Universal Hash Functions for Emerging Ultra-Low-Power Networks

Message Authentication Codes (MACs) are a valuable tool for ensuring the integrity of messages. MACs may be built around a keyed hash function. In this paper, we propose three variations on NH (a universal hash function explored in UMAC [1]), namely PH, PR and WH. Our main motivation was to prove that universal hash functions can be employed to provide provable security in ultra-low-power applications such as the next generation self-powered sensor networks. The first hash function we propose, i.e. PH, produces a hash of length 2w and is shown to be 2−w-almost universal. The other two hash functions, i.e. PR and WH, reach optimality and are proven to be universal hash functions with a much shorter hash length of w. In addition, these schemes are simple enough to allow for efficient constructions. To the best of our knowledge the proposed hash functions are the first ones specifically designed for low-power hardware implementations. We achieved drastic power savings of up to 59% and speedup of up to 7.4 times over NH. Note that the speed improvement and the power reduction are accomplished simultaneously. Our implementation of WH consumes only 11.6 μW at 500 kHz. It could therefore be integrated into a self-powered device. This enables the use of hash functions in ultra-low-power applications such as “Smart Dust” motes and RFIDs. By virtue of their security and implementation features mentioned above, we believe that the proposed universal hash functions will fill an important gap in cryptographic hardware applications.