The transmission of information in a secure manner has been since ancient times a challenge hard to tackle, starting from the immemorial Cesar cipher used by the Romans to the more modern techniques developed in the 20th century. With the coming age of the computer and the internet more advanced and sophisticated algorithms had to be made to resolve the fun- damental problems of secure communication. This project aims to explain some of the main fundamental points of cryptography, what is its history and the current types in existence. In particular, one type of cryptographic algorithms will be further analyzed: Elliptic Curve Cryp- tography (ECC), then implemented these same algorithms in the C programming language and aimed for remote systems. This project will develop the overall concepts concerning cryptography and how to code a working correct implementation with the objective to have a better understanding of the inner- workings of currents elliptic curve cryptographic systems and what are the fundamentals con- cepts one requires to know to implement them. The first part will consist of an introduction to the history and terminology. Followed by an overview of the current existing cryptosystems and algorithms, next a deeper description of a specific cryptography by the name of Elliptic-Curve Cryptography (ECC) will be made and developed. The second part will consist on the task of implementing the ECC algorithm in an embedded microchip device. This part will describe all the steps necessary to archive a correct implemen- tation. Finally, the implementation will be put to test by benchmarking it against popular ECC cryp- tosystem suites, validating the results and correctness.