Análise de algoritmos paralelos de ECC em dispositivos móveis multicore

Abstract

Multicore processors adoption is due to the need of expansion on the computational capacity, what have been done in mobile devices, due to the high availability of online applications in such devices. Elliptic curve cryptography (ECC) can be used in these applications, to ensure the confidentiality in the communication performed by the mobile device. This algorithm has its security on the hardness to solve the elliptic curve discrete logarithm problem (ECDLP), what is harder to solve than RSA s problem, owning equivalent security at the cost of much smaller keys, hence reducing the computational cost of the solutions which implement it. Scalar multiplication is the main and most costly operation in ECC and is composed by the computation of many modular operations. Parallel modular multiplication algorithms where evaluated in this work, which timings were compared with timings of some sequential algorithms. Experiments were performed on a SabreLite IMX6Quad development board, with an architecture similar to a mobile device. On this platform, it was evaluated the transition from the low to the high frequency of CPU, which occurs in ondemand CPU mode during the execution of the algorithms. The relation of proportion among the timings of the algorithms evaluated on performance mode was similar to the powersave CPU mode. Some parallel algorithms were faster than the sequentials in operations among operands with at least 768 bits. Evaluating the behavior of each algorithm when integrated in the computation of scalar multiplication, it was observed that the parallels were faster in operations with a 1536-bit supersingular curve.