An algorithm to generate special type of pairing-friendly elliptic curves

Pairing-friendly elliptic curves are the key ingredients in pairing-based cryptographic applications. The construction of such curves not only influences the implementation efficiency, but concerns the security. In this paper, a more targeted algorithm is proposed for the construction of such curves. By introducing a generalized concept “parameterized families”, we convert this problem to solving equation systems instead of exhaustive searching, and totally classify a type of family of elliptic curves. We demonstrate the utility of the algorithm by generating a parameterized family with embedding degree 12.