We investigate implementations of biometric cryptosystems protecting fingerprint templates (which are mostly based on the fuzzy vault scheme by Juels and Sudan in 2002) with respect to the security they provide. We show that attacks taking advantage of the system's false acceptance rate, i.e. false-accept attacks, pose a very serious risk --- even if brute-force attacks are impractical to perform. Our observations lead to the clear conclusion that currently a single fingerprint is not sufficient to provide a secure biometric cryptosystem. But there remain other problems that can not be resolved by merely switching to multi-finger: Kholmatov and Yanikoglu in 2007 demonstrated that it is possible to break two matching vault records at quite a high rate via the correlation attack. We propose an implementation of a minutiae fuzzy vault that is inherently resistant against cross-matching and the correlation attack. Surprisingly, achieving cross-matching resistance is not at the cost of authentication performance. In particular, we propose to use a randomized decoding procedure and find that it is possible to achieve a GAR=91% at which no false accepts are observed on a database generally used. Our ideas can be adopted into an implementation of a multibiometric cryptosystem. All experiments described in this paper can fully be reproduced using software available for download.