A server is configured to communicate with a group of clients over a network in one embodiment. The server maps the group of clients into a plurality of subgroups of bounded size, communicates to a given one of the clients information identifying the particular subgroup to which that client belongs as well as the other clients in that subgroup. The given client utilizes the communicated information to generate a ring signature over the corresponding subgroup of clients based on the communicated information. The subgroup size may be bounded to a minimum size and a maximum size in accordance with a variable privacy parameter. The server can increase or decrease the value of the parameter in order to provide respective increased or decreased privacy to the clients, by making it respectively more or less difficult to determine which client in a corresponding one of the subgroups produced the received ring signature.