Fingerprint matching systems generally use four types of representation schemes: grayscale image, phase image, skeleton image, and minutiae, among which minutiae-based representation is the most widely adopted one. 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. These techniques try to either reconstruct the skeleton image, which is then converted into the grayscale image, or reconstruct the grayscale image directly from the minutiae template. However, they have a common drawback: Many spurious minutiae not included in the original minutiae template are generated in the reconstructed image. Moreover, some of these reconstruction techniques can only generate a partial fingerprint. In this paper, a novel fingerprint reconstruction algorithm is proposed to reconstruct the phase image, which is then converted into the grayscale image. The proposed reconstruction algorithm not only gives 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 recognition system. Given the reconstructed image from our algorithm, we show that both types of attacks can be successfully launched against - - a fingerprint recognition system.