Designers of RFID security protocols can choose between a wide variety of cryptographic algorithms. However, when implementing these algorithms on RFID tags fierce constraints have to be considered. Looking at the common assumption in the literature that hash functions are implementable in a manner suitable for RFID tags and thus heavily used by RFID security protocol designers we claim the following. Current standards and state-of-the-art low-power implementation techniques favor the use of block ciphers like the Advanced Encryption Standard (AES) instead of hash functions from the SHA family as building blocks for RFID security protocols. In turn, we present a low-power architecture for the widely recommended hash function SHA-256 which is the basis for the smallest and most energy-efficient ASIC implementation published so far. To back up our claim we compare the achieved results with the smallest available AES implementation. The AES module requires only a third of the chip area and half of the mean power. Our conclusions are even stronger since we can show that smaller hash functions like SHA-1, MD5 and MD4 are also less suitable for RFID tags than the AES. Our analysis of the reasons of this result gives some input for future hash function designs.