With the advent of the Internet of Things security features become more and more important. Especially data integrity and authentication of its origin are of utmost importance. Digital signatures are a well-known means to provide these features. In this paper we detail our horizontal Address-Bit DPA attack against a Montgomery kP implementation and applied the attack against the ECDSA-algorithm. Please note that this type of attack is especially harmful as it requires the measurement of only one trace to preparing the attack and only one trace for the attack itself. Even more important well-known countermeasures such as the regularity and atomicity principle successful applied against simple SCA attacks and randomization strategies successfully applied against vertical DPA attacks do not prevent our attack from being successful. The attack allowed us to reveal the private key used to generate a digital signature with a correctness of 100%. Our detailed analysis of the attacked kP design showed that the addressing of registers is dependent on the currently processed key bit value. The average difference of compressed values in the clock cycles with addressing is 25.9mV², whereas the difference of the data storing to the registers is as low as 7.1mV². This difference was detected using the difference of means test analysing a single kP execution. Thus, the original (vertical) Address-Bit DPA can be significantly simplified. Especially hardware implementations of the kP algorithm need a new countermeasure due to the fact that the traditional randomization countermeasures, even applied for the randomizing intermediate data, don't prevent the horizontal Address-Bit DPA.