  Side-channel analysis attacks, especially horizontal DPA and DEMA attacks,
are significant threats for cryptographic designs. In this paper we investigate
to which extend different multiplication formulae and randomization of the
field multiplier increase the resistance of an ECC design against horizontal
attacks. We implemented a randomized sequence of the calculation of partial
products for the field multiplication in order to increase the security
features of the field multiplier. Additionally, we use the partial polynomial
multiplier itself as a kind of countermeasure against DPA attacks. We
demonstrate that the implemented classical multiplication formula can increase
the inherent resistance of the whole ECC design. We also investigate the impact
of the combination of these two approaches. For the evaluation we synthesized
all these designs for a 250 nm gate library technologies, and analysed the
simulated power traces. All investigated protection means help to decrease the
success rate of attacks significantly: the correctness of the revealed key was
decreased from 99% to 69%.
