Fuzzy vault (FV) scheme, proposed by Juels and Sudan, is intended to develop new concepts to bind cryptographic security into biometric authentication to improve security and protect privacy. But FV is vulnerable to some attacks, such as Attacks via record multiplicity or correlation attacks, Surreptitious key-inversion attack and Blended substitution attacks. In this paper, a novel biometric encryption scheme, named Efficient fuzzy vault (EFV), is developed using pairing-based cryptography. EFV scheme provides a higher level of security than FV as adopting random points instead of chaff points to resist the attacks that FV has difficulty to overcome. In addition, a complete implementation procedure of fingerprint-based EFV, based on the automatic alignment of minutiae converted in polar coordinates using a reference point, is developed. The security analysis and experiment results show that EFV is a promising scheme for biometric encryption.