Systems and method are provided for affixing attachments, such as double-sided adhesive slips, to credit cards and other presentation instruments. Certain regions of the tool accommodated by the mount project through the window of the closed lid part, peripheral portions of the window being in contact, or nearly in contact, with at least two positions on the tool. In the computation of scalar multiplications, kP and lQ are set on a Montgomery elliptic curve By2=x3+Ax2+x. The power distribution networks of the integrated circuit and the voltage island are extracted and modeled as a resistive network.