Design of Functionally Graded Alloys for Locks Highly Resistant to Ultrasonic Detector Attacks

Mechanical locks have not been fully replaced by electrical locks and are still being researched and improved, along with advanced electronic methods of attack. Moreover, reading pin lengths by detecting their natural frequencies (lock decoding) to forge copies of a legitimate key can be done quickly using active or passive ultrasonic detectors. One possible method of defence against them is manufacturing lock pins using functionally graded materials (FGMs). A pin's natural frequency (in the range 100 kHz-1 MHz) and hence its ultrasonic pulse transit/reflection time can be correlated to its length if it is made of a homogeneous material. The idea is to design pins made of functionally graded alloys to achieve equal natural frequencies, but also desired positions of standing wave nodes regardless of pin length. To calculate the composition of the FGM alloy, we must first develop mathematical models of a pin's vibrations. Two simple and fast mathematical models are first derived from the finite-element model (FEM) of a pin. These models are used in an optimization procedure based on the Nelder-Mead simplex method to calculate optimal profiles of Young's modulus and density along a pin's longitudinal axis. A successful optimization procedure for 10 key pin lengths is performed to make a pin-tumbler lock resistant to ultrasonic attacks.