Design for test is an integral part of any VLSI chip. However, for secure systems extra precautions have to be taken to prevent that the test circuitry could reveal secret information. This paper addresses secure test for Physical Unclonable Function based systems. In particular it provides the testability analysis and a secure Built-In Self-Test (BIST) solution for Fuzzy Extractor (FE) which is the main component of PUF-based systems. The scheme targets high stuck-at-fault (SAF) coverage by performing scan-chain free functional testing, to prevent scan-chain abuse for attacks. The scheme reuses existing FE sub-blocks (for pattern generation and compression) to minimize the area overhead. The scheme is integrated in FE design and simulated; the results show that a SAF fault coverage of 95.1% can be realized with no more than 50k clock cycles at the cost of a negligible area overhead of only 2.2%. Higher fault coverage is possible to realize at extra cost.