Elliptic curve cryptography has a high significance on secure computer applications, it provides mechanisms to ensure privacy on data, authentication among communicating entities, as well as the integrity of a message sent by an insecure channel. Nowadays, there are cryptographic algorithms that ensure these security services, however, some of them require a large amount of computer processing. Such is the case of the scalar multiplication, which is a fundamental operation for the implementation of elliptic curve cryptography. It is, therefore, essential that this operation be performed efficiently. This thesis has focused on the analysis of algorithms and programming techniques to reduce the computation time of the scalar multiplication. From the algorithmic standpoint, Koblitz elliptic curves allow that the computation of the scalar multiplication can be quickly performed by applying the Frobenius’s endomorphism, without using point doublings. The formulation of a parallel algorithm allows its implementation in a multicore processor. Extended instruction sets included in the latest computer architectures enable parallel processing of multiple data sets. Within these sets, the use of the carry-less multiplier enhances the performance of operations over finite fields, thereby resulting in acceleration of computation of scalar multiplication. The results of this research show the speedup in the parallelization of the scalar multiplication, optimizing both algorithmically and with the use of recent technologies.