An example system can include a reference biometric template (RBT) reader, an authenticator, and an auxiliary system. In some examples, during an initial enrollment process, the RBT reader obtains a biometric from a user, transforms the biometric into an RBT, and provides different shares of the RBT to the authenticator and the auxiliary system. The authenticator and the auxiliary system create respective shares of helper data. In some examples, the authenticator and the auxiliary system use a non-commutative transformation function to embed a secret key in their respective shares of the helper data. The auxiliary system provides its share of the helper data to the authenticator. The authenticator combines its share of the helper data with the share provided by the auxiliary system to create a full version of the helper data. The helper data can be used in a subsequent authentication process between the RBT reader and the authenticator.