Alignment-free fingerprint cryptosystems perform matching using relative information between minutiae, e.g., local minutiae structures, is promising, because it can avoid the recognition errors and information leakage caused by template alignment/registration. However, as most local minutiae structures only contain relative information of a few minutiae in a local region, they are less discriminative than the global minutiae pattern. Besides, the similarity measures for trivially/coarsely quantized features in the existing work cannot provide a robust way to deal with nonlinear distortions, a common form of intra-class variation. As a result, the recognition accuracy of current alignment-free fingerprint cryptosystems is unsatisfying. In this paper, we propose an alignment-free fuzzy vault-based fingerprint cryptosystem using highly discriminative pair-polar (P-P) minutiae structures. The fine quantization used in our system can largely retain information about a fingerprint template and enables the direct use of a traditional, well-established minutiae matcher. In terms of template/key protection, the proposed system fuses cancelable biometrics and biocryptography. Transforming the P-P minutiae structures before encoding destroys the correlations between them, and can provide privacy-enhancing features, such as revocability and protection against cross-matching by setting distinct transformation seeds for different applications. The comparison with other minutiae-based fingerprint cryptosystems shows that the proposed system performs favorably on selected publicly available databases and has strong security.