A Method for Generating Prime Order Elliptic Curves over F(q(2c))

This paper proposes an algorithm for generating prime order elliptic curves over extension field whose extension degree is a power of 2. The proposed algorithm is based on the fact that the order of the twisted elliptic curve is able to be a prime number when the extension degree for the twist operation is a power of 2. When the definition field is F(2(40)−87)(4) , the proposed algorithm can generate a prime order elliptic curve within 5 seconds on PentiumIII (800MHz) with C language.