In this paper we describe how to plant novel types of backdoors in any facial recognition model based on the popular architecture of deep Siamese neural networks, by mathematically changing a small fraction of its weights (i.e., without using any additional training or optimization). These backdoors force the system to err only on specific persons which are preselected by the attacker. For example, we show how such a backdoored system can take any two images of a particular person and decide that they represent different persons (an anonymity attack), or take any two images of a particular pair of persons and decide that they represent the same person (a confusion attack), with almost no effect on the correctness of its decisions for other persons. Uniquely, we show that multiple backdoors can be independently installed by multiple attackers who may not be aware of each other's existence with almost no interference.We have experimentally verified the attacks on a FaceNet-based facial recognition system, which achieves SOTA accuracy on the standard LFW dataset of 99.35%. When we tried to individually anonymize ten celebrities, the network failed to recognize two of their images as being the same person in 96.97% to 98.29% of the time. When we tried to confuse between the extremely different looking Morgan Freeman and Scarlett Johansson, for example, their images were declared to be the same person in 91.51% of the time. For each type of backdoor, we sequentially installed multiple backdoors with minimal effect on the performance of each one (for example, anonymizing all ten celebrities on the same model reduced the success rate for each celebrity by no more than 0.91%). In all of our experiments, the benign accuracy of the network on other persons was degraded by no more than 0.48% (and in most cases, it remained above 99.30%).