Sphere packing lower bound on fingerprinting error probability

We study, the statistical performance of spherical fingerprints for a focused detector which decides whether a user of interest is among the colluders. The colluders create a noise-free forgery by preprocessing their individual copies, and then adding a white Gaussian noise sequence to form the actual forgery. Let N be the codelength, M the number of users, and K the number of colluders. We derive a sphere packing lower bound oil the error probability, valid for any triple (N, M, K) and any spherical fingerprinting code.