What bitstream is the FPGA currently configured with? The one in flash? Really? What's to say the bitstream made it to the FPGA correctly? Can you tell? What if it reconfigured itself [1]?
There's some research [2] into using authenticated, encrypted bitstreams, but even if the implementation matches the theory (and after all, it's crypto, we know how that goes...) this only reaches the same level of security as a fixed-configuration ASIC, since FPGAs are vulnerable to the same nefarious fab attacks as ASICs.
1: http://www.cmpe.boun.edu.tr/caslab/publications/selfreconf_f...
2:
http://www.saardrimer.com/sd410/papers/bsauth.pdf