Many applications use asymmetric cryptography to secure communications between two parties. One of the main issues with asymmetric cryptography is the need for vast amounts of computation and storage. While this may be true, elliptic curve cryptography (ECC) is an approach to asymmetric cryptography used widely in low computation devices due to its effectiveness in generating small keys with a strong encryption mechanism. The ECC decreases power consumption and increases device performance, thereby making it suitable for a wide range of devices, ranging from sensors to the Internet of things (IoT) devices. It is necessary for the ECC to have a strong implementation to ensure secure communications, especially when encoding a message to an elliptic curve. It is equally important for the ECC to secure the mapping of the message to the curve used in the encryption. This work objective is to propose a trusted and proofed scheme that offers authenticated encryption (AE) for both encoding and mapping a message to the curve. In addition, this paper provides analytical results related to the security requirements of the proposed scheme against several encryption techniques. Additionally, a comparison is undertaken between the SE-Enc and other state-of-the-art encryption schemes to evaluate the performance of each scheme.