A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess “good” cryptographic properties of 0-1 distribution, long period and large linear complexity. The results indicate that such sequences provide strong potential applications in cryptography. A series of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess “good” cryptographic properties of 0-1 distribution, long period and large linear complexity. The results indicate that such Sequences provide strong potential applications in cryptography.