  Due to the nature of applications such as critical infrastructure and the
Internet of Things etc. side channel analysis attacks are becoming a serious
threat. Side channel analysis attacks take advantage from the fact that the
behavior of crypto implementations can be observed and provides hints that
simplify revealing keys. A new type of SCA are the so called horizontal SCAs.
Well known randomization based countermeasures are effective means against
vertical DPA attacks but they are not effective against horizontal DPA attacks.
In this paper we investigate how the formula used to implement the
multiplication of $GF(2^n)$-elements influences the results of horizontal DPA
attacks against a Montgomery kP implementation. We implemented 5 designs with
different partial multipliers, i.e. based on different multiplication formulae.
We used two different technologies, i.e. a 130 and a 250 nm technology, to
simulate power traces for our analysis. We show that the implemented
multiplication formula influences the success of horizontal attacks
significantly, but we also learned that its impact differs from technology to
technology. Our analysis also reveals that the use of different multiplication
formulae as the single countermeasure is not sufficient to protect
cryptographic designs against horizontal DPA attacks.
