This paper presents an analysis on the state of the art of several proposals for algorithmic countermeasures to prevent passive side-channel attacks (SCA) on elliptic curve cryptography (ECC) defined over prime fields. One of the main applications of ECC is in the field of Internet of Things, where the interconnection of devices requires public-key technology with small key sizes and high security levels. Since the secure implementation of ECC on embedded devices involves many challenges for security and efficiency, this work evaluates the trade-offs between security and performance of side-channel attack countermeasures for scalar multiplication algorithms without precomputation. The main contribution is to present a panorama of explicit solutions that may be used for the implementation of ECC mechanisms suitable for embedded devices. In addition to the security problems, some countermeasures are also analyzed.