis that applies to elliptic curves over generalized Mersenne prime field $\mathbb{F}_p$. This prime field enables efficient modular reductions which influence the computational performance of an elliptic curve cryptosystem. The general modular reductions stochastically calculate extra operations. Some studies showed the possibility of power analysis attacks to scalar multiplication with a unified code by using the statistical information of extra operations. In this paper, we present the statistical experiment and possibility of attacks, and propose the more sensitive attack and the countermeasure without performance impact.
