Ensuring the physical security of small embedded devices is challenging. Such devices have to be produced under strong cost constraints, and generally operate with limited power and energy budget. However, they may also be deployed in applications where physical access is indeed possible for adversaries. In this paper, the authors consider the case of SIM cards to discuss these issues, and report on successful side-channel attacks against several (old but still deployed) implementations of the COMP128-1 algorithm. Such attacks are able to recover cryptographic keys with limited time and data, by measuring the power consumption of the devices manipulating them, hence allowing cards cloning and communications eavesdropping.