Since their publication in 1998, power analysis attacks have attracted significant attention within the cryptographic community. So far, they have been successfully applied to different kinds of (unprotected) implementations of symmetric and public-key encryption schemes. However, most published attacks apply to smart cards and only a few publications assess the vulnerability of hardware implementations. In this paper we investigate the vulnerability of Rijndael FPGA (Field Programmable Gate Array) implementations to power analysis attacks. The design used to carry out the experiments is an optimized architecture with high clock frequencies, presented at CHES 2003. First, we provide a clear discussion of the hypothesis used to mount the attack. Then, we propose theoretical predictions of the attacks that we confirmed experimentally, which are the first successful experiments against an FPCA implementation of Rijndael. In addition, we evaluate the effect of pipelining and unrolling techniques in terms of resistance against power analysis. We also emphasize how the efficiency of the attack significantly depends on the knowledge of the design.