1. A method, comprising: receiving, by a client computing system, a user login request; identifying, by the client computing system, a plurality of chains of authentication modules to be performed prior to allowing a user to login, each of the plurality of chains being associated with a respective chain manager of a plurality of chain managers, each of the plurality of chains having a plurality of authentication modules, each of the plurality of chain managers having configuration information identifying authentication modules of a respective chain, a module execution order of the authentication modules of the respective chain, and an effect of an execution result of each of the authentication module; determining, by a processing device of the client computing system, current dependencies between the plurality of chain managers; determining a chain execution order for the plurality of chains of authentication modules based on the current dependencies between the plurality of chain managers, wherein the chain execution order indicates a parallel execution of at least two of the plurality of chains of authentication modules, each of the at least two of the plurality of chains of authentication modules having a modifiable number of the plurality of authentication modules, and corresponding to at least two of the plurality of chain managers with modifiable dependencies; executing the plurality of chains of authentication modules in the chain execution order; and responding to the user login request based on execution results of the authentication modules.