In this paper, we propose an efficient biometric authentication protocol for fingerprints particularly suited for the minutia-based representation. The novelty of the protocol is that we integrate the most efficient (linear complexity) private set intersection cardinality protocol of Cristofaro et al. and a suitable helper data system for biometrics in order to improve the accuracy of the system. We analyze the security of our scheme in the standard model based on well-exploited assumptions, considering malicious parties, which is essential to eliminate specific attacks on biometric authentication schemes designed for semi-honest adversaries only. Finally, the complexity is compared to the existing provably secure schemes for fingerprint matching, which shows that the new proposal outperforms them both in semi-honest and malicious security models.