The modular exponentiation function used in public key encryption and decryption systems is implemented in a standalone engine having at its core modular multiplication circuits which operate in two phases which share overlapping hardware structures. The array includes conductive regions separated by insulated regions arranged to produce ablation to a predetermined depth. Here, in a plan view of the web, a distance between the arm member and a nip point becomes largest when the nip point goes beyond a position on the predetermined waveform where an angle between the predetermined direction and a tangent line to the predetermined waveform becomes largest.