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Elliptic Curve Cryptography (ECC) is a promising cryptosystem as it presents the ideal choice for implementing public-key cryptography in resource-limited devices, such as those found in envisioned Internet of Things applications, e.g. wireless sensors. Elliptic Curve ElGamal (ECEG) is a renowned member of the ECC family. However, it requires encoding the message before encryption and decoding it after decryption. To better improve the processing time and to avoid sharing a lookup table, we propose, in this document, a new method that exchanges encoding parameters and authenticates endpoints at the same time. So, our new protocol ensures the authentication of communication parties and integrity of ephemeral encoding parameters. The robustness of our solution is proven by the Scyther tool. Experimental tests have been carried out, and the performance of the new methods is provided and compared with RSA and related work. Security and performance analysis show that our new scheme has achieved improved functionality and higher security while maintaining low computational. [ABSTRACT FROM AUTHOR]