Performance evaluation of ECC scalar multiplication using parallel modular algorithms on mobile devices

Mobile devices, such as smartphones, allow people around the world to access a huge amount of online applications anywhere and anytime. Elliptic Curve Cryptography (ECC) algorithm can be used in mobile devices to trust the access to these applications. Scalar multiplication is the main and most expensive operation in ECC and its cost is directly related to the size of the key used. It is composed of a lot of modular arithmetic operations (addition, subtraction, squaring, multiplication and inversion), defined by the coordinate system used. Using the short Weierstrass Jacobian coordinate system, the modular multiplication and squaring are the most costly operations performed in our experiments. In this paper we analyze the performance of scalar multiplication using a variety of sequential and parallel modular multiplication algorithms with standardized NIST curves. To predict the timings for highorder curves, it is used a 1536-bit pairing-friendly curve available on RELIC. Experiments were performed on a SabreLite IMX6Quad board with a quad-core ARM cortex A9 (ARMv7 architecture) processor, which allows the analysis of these scalar multiplications on a mobile device architecture. Results show that Bipartite 2th timings were faster than the sequential ones for 1536-bit curves. Bipartite timings were strictly close to the best sequential timing for 521 bits, indicating that for a not too much longer key, parallel algorithms´ timings are capable to overcome the sequential ones.