The Internet of Things (IoT) paradigm envisions a world where everyday things interchange information between each other in a way that allows users to make smarter decisions in a given context. Even though IoT has many advantages, its characteristics make it very vulnerable to security attacks. Ciphers are a security primitive that can prevent some of the attacks; however, the constrained computing and energy resources of IoT devices impede them from implementing current ciphers. This article presents the stream cipher Generador de Bits Pseudo Aleatorios (GBPA) based on Salsa20 cipher, which is part of the eSTREAM project, but designed for resource-constrained IoT devices of Class 0. GBPA has lower program and data memory requirements compared with Salsa20 and lightweight ciphers. These properties allow low-cost resource-constrained IoT devices, 29.5% of the embedded systems in the market, to be able to implement a security service that they are currently incapable of, to preserve the user’s data privacy and protect the system from attacks that could damage it. For the evaluation of its output, three statistical test suites were used: NIST Statistical Test Suite (STS), DIEHARD and EACirc, with good results. The GBPA cipher provides security without having a negative impact on the computing resources of IoT devices.