Proposal of a lightweight differential power analysis countermeasure method on elliptic curves for low-cost devices

Elliptical curves are dedicated for several security applications including Radio Frequency Identification (RFID) devices, smart cards, bankcards, etc. To guarantee effective security of such applications, these cryptographic systems require effective resistance to various types of physical attack. Differential Power-Analysis (DPA) attacks were considered the most efficient attacks against scalar multiplication calculation algorithms. In this paper, we propose a countermeasure method against the DPA attacks, for a scalar multiplication algorithm that is basically secure against Simple Power Analysis (SPA) and safe-error attacks. Our proposal is intended for Elliptic Curves Cryptosystems (ECC) algorithms dedicated to low cost applications. We first introduce the different types of side-channel attacks that ECC-based cryptographic algorithms can suffer, as well as their countermeasure methods existing in the literature. We then present an optimized hardware implementation of the most effective scalar multiplication algorithm against SPA and safe-error attacks. Finally, we present our proposed DPA countermeasure method and its effectiveness against other extensions of DPA attacks. Our proposed method is similar to the Basic Random Initial Point (BRIP) method except that the latter is only applicable for the left-to-right algorithm. The proposed method is based on the randomization of processed data during the computation of the scalar multiplication algorithm and prevents vulnerability to Zero-value Point Attack (ZPA), Refined Power analysis (RPA) attack and double attack. In the last part of our paper, we present comparative analysis in terms of computational cost between our proposed method and other countermeasure algorithms presented in the literature, such as Montgomery-ladder, the BRIP algorithm, the left-to-right algorithm and the Co-Z Mont-Ladder algorithm.