Minutiae-based representation is the most widely adopted representation scheme. The compactness of minutiae representation has created an impression that the minutiae template does not contain sufficient information to allow the reconstruction of the original grayscale fingerprint image. This belief has now been shown to be false; several algorithms have been proposed that can reconstruct fingerprint images from minutiae templates. However, they have a common drawback: many spurious minutiae are generated in the reconstructed image. In this paper, a novel fingerprint reconstruction algorithm is proposed to reconstruct the phase image, which is then simply converted into the grayscale image. The proposed algorithm not only reconstructs the whole fingerprint, but the reconstructed fingerprint contains very few spurious minutiae. Specifically, a fingerprint image is represented as a phase image which consists of the continuous phase and the spiral phase (which corresponds to minutiae). An algorithm is proposed to reconstruct the continuous phase from minutiae. The proposed reconstruction algorithm has been evaluated with respect to the success rates of type-I attack (match the reconstructed fingerprint against the original fingerprint) and type-II attack (match the reconstructed fingerprint against different impressions of the original fingerprint) using a commercial fingerprint SDK. Both types of attacks are shown to be successful in defeating the fingerprint SDK.