Finite field for scientists and engineers
Finite field for scientists and engineers
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Message Authentication Codes (MACs) are valuable tools for ensuring the integrity of messages. MACs may be built around a universal hash function (NH) which was explored in the construction of UMAC. In this paper, we use a variation on NH called WH. WH reaches optimality in the sense that it is universal with half the hash length of NH and it achieves perfect serialization in hardware implementation. We achieved substantial power savings of up to 59 percent and a speedup of up to 7.4 times over NH. Moreover, we show how the technique of multihashing and the Toeplitz approach can be combined to reduce the power and energy consumption even further while maintaining the same security level with a very slight increase in the amount of the key material. At low frequencies, the power and energy reductions are achieved simultaneously while keeping the hashing time constant. We developed formulae for estimation of the leakage and dynamic power consumptions as well as the energy consumption based on the frequency and the Toeplitz parameter t. We introduce a powerful method for scaling WH according to specific energy and power consumption requirements. Our implementation of WH-16 consumes only 2.95\,\mu{\rm W} at 500 kHz. It can therefore be integrated into a self-powered device.