Recent developments of multicore architectures over various platforms (desktop computers and servers as well as embedded systems) challenge the classical approaches of sequential computation algorithms, in particular elliptic curve cryptography protocols. In this work, we deploy different parallel software implementations of elliptic curve scalar multiplication of point, in order to improve the performances in comparison with the sequential counter parts, taking into account the multi-threading synchronization, scalar recoding and memory management issues. Two thread and four thread algorithms are tested on various curves over prime and binary fields, they provide improvement ratio of around 15% with best their sequential counterparts.