The essential requirements of electronic voting mechanisms include convenience, anonymity, efficiency, and robustness. In 2006, Chang and Lee proposed a t -out-of- n electronic voting method, and Chang and Cheng proposed another one based on -out-of- requirements in 2009. However, the security in their methods is based upon the asymmetric and symmetric cryptosystems like the RSA public-key cryptosystem and the DES cryptosystem. The RSA public-key cryptosystem must use a key size of 1024 bits to protect security, but this leads to higher computational cost in the voting mechanism. Therefore, we propose in this article a novel version based upon an elliptic curve cryptosystem to reduce the computational cost. Our mechanism meets the essential requirements of the electronic voting mechanism.